RICE UNIVERSITY
Development of an Active Display Using Plasmonic Nanorods and Liquid Crystals
by
Jana Olson
A THESIS SUBMITTED
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE
Doctor of Philosophy
APPROVED, THESIS COMMITTEE
Stephan Link, Chair
Associate Professor of Chemistry and of
Electrical and Computer Engineering
Naomi Halas
Stanley C. Moore Professor in Electrical
and Computer Engineering, Professor of
Biomedical Engineering, Chemistry, and
of Physics & Astronomy
Peter Nordlander
Weiss Chair and Professor of Physics and
Astronomy, Professor of Electrical and
Computer Engineering, and of materials
Science and NanoEngineering
HOUSTON, TEXAS
December 2015
ABSTRACT
Development of an Active Display Using Plasmonic Nanorods and Liquid Crystals
by
Jana Olson
The current generation of display technology has already provided the public
with displays that exhibit high color fidelity, faster than the eye can see frame rates,
and screens spanning an order of magnitude in size, from hand-held to wall-sized.
What has yet to be achieved is for display technology to become versatile, fitting
into the human environment in a way that is unobtrusive, ergonomic, and promotes
an improved quality of life. This thesis points to nanotechnology, particularly
plasmonic nanomaterials, as a way to bring display technologies to that next level.
The work presented in this thesis is the development of a nanomaterial that
is vividly colored, electronically controllable, and highly versatile in its possible
applications. First, an understanding of the electronic switching of nematic liquid
crystals is gained via combination of randomly oriented gold nanorods with
homogeneously aligned nematic liquid crystal. The nanorods are used to probe the
birefringence of the liquid crystal as an in-plane bias is used to switch the alignment
of the liquid crystal from a uniform parallel alignment to a 90 degree twisted
alignment. This mechanism is confirmed with theoretical modeling using Jones
Calculus. Second, the polarization sensitivity of the nanorods is exploited by creating
a hexagonal array of co-oriented nanorods to form a plasmonic pixel using electron
beam lithography. Aluminum was chosen as the plasmonic material because its
plasmon resonance can span the whole visible region, and because of its
compatibility with the semiconductor manufacturing industry. The outstanding
vivid color of these pixels is dependent on the physical characteristics of the
individual nanorods, and also on the inter-rod spacing. Dipole coupling within the
array of ~300 nm separated nanorods is used to restrict plasmon scattering at both
long- and short-wavelengths. A simple 3-step color control mechanism was
developed that others can use to produce aluminum plasmonic pixels with colors
on-par with standard red, green, and blue displays. Finally, mm-scale colored pixels
are demonstrated to be switchable with a liquid crystal display, and therefore
immediately compatible with current liquid crystal display technology.
Acknowledgments
This thesis is dedicated, simply, to the people who made it possible. To my
family: Evan, Fran, Regis, and Jill, James, Maxwell, and Conan, for your love, your
support, and your patience. Also to my friends, coworkers, and coauthors, who are
too many to name here but too important not to mention.
This thesis is also dedicated to my mentors, including my family and friends,
but also especially my professors. To professors Viktor Martisovits and Catherine
Haustein for helping me to learn who I was in college. To Professors Jason Hafner
and Bruce Johnson for listening and providing insight into my professional future.
To my committee members Professors Peter Nordlander and Naomi Halas for their
continued support and direction in my research. To Professor Christy Landes, who
provided an alternative view and excellent career advice. And to my biggest mentor,
Professor Stephan Link, whose roll has included encouragement, criticism,
emotional support, lofty expectations, and both personal and professional
validation.
Thank you
Contents
Acknowledgments ..................................................................................................... iv
Contents .................................................................................................................... v
List of Figures ...........................................................................................................viii
List of Equations ......................................................................................................... x
Nomenclature ...........................................................................................................xii
Chapter 1 ................................................................................................................... 1
Introduction ............................................................................................................... 1
1.1. Motivation ............................................................................................................ 1
1.2. Specific Aims ......................................................................................................... 6
1.3. Overview ............................................................................................................... 7
Chapter 2 ................................................................................................................... 9
A Powerful Combination: Liquid Crystals and Nanomaterials ..................................... 9
2.1. Liquid Crystals ..................................................................................................... 10
2.1.1. Physics of Liquid Crystals ............................................................................. 11
2.1.2. Applications in Nanotechnology .................................................................. 14
2.2. Nanodisplays ....................................................................................................... 17
2.2.1. Physics of Plasmonic Structures ................................................................... 17
2.2.2. Single-Layer Arrays for Nanodisplays........................................................... 20
2.2.3. Production Methods for Large-Area Nanoparticle Arrays ........................... 22
2.2.4. Measurement Strategies and Applications .................................................. 24
2.3. Conclusions ......................................................................................................... 25
Chapter 3 ................................................................................................................. 27
vi
General Methods ..................................................................................................... 27
3.1. Experimental Methods for Chapter 4 ................................................................. 27
3.1.1. Sample Preparation...................................................................................... 28
3.1.2. Single Particle Spectroscopy ........................................................................ 30
3.2. Experimental Methods for Chapter 5 ................................................................. 31
3.2.1. Sample Preparation...................................................................................... 32
3.2.2. Optical and Physical Characterization.......................................................... 33
3.3. Experimental Methods for Chapter 6 ................................................................. 34
3.3.1. Sample Preparation...................................................................................... 34
3.3.2. Optical and Physical Characterization.......................................................... 36
3.3.3. Digital Camera Images ................................................................................. 37
3.4. Colorimetry ......................................................................................................... 38
Chapter 4 ................................................................................................................. 41
Detailed Mechanism for the Orthogonal Polarization Switching of Gold Nanorod
Plasmons.................................................................................................................. 41
4.1. Abstract ............................................................................................................... 41
4.2. Background and Motivation ............................................................................... 42
4.3. Results and Discussion ........................................................................................ 46
4.3.1. Description of Sample Geometry ................................................................. 46
4.3.2. Theoretical Model Using Jones Calculus ...................................................... 48
4.3.3. Theoretical Results ....................................................................................... 54
4.3.4. Experimental Results.................................................................................... 60
4.4. Conclusions ......................................................................................................... 68
4.5. Acknowledgements ............................................................................................ 69
Chapter 5 ................................................................................................................. 70
Vivid, Full-Color Aluminum Plasmonic Pixels ............................................................ 70
5.1. Abstract ............................................................................................................... 70
5.2. Background and Motivation ............................................................................... 71
5.3. Results and Discussion ........................................................................................ 73
5.3.1. Coupled Dipole Model of Nanorod Arrays ................................................... 73
5.3.2. Sample Design .............................................................................................. 76
5.3.3. Experimental Results.................................................................................... 82
5.4. Conclusions ......................................................................................................... 95
vii
5.5. Acknowledgements ............................................................................................ 96
Chapter 6 ................................................................................................................. 97
Enhanced Chromaticity in LCD-Compatible Aluminum Plasmonic Pixels .................... 97
6.1. Abstract ............................................................................................................... 97
6.2. Background and Motivation ............................................................................... 98
6.3. Results and discussion ...................................................................................... 101
6.3.1. Theoretical Model ...................................................................................... 101
6.3.2. Experimental Results.................................................................................. 105
6.4. Conclusions ....................................................................................................... 125
6.5. Acknowledgements .......................................................................................... 126
Chapter 7 ............................................................................................................... 127
Conclusions and Outlook ........................................................................................ 127
References ............................................................................................................. 131
List of Figures
Figure 2.1 – 5CB LC molecule ............................................................................................. 11
Figure 4.1 – Scattering of individual gold nanorods in a LC device ...................... 47
Figure 4.2 - Simulations of the output polarizations of a LC device as a function
of χ (x-axis) and incident polarization (y-axis) ................................... 56
Figure 4.3 –Calculated output polarization of a device switched between HN
and TN LC alignments................................................................................... 59
Figure 4.4 - Experimental characterization of a 4π-type device ........................... 62
Figure 4.5 - Experimental characterization of a 3π-type device ........................... 65
Figure 4.6 - DOP of the output polarization as a function of gold nanorod
orientation in the HN and TN LC phases for the 3π- and 4π-type
devices discussed in Figure 4.4 and Figure 4.5 ................................... 67
Figure 5.1 – Comparison between the scattering spectrum of a nanoparticle
using two different theoretical methods ............................................... 75
Figure 5.2 – Calculated scattering spectra of pixels composed of nanorods and
nanospheres .................................................................................................... 77
Figure 5.3 – Thickness data for both PI and ITO layers of a sample substrate. 78
Figure 5.4 – Design of an aluminum pixel ..................................................................... 80
Figure 5.5 – Scattering DSLR camera images of aluminum pixels ........................ 83
Figure 5.6 - Unpolarized experimental and theoretical spectra of the
aluminum pixels from Figure 5.2, and corresponding chromaticity
calculations. ..................................................................................................... 87
Figure 5.7 – Dark field spectra of all pixels shown in Figure 5.5 ........................... 88
Figure 5.8 – Simulations of pixel spectra with l, Dx, and Dy varied individually
.............................................................................................................................. 93
Figure 6.1 – Plasmonic pixel scheme............................................................................ 106
ix
Figure 6.2 – Theoretical basis for the three-step color design method ........... 109
Figure 6.3 – Color range of plasmonic pixels ............................................................. 112
Figure 6.4 – Break-down of large area pixels into 5-μm subpixels ................... 115
Figure 6.5 – Viewing angle dependence of a single macroscopic plasmonic
pixel ................................................................................................................. 116
Figure 6.6 – LC-based on/off switching of large scale plasmonic pixels .......... 118
Figure 6.7 – Color control over various pixel sizes ................................................. 121
Figure 6.8 – Complete color coordinate dataset of pixels of increasing size . 123
List of Equations
Equation 2.1 –LC order parameter................................................................................... 11
Equation 3.1 – Conversion matrix for [X,Y,Z] to [R, G, B] color coordinate
conversion ................................................................................................... 40
Equation 3.2 – Conversion from [X,Y,Z] to [R, G, B] color coordinate systems . 40
Equation 4.1 – Degee of polarization .............................................................................. 50
Equation 4.2 – Transmitted light intensity through HN LC ..................................... 52
Equation 4.3 – Transmitted light intensity through TN LC...................................... 52
Equation 4.4 – Electric field vector for incident light ................................................ 53
Equation 4.5 – Jones matrix for HN LC ............................................................................ 53
Equation 4.6 – Jones matrix for TN LC ............................................................................ 53
Equation 4.7 – Electric field vector for transmitted light ........................................ 53
Equation 4.8 – Generalized transmitted light intensity ........................................... 54
Equation 5.1 – Induced dipole within each nanorod in a finite array ................. 74
Equation 5.2 – Self-consistent induced dipole in a finite array ............................. 74
Equation 5.3 – Power scattered by a finite array of nanorods ............................... 74
Equation 5.4 – Maximum wavelength exhibiting constructive interference .... 91
Equation 6.1 – Induced dipole in each nanorod in an infinite array................. 103
Equation 6.2 – Dipole amplitude for an infinite array ........................................... 103
Equation 6.3 – Wavelength of the lattice resonance ............................................... 104
Equation 6.4 – Reciprocal lattice vector for (1,0) lattice resonance ................. 104
Equation 6.5 – General equation for the reciprocal lattice vector ..................... 104
Equation 6.6 – Wavelength at which lattice resonance (i,j) occurs ................... 104
xi
Equation 6.7 – Geometry dependent parameters for Equation 6.6 ................... 105
Equation 6.8 – Dipole amplitude for an infinite array reorganized .................. 105
Equation 6.9 – Power scattered per nanorod in an infinite array ..................... 105
Nomenclature
CRT
Cathode Ray Tube
LCD
Liquid Crystal Display
LED
Light Emitting Diode
LCoS
Liquid Crystal on Silicon
LSPR
Localized Surface Plasmon Resonance
LC
Liquid Crystal
5CB
4-Cyano-4’pentylbiphenyl liquid crystal
HN
Homogeneous Nematic
TN
Twisted Nematic
DOP
Degree of Polarization
CMOS
Complimentary Metal-Oxide Semiconductor
sRGB
Standard Red, Green, Blue
ITO
Indium Tin Oxide
SEM
Scanning Electron Microscope
PI
Polyimide
CIE
International Commission on Illumination
Chapter 1
Introduction
1.1. Motivation
Display technology is ubiquitous in a consumer society, inevitably becoming
even more so, and so future iterations of these technologies should be adapted to
promote a healthy human lifestyle in multiple ways: intellectually, emotionally, and
physically. Our intellectual health is already enhanced by technological
improvements to displays because they continue to increase the availability, and
arguably the quality, of information. A person’s emotional state and productivity can
be affected not only by new information, but also by the beauty of his or her
surroundings, placing unexpected importance on gravitation toward more beautiful
and refined display media. Display technology that is mobile or can be integrated
into our surroundings can help people stay physically active, embracing the
insistence of the Center of Disease Control and Prevention that physical activity is
1
2
most effective when it is incorporated into a daily routine1. New display
technologies may even help to maintain or improve peoples’ eyesight. Building
designs can change to have more windows, letting in more light and thereby
reducing instances of myopia in the public2. These additional windows could double
as directional displays, improving peoples’ ocular health while simultaneously
increasing their useable workspace. The potential impact that display technology
could have on the wellbeing of society is immense, necessitating that display
technology should focus on an additional target: to become more versatile and less
restrictive or intrusive in how people interact with technology, thereby promoting
healthier and happier lives.
Display technology has already made incredible leaps since the original
motion picture color displays that were developed using cathode ray tube (CRT)
technology, which boasts a wide color gamut and excellent viewing angles3,4, but
such displays are very bulky. Although the CRT is still strong in niche markets, even
the most recent versions with more compact methods to control the electron beams
are still about one foot deep5,6. Liquid crystal displays (LCDs) are far thinner than
CRTs because the active element is a 5-20 micron thick layer of liquid crystal (LC),
and unlike their predecessors, they don’t require high-vacuum internal components,
and so are not implosion hazards. Despite the reduced contrast ratios and viewing
angles of LCDs7, they are among the most popular for general consumers because of
their low cost and slim profiles.
3
Other display types also have improved thinness relative to CRTs and
improved viewing angles compared to LCDs, but they too suffer shortcomings.
Plasma displays incorporate phosphors that are excited by ultraviolet (UV)
radiation from an electrically charged ionized gas instead of an electron beam. One
problem with thee displays is that they require high voltage (roughly 100V) to
produce the plasma. This process causes them to become extremely hot during long
operation. Another problem with both plasmas and CRTs is that they can suffer from
screen burn-in, or selected area phosphor degradation, if the phosphors in one part
of the screen are excited significantly more often than others. Light emitting diodes
(LEDs) lack these phosphor-based issues, and they work at approximately 3V
applied voltage at 20 mA – far lower power than plasmas. Additionally, organicbased offshoots of LEDs have shown significant promise in paper-thin, flexible, and
transparent displays8. One of the downsides of LEDs is that they are temperature
dependent, so they require appropriate heat management to maintain a stable color.
This is especially the case when LEDs are operated with high current for improved
brightness, though doing so results in reduced efficiency9. LEDs also exhibit
directional emission10, requiring either that LEDs be covered by a diffuser, or
grouped together so as to radiate more uniformly, making the display larger.
Clearly, display technology is ultimately heading toward thin-film color
displays with increasing resolution. The resolution of a typical human eye allows it
to discern two objects that are roughly 1 arc minute apart from one another11. This
translates to about half a millimeter at optimal reading distance and allows for even
larger pixels in traditional displays used at farther viewing distances. For near-eye
4
applications, on the other hand, the necessary pixel size must be reduced to tens of
microns or smaller to maintain a display that does not appear pixilated when
observed at a distance of 6 inches or less. The limit of cutting-edge display
technology currently lies with a projection-type display: LC on silicon (LCoS)
technology. An LCoS display is manufactured by placing a LC-based spatial light
modulator directly on top of a silicon back reflector. Achievable pixel pitches using
LCoS technology are approximately 3 microns12, though many displays have larger
pixels. This is excellent resolution for near-eye display applications, though a multicolor light source is still required, and convergence between the projected light and
the activated pixel position must be maintained within strict tolerances.
Regardless of display type, these technologies are increasingly difficult to
manufacture as the pixel size become smaller, so many researchers have turned to
nature for inspiration and nanotechnology for the ability to improve displays while
maintaining or improving their production success rate. Biomimetic displays might
include expanding and retracting colored regions using polymers for example 13.
LCDs themselves are similar to many biological systems, including color-changing
and polarization-controlling structures14, and so they could be adapted to more
closely mimic biology. Butterfly wings, which use structural coloration rather than
pigmentation, have been studied and emulated15,16. There are so many different
organisms from which to draw inspiration for our displays that the applications of
these myriad displays are projected to be equally varied. Already, bio-inspired
materials and nanotechnology are projected to have footholds in paper and
consumer
products17,
electronics18,19,
clothing20,21,
imaging22,
and
nano
5
barcodes23,24, to name just a few. Ideally, these displays will not only be small, but
also completely self-contained, requiring no additional power or light source
beyond what they incorporate or is available in their immediate surroundings.
Nanotechnology, and in particular metal nanoparticles, may provide the key
to many of the problems that engineers will encounter in their progress toward
nontraditional display. Nanotechnology is inherently well suited to small-scale
applications and can push the lower limit on display technology and improve its
versatility. Arrays of nanoparticles can help harvest solar energy25–27 while doubling
as display elements. Nanoparticles can potentially serve as a color element in a
display without the need for an internal light source because their strong color
selectivity can allow them to utilize ambient light28, or they can include a small laser
to “power” the display29. Reliance on the environment would make the
nanomaterials-based display, or nanodisplay, immediately and automatically
responsive to the intensity and color of environmental lighting. Environmental
responsiveness points to nanotechnology as a strong front-runner in the race for
active camouflage in the visible region. Researchers are already developing
appropriate nanomaterial color elements for all of these described applications, as
will be discussed in Chapter 2. However, these developing nanodisplays will only be
commercially competitive after the development of a viable method of active on/off
or brightness control and compatibility with large-scale fabrication methods.
6
1.2. Specific Aims
The goal of this work is to develop a rationally-designable nanodisplay
material, focusing specifically on the relationship between the physical structure
and the optical characteristics of the component materials. This display can produce
vivid colors visible to the naked eye, is compatible with current display technology
manufacturing methods, and is readily compatible with currently popular LCD
technology. The nanodisplay described here is versatile enough to be used for
applications requiring few hundreds of nanometer footprint pixels up to large-area
displays, and can be incorporated into either active or stationary display types.
Three specific aims have been achieved in this thesis.
Specific Aim I: Demonstrate an LCD active control mechanism
Demonstrate and theoretically model an LCD-based active control
mechanism that can be used to rotate the polarization of optical signals, thereby
providing a capability to turn those signals completely on and off.
Specific Aim II: Develop the display’s color control elements
Develop a series of full-color aluminum-based pixels that is compatible with
the LC active switching mechanism. This material will rely on the light-scattering
properties of single nanorods as well as collective responses of an array of identical
nanorods.
Specific Aim III: Combine these two elements and test the limits of
applicability
Fully explain the mechanism of color control for the pixels described in aim
II. Test the upper and lower size limits on the pixel footprint to determine
7
appropriate-scale applications. Recombine the pixels with an LCD to demonstrate a
full-color and large-scale active display.
1.3. Overview
Background information related to nano-technological advances in display
technology is presented in Chapter 2, including both work describing LC technology
and nanoscale colorants. This review will be discussed in light of their
characterization methods and the viewing geometry used to study these materials,
as well as flexibility with regard to potential applications of these materials.
The content of Chapter 3 will detail the fabrication and characterization
methods for the work completed in this thesis. Rationale for specific design choices
will also be included, as well as a discussion of colorimetry and methods of
conversion between calculated or measured optical spectra and their representative
color pallets.
Chapter 4 will present work published in Physical Chemistry Chemical Physics
in 2013,30 in which the active control mechanism of a previously described LC
material31 is elucidated. The optimal operation conditions for this new LCD material
are identified through a combination of experimentally prepared samples, and
theoretical calculations using Jones calculus. These calculations model the two
different states of the LC, with and without voltage applied, as independent and
ideal LC states. The polarization control exhibited by these ideal LC states is then
8
compared against experimental samples constructed to match the theoretical
parameters.
Transitioning to the color production aspect of display development, Chapter
5 describes the first implementation of an aluminum pixel that provides vivid color
while also providing a polarization-based on/off switching mechanism. This work
was published in Proceedings of the National Academy of Sciences in 2014,32 and the
pixels described therein are among the first nanodisplays to utilize aluminum
nanoparticles. This work uniquely incorporates single nanorods as the basic
component to provide polarization control, and also embraces optical interactions
between elements within the array of nanorods to enhance both polarization- and
color-control.
The work presented in Chapter 6 expands upon that presented in Chapter 5,
by demonstrating pixels with increased vividness, improved color control
mechanisms, and demonstration of minimal reliance on the pixel size. A standalone
set of red, green, and blue pixels observed outside the microscope will be
demonstrated, as well as its performance when combined with an electrically
switchable LCD. This chapter will also include a discussion of the viewing-angle
dependent nature of the pixels. This work is in preparation.
9
Chapter 2
A Powerful Combination:
Liquid Crystals and Nanomaterials
This chapter describes the physical phenomena behind the two main
components in my research: LCs and plasmonic nanoparticles. The work presented
in Chapter 4 demonstrates the orthogonal polarization switching of nanorod
plasmons, work that was initiated by my predecessor Saumya Khatua. LCs were the
main focus of this work. Single gold nanorods probed the response of the liquid
crystal on a smaller spatial scale than traditional transmissive measurements can
achieve. Working toward the goal of making nanomaterials-based displays, larger
area colorants with pre-defined polarization orientations were determined to be
necessary. With this in mind, I stopped working with liquid crystals and started
making larger and larger groups of lithographically prepared nanorods,
transitioning from the single nanorod to the large scale arrays presented in Chapter
10
6. Bringing the work full-circle, I recombined those plasmonic pixels with an LCD,
the physics of which will be discussed in the following section.
2.1. Liquid Crystals
Current display technologies that are the most popular rely on LCs. This is
because LCs can control the polarization of light, thereby permitting or restricting
light from being observed by a viewer. However, LCs could not have attained such a
dominant position in display technologies without their switching ability that arises
from the responsiveness to an applied electric field, or bias, that many of these
molecules exhibit. These properties, among others, have also made LCs equally
powerful additions to basic research in a myriad of fields, nanotechnology not least
among them.
The molecules that form LCs have orientational and in some cases limited
positional order within the bulk of the material, providing these materials with
characteristics similar to both solids and liquids. LCs can be either pure compounds
or mixtures, and can occupy several LC phases, which are also called mesophases33.
Which mesophases a particular LC adopts, and therefore the optical properties of
the bulk layer of LC, may depend on one or more of the following: the identity and
shape of the LC itself,33–39its temperature,40–42 the concentration and location of
additives in the LC,43–47 interactions with the LC surroundings,39,48–50 or applied
fields.30,31,51–54 By far, one of the most well studied mesophases is the nematic LC55,
which is typified in the literature by 4-Cyano-4’pentylbiphenyl (5CB, shown in
11
Figure 2.1), a rod-shaped pure LC. It is also the only LC used in this thesis, and so the
following discussion on LCs will focus primarily on thermotropic nematic LCs, with
a strong emphasis on literature pertaining to 5CB.
Figure 2.1 – 5CB LC molecule
2.1.1. Physics of Liquid Crystals
LCs are birefringent materials, meaning that their refractive index is
anisotropic. In the LC state, the molecules have orientational order but little or no
translational order – none in the case of a nematic LC. Rod-like LC molecules like
5CB prefer to align roughly with their long axes parallel to one another, where the
average direction of the long axis is defined as the nematic director.7 Because the
molecules are free to rotate, we can define an order parameter, S, which describes
the rotational fluctuations of the bulk LC around the nematic director:7
𝟏
⟨𝟑 𝒄𝒐𝒔𝟐 𝜽 − 𝟏⟩
𝟐
Equation 2.1 –LC order parameter
𝑺=
where θ is the angle between a single molecule’s long axis and the nematic director,
and the angled brackets denote a statistical average over the allowed rotational
angles for a given molecule.7 Equation 2.1 is derived from the 2nd order Legendre
polynomial. In general for LCs, the value of S is between 0 and 1. A value of 0
12
represents an isotropic liquid which has no order, mathematically modeled as
variation in θ from 0 to 180 degrees. The case where S = 1 represents a crystalline
solid where θ can only be very near zero. Most LCs, such as 5CB, have a value of
approximately S = 0.5. This organization, in conjunction with the electric
permittivity of the molecular structure, dictates the birefringence of a LC. Larger
values of S tend to lead to stronger birefringence because the refractive indices
associated with the two axes of the molecule are more rotationally separated.
Transmitted light with an electric field oscillating parallel to the nematic director
will experience the extraordinary refractive index ne, while electric fields
perpendicular to the nematic director experience the ordinary refractive index, no.7
The LC therefore controls the polarization of the light passing through it by
retarding one component of polarized light relative to the other. Birefringence is
defined as Δn = ne – no. A LC’s birefringence can be controlled by changing the
orientation of the molecules or the order parameter.
5CB is a member of a class of LCs, called thermotropic LCs, whose order
parameter and certain other properties vary with temperature. 5CB, specifically,
behaves like an optically isotropic liquid at temperatures above its clearing point at
approximately 32 °C, but has a birefringence of at least 0.2 at lower temperatures.41
The change between birefringence and isotropy in 5CB occurs sharply at the
clearing point, and so lower temperature LC molecules throughout the bulk can
exert a significant influence on the average orientation of their immediate
neighbors. To promote uniform LC alignment across a sample area and reduce the
13
number of individual alignment domains, the LC must cool slowly from a
temperature above the isotropic point to the working temperature of the device.
The alignment that is reached after this slow-cooling process is highly
dependent on the surroundings of the LC material, namely the alignment layers that
are used. Typically, both industrial-scale and research-scale LC devices are prepared
by mechanically rubbing a polymer layer either by hand30 or using a motorized
rubber.56 This process allows the polymer to align the LC via two methods. On one
hand, the rubbing action creates grooves in the surface parallel to the rubbing
direction, along which the rod-like LC molecules tend to align. This effect has been
successfully replicated via mechanically stamping the polyimide (PI) surface.48 On
the other hand, the rubbing process also induces the side chains of the polymer to
align to a certain angle relative to the surface.57,58 This side-chain alignment
subsequently induces the LC molecules to align at an inclination angle near the
surface. This is called a pre-tilt angle and is highly dependent on the nature of the
polymer, the method with which the polymer is coated onto the substrate, and the
rubbing strength and material.59
5CB and similar LCs are so dependent on the specific treatment of the
alignment layer that a patterned alignment layer has been predicted to produce a
varied nematic LC director even in the bulk of the material.60,61 However, the
thickness of the LC layer also plays a significant role in the optical properties of LC
devices, even when the alignment layers are identical for the two different
thicknesses.49 This thickness dependence is also affected by the strength of the
14
interaction between a LC and the alignment material. The interaction is best
described by the anchoring energy, where the alignment at the surface
exponentially decays into the bulk of the material, decaying more slowly (or
reaching farther into the bulk material) as the anchoring energy or the strength of
the interaction between the LC and the alignment layer is increased. Research into
these interactions have produced unique results,39,50,62–64 but the effects of the pretilt angle fall off significantly as the bulk thickness of the LC increases to the micron
scale,49 the regime where LC is most commonly integrated with nanomaterials. It is
in this regime that the LC devices discussed in Chapter 4 and Chapter 6 are
presented.
2.1.2. Applications in Nanotechnology
Three of the most heavily exploited aspects of LCs since their introduction to
nanotechnology have been their responsiveness to an applied bias, their
birefringence, and their varied alignment methods. The ability of liquid crystals to
reorient themselves parallel to an applied bias, and subsequently relax to the initial
alignment after removal of the bias, has boosted the field of active plasmonics by
providing an active material with easily controlled switching on the millisecond
timescale.65–67 LCs are uniquely suited for combination with nanomaterials because
of the localized surface plasmon resonance (LSPR), which will be described in more
detail in Section 2.2. Briefly, the plasmon resonance is an excitation of the
conduction band electrons in a nanometer scale particle caused by light irradiation.
This excitation causes the particle to exhibit wavelength-dependent scattering and
15
absorption of light, which is exploited in this work and many others as colorproduction for sensing or displays. The particles’ size, anisotropy, material, and
surroundings all contribute to the wavelength-dependent properties and
anisotropic particles will also exhibit angular dependence in their scattering.
This angular dependence in anisotropic nanoparticles allows them to be
uniquely combined with liquid crystals in order to better control the orientation and
position of the nanoparticles in a 3-dimensional material.55 In many cases, rodshaped nanoparticles embedded in a nematic liquid crystal will be induced to
reorient along with the liquid crystal when a bias is applied.
44,51,53,68–70
These
results showed that it was possible to actively modulate the plasmonic or
photoluminescent signal via reorientation of the nanoparticles relative to the
viewer. In other cases, the orientation or reorientation of the LC molecules can force
the nanoparticles to desired locations within the bulk LC.71,72
Nanoparticles can also be embedded into a LC layer to exert an effect on the
LC itself. Ferromagnetic nanoparticles (or even gold nanoparticles73) can be
embedded into a LC host, creating a ferronematic, which can cause the LC mixture to
be highly responsive to magnetic fields and even exhibit hysteresis.43,74 When
carbon nanotubes are doped into a nematic LC, some regions may remain in a
nematic alignment and exhibit standard bias-responsive reorientation, while other
regions that exhibit more complicated alignment may not relax after the bias is
turned off.75 The incorporation of nanowires can also impose changes to the electrooptic properties of the LC.76
16
Standard LCDs, as briefly described in section 1.1, typically include a fewmicron layer of LC, sandwiched between conductive layers. In the most common
construction, a 90°-twisted nematic (TN) is prepared as the initial alignment and a
bias can be applied across the thickness of the LC, inducing out of plane
reorientation. In this system, the polarization of light passing through the LC is
rotated by 90° without bias. When bias is applied, the light is no longer rotated. In
this way, a pair of polarizers with orthogonal optical axes can sandwich the LCD.
Then, the light passes through the TN and the second polarizer in the bright state,
and when the bias is applied the light is not rotated by the LC and is blocked by the
second polarizer in the dark state. LCDs of this or similar design have been
combined with nanoplasmonic displays where the colorants are part of the LC itself
as described earlier in this section.51–53 Alternatively, the nanomaterial can be
placed in a layer on one side of the LC so that the color produced by the
nanomaterial can pass through the LC.30,77
The following sections will discuss a host of such single-layer display
materials, most of which have not yet been combined with LCs or have not been
designed to be compatible with them. Although this compatibility is not necessary
and in some cases is not beneficial, an ideal material would be versatile enough to be
compatible with a large variety of excitation schemes and on/off switching
mechanisms. The physics behind these displays is discussed next.
17
2.2. Nanodisplays
The localized surface plasmon resonance of a metallic nanoparticle is an
important part of nanodisplays, as well as a host of other applications including
chemical and environmental sensing,78–80 nanoparticle-based catalysis,81–83 and
nanomaterial-based solar cells.26,27,82,84,85 This section focuses on the physics of the
LSPR of single particles, especially as it relates to display and color filter
applications, and how inter-particle interactions can enhance the LSPR for these
purposes.
2.2.1. Physics of Plasmonic Structures
The LSPR is a coherent oscillation of conduction band electrons in a metal
nanoparticle, and it is this phenomenon that determines the color of a single
nanoparticle.86,87 When light of a particular wavelength of light excites a plasmon in
a sub-wavelength sized particle, then the particle can be generally described as a
point dipole oscillating in phase with the electric field of the incident light. This
resonant oscillation and the wavelength at which it occurs is determined by the size,
shape, and material of the nanoparticle, as well as the refractive index of its
surroundings.88,89 The electronic load imposed by the surroundings can also shift
the plasmon resonance and the resonance linewidth.90 Metallic nanospheres, disks,
and nanorods are the most studied nanoparticles because of their simple shapes,
multiple
available
chemical91,92
and
lithographical93–99fabrication
methods,
significant spectral tunability, and strong polarization sensitivity in nanorods.100–106
18
Although their limited spectral range in the visible region prevents them
from producing all the necessary colors in a display, gold nanoparticles can exhibit
narrow LSPRs. The LSPR of gold nanoparticles can be tuned from approximately
550 nm through the infrared region.107,108 The linewidths (full peak width at half
maximum) of these individual particles can be as small as 100 meV. 90 These optical
characteristics make gold nanoparticles, nanorods especially, good chemical
sensors; they tend to respond to minute changes in their environment with smallbut-measureable
variations
in
both
the
LSPR
wavelength
and
the
linewidth.79,80,90,91,109–112 However, the strongest spectral tunability is achieved
through controlling the physical parameters of the nanoparticles and their few-nm
distance from their nearest neighbors.
Small groups or clusters of nanoparticles, including placement of
nanoparticles near to a metal film, can add new and useful spectral features. When
two particles are placed in close proximity to one another, typically within a fewnm, the electric field near the surface of the nanoparticles overlap and couple with
one another.113–115 This coupling has been intuitively likened to molecular orbital
hybridization,116 and is sensitive to the shape and orientation of the component
plasmonic nanoparticles.117 With this model in mind, research on coupled
nanoparticles has led to Fano resonant structures where broad resonant modes that
scatter to the far field interfere destructively with narrower resonances that are also
supported by the structure.113,118–120 Because of the ability to engineer narrow dips
in the spectra of most Fano structures, these composite structures are highly
favored in sensing applications. Fano structures have also been adapted for use as
19
structural color elements,121 and can even be incorporated into LCDs because of
their polarization sensitivity.77 Larger groups of nanoparticles also exhibit polymerlike behavior in that the optical response of a collection of particles is reliant both
on the subunit and the organization of those subunits.122,123
The overlap in the enhanced electric field near the surfaces of the particles
diminishes as the nanoparticles are separated by larger distances. The nanoparticles
still interact with one another when their separation is on the order of the
wavelength of light incident on them, and this interaction is called diffractive
coupling or radiative dipole coupling.97,124 When the particles in question are
arrayed at regular intervals on a substrate, diffractive coupling is at its strongest
and can produce both narrowed LSPRs95,125–128 and also extremely sharp lattice
resonances called Wood anomalies,124,129–131 and in some cases both phenomena can
be observed.97 In many cases, sufficient overlap between the lattice resonances and
the broad nanoparticle LSPRs can interfere, producing Fano dips in the spectrum at
the location of the lattice resonance.132–134
Diffractive coupling can be physically described in two ways. First, we can
consider that two adjacent nanoparticles in an array that have an interparticle
distance equal to or less than the wavelength of an incident photon. In such a case,
we can assume that even under incoherent excitation conditions, one nanoparticle is
excited with a phase shift relative to the other adjacent structure, resulting in a
subsequent phase shift in the scattered light from the two nanoparticles. These
scattered photons interfere in the far field. This phenomenon, which will be
20
discussed in more detail in Chapter 5, allows us to think of the array of plasmonic
nanoparticles essentially as a two dimensional grating excited from one direction at
an oblique angle.
In the second description of diffractive coupling, we can avoid the
requirement of a limit to the interparticle distance, instead considering that each
nanoparticle is approximated by a point dipole located at the center of its position
within the array. If one nanoparticle’s LSPR is excited by light, that nanoparticle will
radiate in all directions. Nearby nanoparticles may be excited by the re-radiated
light, and will subsequently re-radiate as well. In this way, the nanoparticles in the
array “communicate” with one another, creating a large-area array analogue of an
LSPR, which is the lattice resonance. These lattice resonances yield only sharp peaks
with otherwise minimal far-field spectral activity because the wavelengths of light
that do not match the interparticle distances undergo destructive interference
within the array. Only those wavelengths that match interparticle distances will
constructively interfere and be re-radiated to the far-field. This second description
of diffractive coupling is mathematically described in Chapter 6.
2.2.2. Single-Layer Arrays for Nanodisplays
Most recent examples of nanodisplays and color filters based on plasmonics
have relied primarily on the plasmon resonance of the individual scattering
structures, with some additional color tuning provided by adjustments to the
interparticle spacing. These examples can be split into categories according either to
the structures forming them (nanoparticles or nano-holes) or into the optical
21
geometry for which they were designed (transmission or reflection/scattering). This
second distinction is somewhat superficial because all plasmonic structures exhibit
optical activity arising from both scattering and absorption mechanisms, and so
most of the examples presented here could be re-designed with a different viewing
geometry in mind. Even so, examples discussed herein will be presented in light of
the viewing geometry they were designed for as well as the structures that comprise
them.
The vast majority of color displays, especially utilizing aluminum in recent
work, focus on color filters. These structures are unique in that many of them can be
used as color filters for combination with image sensors22,135,136 as well as
displays.22,136–139 These color filters can produce bright colors because of their
reliance on the plasmon resonance and the array spacing, but these filters generally
do not produce polarized color. On the other hand, carefully oriented asymmetric
structures, such as nanocrosses140 or overlapped nanowires,141 can produce
polarization filters. These filters can also change color depending on which
polarization of light is passed through it.
The reflective or scattering-based displays that have been designed so far are
generally dependent on the single nanodisk resonance to tune the color,142–144
ignoring or avoiding array spacing-based color contribution. Because both the
individual nanoparticles and the array spacing are symmetric, the light scattered
from these examples is unpolarized. More complicated structures can produce more
useful optical responses. Although nanorods have not been used in research geared
22
toward displays prior to the work presented in this thesis, theoretical calculations
on both nanorods and nanospheres in 1- and 2 dimensional arrays have
demonstrated how important the array spacing can be.126,127,131,145,146 Further detail
on many of these topics are also presented in sections 5.2 and 6.2.
2.2.3. Production Methods for Large-Area Nanoparticle Arrays
Utilization of nanoparticles in commercial displays requires us to produce
nanoparticles at consistent dimensions over large areas. This result is unobtainable
via the serial single-beam electron beam lithography that is available at most
materials fabrication and research facilities. The two fabrication methods that may
yield the quickest fabrication times include extreme UV lithography,147,148 and
interference lithography.141,147–149 Extreme UV lithography allows for the use of
standard photolithography methods to produce nanoscale features in a resist.
Interference lithography, on the other hand, overlaps lasers so that the interference
pattern incident on a resist produces an array of exposed shapes in the resist. Both
of these methods require a silicon-based master with the appropriate level of detail
to provide either the direct transmission mask for the photolithography or an
interference mask for the interference lithography. This master is typically prepared
via electron beam lithography so that nano-scale features can be precisely written.
Other methods for large-area reproduction of arrays include nanoimprint150–
152
and nanotransfer processes.153,154 Nanoimprint lithography, similarly to the
previous lithography methods, also requires an original silicon master. This master
is used to produce a stamp that will imprint a resist or other sacrificial layer with
23
the desired pattern. Unlike the previously discussed lithography methods, the
master is not directly used to prepare the substrate; instead it forms the stamps, and
so the longevity of the maser is increased. Additionally, no development step for the
substrates is necessary, because the stamping physically pushes the soft sacrificial
layer out of the way. After stamping, the desired metal can be deposited onto the
substrate. Nanotransfer processes can be utilized after patterning via nanoimprint
or another lithography step when the substrate on which the nanoparticles are
formed is not the final substrate they are intended to rest on. As the name implies,
the structures can be transferred either directly or indirectly to their final substrate
while maintaining their physical dimensions and positions. Typically, if
nanotransfer processes are to be used, the structures will be formed on a substrate
that only weakly binds to the nanoparticles, and then a stronger-binding substrate is
placed in contact with the structures, allowing them to be removed from the first
substrate.
Other,
longer
run-time
methods
of
fabrication
include
patterned
lithographical etching,155–160 focused ion beam milling,154,161–163 and standard
electron beam lithography methods.96,98,99,164–168 In general, these serialized patternwriting methods are the slowest processes but provide the highest resolution and
most control over the final product, and so these techniques are typically reserved
for master-making, writing of smaller and sparser structures, or small-scale
exploratory research as is presented in this thesis.
24
2.2.4. Measurement Strategies and Applications
The color-producing capabilities of these materials, from single particle to
large array, are only useful if we can measure them, test them, and therefore
improve them. Measurement techniques can be categorized into bulk measurement,
such
as
UV-Vis
transmission
or
extinction
measurements,
and
single
molecule/particle techniques such as diffraction-limited dark field microscopy. The
benefit to bulk measurements is that they can provide information about the whole
sample in a relatively quick measurement of a sample, like a solution of
nanoparticles or a large area of a patterned surface. For displays, this kind of
measurement is closer to what a “user” would see under similar conditions,
especially for transmissive filters. On the other hand, bulk measurements can
provide little mechanistic information about how the individual nanoparticles
contribute to the properties of the whole system. Single particle measurements can
provide this insight, at the cost of slower measurements over a far smaller number
of individual particles.
The experimental work in this thesis is mostly composed of electronic
measurements via scanning electron microscope (SEM), and optical scattering
measurements via a diffraction-limited dark field microscope. This combination of
techniques is particularly powerful because we can exactly identify the same
structures across these two different platforms. Although similar imaging work can
be done using transmission electron microscopy (TEM) for higher magnification
imaging,169 we have found the TEM grids to be more difficult to work with in an
25
optical
microscope
than
standard
slides
without
providing
significant
improvements to resolution.
Dark field scattering is a staple measurement technique for plasmonic
nanoparticle research because the particles are often too small to provide sufficient
signal to background ratios for extinction measurements. Dark field geometry is
achieved in an optical set up in two ways. One way is to use a microscope condenser
with a stop in the middle, which can excite a sample at an oblique angle that is larger
than the collection cone of the objective. In this way, a sample is excited from all
directions and with all polarizations. Dark field geometry requires the use of a
wedge and polarizer in the condenser to restrict the polarization and angle at which
the excitation light is incident on the sample. Alternatively, a prism can replace the
wedge, allowing for the focusing of polarized white light from one direction. These
two similar geometries restrict the excitation in a way that can be easier to model
theoretically than full dark field, and they allow the researcher to probe different
polarized plasmon modes more directly. The scattering of a particle scales with its
volume squared while the absorption scales with volume,170 and so for the particles
used in this work, which have at least 25 nm diameters across their smallest
dimensions, scattering is the preferred optical phenomenon to probe.
2.3. Conclusions
Regardless of the methods used to prepare them, nanodisplays have the
potential to make a significant impact on display technology. Details on specific
26
examples of nanodisplays are presented in sections 4.2 and 5.2, along with
information on the strengths and weaknesses of the individual designs. On their
own, nanodisplays can produce bright and vivid colors, determined by their shape
and material thanks to the LSPR and the LSPR coupling both at few nm- and
hundreds of nm-distances between particles. Many of these displays rely on the
anisotropy of their component nanoparticles to produce a polarized response to
incident light, which sets the stage for the inclusion of birefringent liquid crystals.
With strong colors produced by nanodisplays and on/off tunability imparted by
liquid crystals, the applications to which these kinds of hybrid display materials can
lend themselves is nearly limitless.
27
Chapter 3
General Methods
This chapter provides high level rationale for the methods used in this body
of work. The experimental methods section associated with each chapter is printed
here exactly as they appeared in the original publications with minor edits to
improve clarity or provide additional context beyond what the individual
publications provided. The section on colorimetry has not been previously
published in either publication or supplemental information, but may prove useful
to others working on this or similar projects.
3.1. Experimental Methods for Chapter 4
The work presented in Chapter 4 demonstrates how the scattered light from
randomly oriented gold nanorods can be turned on and off from the perspective of a
viewer, using a layer of liquid crystal and an applied bias. 30 Gold nanorods were
28
used to probe the liquid crystal alignment as a function of signal polarization on a
smaller scale than simple bright field polarization measurements could provide.
Proficiency in photolithography and dark field spectroscopy were imperative for the
success of this work. This work is meant to support or disprove the hypothesis
posed by Khatua et al. in our earlier publication, which demonstrated orthogonal
rotation of the gold nanorod plasmon’s polarization. The hypothesis was that the
application of an applied electronic bias in-plane on one substrate created an
alignment change between ideal homogeneous nematic (HN) to TN LC alignments.
Because the samples are prepared by hand, it was difficult to create samples
with well-aligned LC that had the desired thickness at the active area of the sample.
A phenomenon called “Newton’s Rings”, regions in the glass-air-glass sample that
appeared different colors with respect to spatially changing thickness, could be used
to determine whether we had achieved a spatially uniform thickness over the active
area. Application of this knowledge allowed us to more easily fabricate samples of
uniform thickness, and also measure said thickness using UV-Vis spectroscopy.
3.1.1. Sample Preparation
To prepare an LC device, an interdigitated array of electrodes (10 µm wide
fingers alternating with 10 µm gaps) was first prepared on a clean glass microscope
slide via photolithography. After development, 5 nm titanium and 50 nm gold were
deposited by electron-beam evaporation, followed by lift-off in acetone. A gold
nanorod solution (Nanopartz, 30-25-700) was drop casted on the slide and dried
with compressed nitrogen, isolating randomly oriented single gold nanorods in the
29
electrode gaps. The gold nanorods had an average aspect ratio of 2.7, with an
average width of 18 nm and an average length of 46 nm. The bulk extinction
spectrum in water had an LSPR maximum of 689 nm, and single particle scattering
spectroscopy measurements identified an average LSPR maximum of 730 nm ± 50
nm on indium tin oxide (ITO) coated glass substrates when covered by the LC. To
control the thickness of the device, a solution of silica beads (Microsil microspheres,
SS06N, 6 µm in diameter) was then spin-coated on the slide, avoiding the electrode
area. An ITO glass cover slip was coated on its untreated glass surface with PI
(Nissan Chemical, SE-3510). The cover slips were then pre-baked at 80 oC for 5
minutes on a hot plate, followed by oven baking at 180 oC for 45 minutes
immediately before use. After baking, a lens cloth was used to rub the PI
unidirectionally to create micro grooves for the LC alignment. The alignment
direction of the LC director and hence the main optical axis of the birefringent LC
was predefined in this way. The prepared microscope slide and cover slip were
assembled into a LC cell so that the nematic director was oriented parallel to the
electrodes. Two sides of the LC cell were glued using a clear epoxy (Norland
Products Inc., UVS91) between the slides, followed by curing with an UV lamp
(Spectronics, EA-160) operating at 365 nm for 20 minutes. Before addition of the LC
into the sample, the thickness was determined via UV-Vis extinction measurements
which showed interference fringes caused by multiple reflections at the glass-air
interfaces in the gap of the cell, the distance between which relates directly to the
thickness of the air gap.171 5CB (Tokyo Chemical, C1550), in its isotropic phase at 65
oC,
was then inserted into the cell via capillary action and allowed to cool to room
30
temperature over approximately 1.5 hours. Finally, the LC cell was sealed at the
edges with epoxy glue (Varian Inc., Torr Seal 953001), and copper wires were
connected to the interdigitated electrodes with a conductive silver epoxy
(Chemtronics, CW2400).
3.1.2. Single Particle Spectroscopy
Single particle spectroscopy of the gold nanorods in the LC devices was
carried out using dark-field excitation in a transmission geometry on an inverted
microscope (Zeiss, Observer D1m). Unpolarized white light from a halogen lamp
was focused on the LC devices by a dark-field condenser with a numerical aperture
(NA) of 1.4. Scattered light from individual gold nanorods was collected with an oil
immersion objective (Zeiss, Plan-Apochromat, 63x, 0.7 NA), directed through an
analyzer, and detected by a nitrogen cooled CCD camera (Horiba Symphony)
attached to a spectrograph (Horiba Triax). Scattering images of gold nanorods were
acquired with the grating set to the zero order reflection. The analyzer and the
interdigitated electrodes were aligned so that they were parallel to each other
defining the 0o direction for all subsequent measurements. The nematic director of
the LC cell in the voltage off state was therefore orientated parallel to the analyzer.
Polarized images were taken of each LC sample in 30° increments from 0° to 180°,
while an AC voltage (~6 V, 1 kHz) was applied (Von), with the voltage switched off
(Voff), and in the isotropic phase, which was achieved by increasing the intensity of
the halogen lamp to its maximum setting, effectively melting the LC phase. For the
collection of single gold nanorod scattering spectra, the grating was set to the first
31
order reflection and a 50 μm pinhole was added in the detection path at the first
image plane of the microscope so that only the region of interest would be detected
by the spectrometer.
3.2. Experimental Methods for Chapter 5
Chapter 5 presents work using lithographically prepared nanorods
composed of aluminum that are co-oriented in an array, which is a significantly
different system than the randomly oriented and positioned chemically prepared
gold nanorods from Chapter 4. This switch provided the opportunity to produce
color spanning the whole visible region, and appealed to electronics-based
applications. Initially, smaller versions of these arrays were intended to provide
brighter, still polarized scattering from a nearly diffraction-limited area while
avoiding near-field coupling of the nanorod LSPRs on the few-nm distance regime.
Of course, diffractive coupling among the nanorods within an array provided for
additional enhancements to the color and intensity of light scattered from these
arrays of nanorods. Larger arrays provided stronger lattice resonances. These
enhancements initially presented themselves as hindrances to obtaining vibrant
color, but perseverance helped to produce the series of vibrant pixels in Chapter 5.
Theoretical calculations, provided by Dr. Alejandro Manjavacas, were invaluable to
this work. The discovery of these beautiful pixels prompted rapid publication in the
Proceedings of the National Academy of Sciences of the United States of America.32
Diffraction-limited dark field microscopy was used to study these pixels, despite our
choice of a large 5 micron footprint. This technique was chosen because it would
32
allow for future comparison against single aluminum nanorods, and because the 5
micron pixels were too small to be measured via bulk-scale UV-Vis spectroscopy.
Additionally, the dark field excitation geometry highlights the diffractive coupling
effects while avoiding the zero order grating mode that would be apparent with
normal incidence excitation.
3.2.1. Sample Preparation
A clean glass slide coated with ITO (8-12 ohm sheet resistance, Delta
Technologies LTD) was spin coated with a positive electron beam resist (a 50/50
mixture of PMMA 495 A4 and A2, MicroChem) and baked at 180°C for 90 seconds.
After patterning (JEOL 6500F SEM equipped with beam blanker and associated with
Nabity NPGS software) and development, 35 nm of aluminum was evaporated onto
the substrate at a base pressure of ~2 x 10-7 torr to promote low oxide content in
the bulk aluminum.172 Liftoff consisted of soaking the sample in acetone for 15
hours, followed by gentle rinsing with fresh acetone. Shorter soaking times resulted
in nanorods with rough edges or pixels with missing regions. The substrate with
aluminum structures was then spin coated with a PI solution (Nissan Chemical, SE3510), and baked at 180 °C for 45 minutes.
The general layout of a single pixel is an array of co-oriented nanorods in an
approximately hexagonal array, with the y-axis parallel (x-axis perpendicular) to the
nanorods’ long axes. The center to center distances between nanorods along their
widths is called Dx, and the distance between rows of nanorods is called Dy.
Individual pixels were designed to fit within a footprint of 5 μm x 5 μm, so that the
33
number of nanorods in the x direction is 5,000 nm/Dx and the number of rows in the
y direction is 5,000 nm/Dy. These numbers were rounded to the lowest whole
number and used to prepare the design.
3.2.2. Optical and Physical Characterization
The aluminum pixels were characterized using SEM (JEOL 6500F or FEI
Quanta) and dark field scattering microscopy. For scattering images and spectra, the
sample was placed on an inverted microscope (Zeiss, Axiovert 200) with the glass
substrate side facing up and the pixel side facing down toward the objective (50x,
NA = 0.8, Zeiss, Epiplan-Neofluar). An equilateral prism (Thorlabs) was used to
couple white light from a tungsten lamp (Newport) into the sample. The lamp was
mounted in a cage system (Thorlabs) which included a polarizer set to select only ppolarized excitation light. Images were collected using a Canon Rebel DSLR camera
with ISO set to 100 and various exposure times on the order of 1 second. Spectra
were collected by passing the light scattered from an individual pixel through a 50
μm pinhole at the first image plane of the microscope to a spectrometer (Princeton
instruments, Acton SP2150i) and CCD camera (Princeton Instruments, PIXIS
400BR). The CCD camera exposure time was 40 seconds with the grating set to a
center wavelength of 600 nm. For each spectrum three repetitions were averaged.
All spectra were corrected by subtracting a background spectrum recorded with the
same exposure time from the pixel spectrum, and dividing by a transmission
spectrum of the lamp through the same substrate at a location with no structures
present.
34
3.3. Experimental Methods for Chapter 6
Chapter 6 is essentially the marriage of Chapter 5 with Chapter 4, in that the
work improves the colored pixels composed of aluminum nanorod arrays, followed
by a combination of these pixels with an LCD on a macroscopic scale. This chapter
utilizes the same lithography and characterization methods as in Chapter 5 while
also incorporating a new excitation geometry devised for viewing and imaging
outside the microscope. This work focuses on two aspects: 1) the potential for
future incorporation into commercial devices, considering the scalability and
reproducibility of the optical features of these pixels, and 2) More fully
understanding the available color control mechanisms caused by the size and
spacing of the nanorod array. During the progress of this work, I also trained a new
student, Tiyash Basu, in the techniques associated with my research, and his quick
learning allowed him to contribute to the research. Under my direction, he produced
pixels smaller and larger than the standard 5 micron pixels, measured these pixels,
and analyzed the data. He also prepared the first draft of the methods section that
follows.
3.3.1. Sample Preparation
An ITO coated clean glass slide (120 nm thick ITO, Sheet Resistance: 8–12
ohm; Delta Technologies Ltd) was spin-coated with a high resolution positive
electron beam resist (50% by volume of PMMA 495 A4 and A2; MicroChem) and
baked at 180 °C for 90 s. The substrate was then patterned in an SEM (FEI QUANTA
650 equipped with a beam blanker and associated with the Nabity NPGS software)
35
and developed in a 1:3 v/v solution of MIBK:IPA for 30 s. 35 nm of aluminum was
then deposited onto the substrate via electron beam evaporation, at a rate of 0.80.9Å/s and a base pressure approximately 2.2 × 10−7 torr. Lift-off was carried out by
soaking the sample in acetone for approximately 15 h, followed by gentle rinsing
with fresh acetone and drying under a flow of nitrogen gas. After SEM
characterization using the same electron microscope, the sample was spin coated
with polyimide solution (SE-3510; Nissan Chemical) and baked at 180 °C for 45 min.
and cooled to room temperature. Unless otherwise noted, all pixel footprints are 5
μm x 5 μm.
To prepare a LCD device, a plasmonic pixel sample was first prepared as
noted above. An additional substrate was prepared by cleaning an ITO slide and spin
coating it with polyimide and baking, following the aforementioned procedure.
Micro grooves for alignment of the liquid crystal were created by gently rubbing the
polyimide coated surface of both samples unidirectionally with a lens cloth. For the
slide with the pixels, the rubbing direction was chosen to be parallel to the
nanorods’ long axis. In this way, the alignment of the liquid crystal director and
therefore the main optical axis of the birefringent liquid crystal was predefined. A
silica beads solution (Microsil microspheres, SS06N, 6 μm in diameter) was then
spin-coated onto the polyimide side of the slide containing the pixels, avoiding the
pixel area, to control the device thickness. The two substrates were then assembled
into a liquid crystal cell so that the polyimide surfaces faced each other, with
rubbing directions perpendicular to each other to promote a 90° twisted alignment.
Clear epoxy (Norland Products Inc., UVS91) was used to glue two edges of this cell.
36
The epoxy was then cured with a UV lamp (Spectronics, EA-160) operating at 365
nm for 20 minutes. Capillary action was used to insert the liquid crystal 5CB (Tokyo
Chemical, C1550), at 60 °C in its isotropic phase, into the prepared cell. The filled
liquid crystal cell was allowed to cool to room temperature over approximately 1.5
hours before sealing the two open sides with the same epoxy glue. Finally, a
conductive silver epoxy (Chemtronics, CW2400) was used to connect copper wires
to the ITO surface of each slide.
3.3.2. Optical and Physical Characterization
For every sample, SEM characterization of the nanorod size and array
spacing within an aluminum pixel was carried out with the same SEM as was used
for lithography (FEI QUANTA 650), performed before optical characterization
because the SEM could not be used with the polyimide layer in place. Multiple
iterations of the same pattern were prepared in the same region so that SEM
characterization could be performed on a nearby but identical set of pixels, and not
on the pixels that were later characterized optically. In this way, damage to or
contamination of the pixels caused by SEM imaging could be avoided. Samples were
imaged at a working distance of 10 mm and with 100,000x magnification for
automated size analysis carried out in Matlab. Scattering images and spectral
measurements were taken by placing the sample on an inverted microscope
(Axiovert 200; Zeiss) with the pixel side facing down towards the objective (50×,
N.A. = 0.8, EC Epiplan-NEOFLUAR; Zeiss). P-polarized white light excitation from a
tungsten lamp (Newport) mounted in a cage system (Thorlabs) was coupled into the
37
inverted substrate using an equilateral prism (Thorlabs). Spectra from individual
pixels were collected by passing the scattered light through a 50-μm pinhole at the
first image plane of the microscope to a spectrometer (Acton SP2150i; Princeton
Instruments) and CCD camera (PIXIS 400BR; Princeton Instruments). A center
wavelength of 600 nm was used for all spectra. Each spectrum represents an
average over three spectra taken. All spectra were background corrected by
subtracting a background spectrum recorded with the same exposure time at a
position with no pixels present. Each spectrum was further divided by a
transmission spectrum of the lamp through the same substrate at a position with no
pixels present.
The integrated intensities of the pixels of varying sizes were obtained by
imaging the pixels on the same excitation and collection geometry that is described
above. In this case, the pinhole was removed from the detection path, and the
grating was set to the zero order reflection and imaging mode. The exposure time of
the CCD camera was set to 2s for all image acquisitions. Image analysis was
performed in Matlab by subtracting the average background intensity from the
whole image, and then summing the intensity from the resulting image. Multiple
images of the same type of pixel were taken, using the same exposure time, to build
up statistics, as is further explained in Chapter 6.
3.3.3. Digital Camera Images
The sample was mounted vertically and white light was coupled in from the
side of the slide using a glass fiber bundle (Newport, part no. 77538) with a
38
rectangular output slit. The unpolarized white light entered the slide normal to the
edge surface and propagated within the slide along the long axes of the nanorods in
the pixels. Digital camera images were taken using a Canon EOS Rebel T2i digital
single lens reflex camera with the ISO setting adjusted to minimum (value equal to
100) and various exposure times. The camera was mounted in a slider situated on a
semicircular track (Movo Photo CTS500, 51" Length) to obtain images from various
angles at the same viewing distance. For some images, a polarizer was placed
between the camera and the sample. For single-substrate samples, the pixels were
viewed through the glass surface because the pixels were bright enough to create a
reflection on the glass surface when viewed through the polyimide surface, making
it difficult to focus the camera. The LCD was imaged through the liquid crystal, and
therefore the pixel substrate’s polyimide surface was facing the camera. The pixels
were also viewed under the same conditions through an additional small sheet of
80° optical diffuser, commercially available from Luminit.
3.4. Colorimetry
Chapter 5 and Chapter 6 both utilize colorimetry, which is the quantitative
representation of what color an observer would see if an object gives off a specific
spectrum of visible light. Neither I nor our lab had prior experience with
colorimetry, and so I turned to the literature and to Halas lab member Nicholas
King, who was as new to the subject of colorimetry as I was.
39
This kind of calculation requires knowledge of how a standard observer
recognizes different colors, and it also requires the ability to convert spectral
information to a common mathematical description. I chose to use the series of
standard observer spectra developed by the International Commission on
Illumination (CIE) in 1931, because it is the definition that is standard in display
technology. These spectra were downloaded in Excel format from:
“http://www.cie.co.at/index.php/LEFTMENUE/index.php?i_ca_id=298”
This file contains a matrix of four columns of data: the wavelength, and the
“sensitivity” for the red, green, and blue channels. I prepared a Matlab function that
would load the standard observer spectra and the sample spectrum, and then
interpolate the sample spectrum to match the observer spectrum wavelength
values. The interpolated sample spectrum was then multiplied against each of the
red, green, and blue spectra, which essentially scales the spectrum according to the
“sensitivity” of the observer for each optical receptor. The resulting intensity vector
for each of the “x”, “y”, and “z” spectra were then summed and normalized to obtain
a color value in xyz color space: [X Y Z], where none of the three parameters was
larger than 1. To convert from xyz color space to sRGB, the following 3x3 conversion
matrix was obtained from:
“http://www.cs.rit.edu/~ncs/color/t_convert.html#RGB.”
M = [3.240479, -1.537150, -0.498535;
-0.969256, 1.875992, 0.041556;
40
0.055648, -0.204043, 1.057311];
Equation 3.1 – Conversion matrix for [X,Y,Z] to [R, G, B] color coordinate
conversion
So that
𝑅
𝑋
[𝐺 ] = 𝑀 [𝑌 ].
𝐵
𝑍
Equation 3.2 – Conversion from [X,Y,Z] to [R, G, B] color coordinate systems
The RGB values that result from this calculation can be scaled
homogeneously to adjust the lightness of the color, and then multiplied by the
number of levels for RGB possible in the desired display format. For example, 8-bit
displays are capable of producing 256 shades each of red, green, and blue colors, for
a total of 16,777,216 possible colors, though not all are distinguishable to the human
observer. It is possible for a measured spectrum to produce a color whose x, y, or z
values lie outside of the sRGB color gamut, which means that an sRGB defined color
space cannot accurately reproduce that color. There are other, larger gamut displays
available; however, the most commonly used display definition is sRGB. Even wide
gamut displays are rated based on the gamut area percent relative to sRGB, and so
this was chosen as the appropriate comparison between plasmonic pixels and
current display technology.
41
Chapter 4
Detailed Mechanism for the
Orthogonal Polarization Switching
of Gold Nanorod Plasmons
4.1. Abstract
This chapter, originally published in the journal Physical Chemistry Chemical
Physics in 2013,30 describes an electro-optic material capable of orthogonally
switching the polarization of the LSPR scattering of single gold nanorods,
independent of their orientation. LC samples are prepared in a sandwich
configuration with electrodes arranged so that an applied voltage induces
alignment-switching of the LC molecules covering individual gold nanorods. Due to
the birefringence of the nematic LC, the reorientation in the nematic director
alignment causes a change in the output polarization of the scattered light. We
propose the underlying mechanism to be based on a HN to TN phase transition and
42
provide support for it via Jones calculus by modeling the effect of ideally aligned HN
and TN phases on polarized light transmitted through the sample. In the model, we
include the effects of sample thickness and LSPR wavelength, expressed in terms of
the phase retardation, χ, on the observed output polarization. We find four
distinctively different trends for the output polarization as a function of the incident
polarization as χ is varied. Two of these cases provide reproducible orthogonal
polarization switching of the LSPR while maintaining a high degree of polarization.
These results are verified experimentally with LC cells of different thicknesses. The
deviation of the experimental samples from ideal behavior can be explained by the
inherent variations in the LSPR maximum and local cell thickness.
4.2. Background and Motivation
Technology for the next generation of photonic devices requires the
manipulation of light on length scales smaller than the diffraction limit. One
potential solution is to utilize the LSPR, a coherent oscillation of conduction band
electrons of a metal nanoparticle. The wavelength tunability of the LSPR has been
demonstrated by many approaches79,120,173–184. For example, varying the
nanoparticle’s size and shape79,173,183, the medium refractive index79,174, or the
substrate permittivity175–179 all affect the LSPR, as does allowing interactions
between adjacent nanoparticles120,180–182,184. However, active control of the LSPR is
also necessary in order to employ nanoparticle LSPRs as a platform in nanophotonic
device applications.
43
A variety of methods have been shown to be capable of actively controlling
the LSPR maximum78,185–193. Reversible shifting of the LSPR wavelength via external
control has been achieved by modulating the properties of a VO2 substrate, which
underwent an insulator-metal phase transition at elevated temperatures, leading to
changes in permittivity185,186. Thermally controlling the local refractive index of a
nanoparticle by changing the surrounding polymer’s morphology has also been
demonstrated188. Instead of heat light has been applied to a photo-sensitive organic
film, which upon irradiation at a certain wavelength experienced a change in
chemical bonding, therefore causing a change in refractive index187. Another
approach is the injection of charges into a nanoparticle via an electrochemical cell
leading a modification of the nanoparticle electron density to induce voltagetuneable reversible shifts of the LSPR maximum189. Spectral shifts of the LSPR have
furthermore been accomplished by modulating the plasmon coupling strength
between neighbouring nanoparticles through varying the interparticle gap with an
elastomeric supporting material78,190. However, all of these methods yield only
relatively small LSPR shifts of less than 30 nm in the visible region78,185–189 or larger
shifts of ~ 400 nm in near infrared region190 and are therefore less useful in colour
display applications.
An interesting strategy to modulate the LSPR of plasmonic nanoparticles is to
use LCs,51–54,67,194–201 as their refractive index is anisotropic and can be changed
through the alignment of the LC molecules. The average alignment direction of the
LC molecules for a nematic LC is known as the nematic director, and its orientation
44
is controllable by an externally applied voltage.
51–54,67,194–199
Refractive index
differences between the extraordinary and ordinary axes (parallel and
perpendicular to the nematic director) for thermotropic LCs can be as large as Δn =
0.2 and should theoretically shift the LSPR up to 100 nm for gold nanorods or
nanoparticle dimers surrounded by a LC medium.202–204 Instead, only moderate
LSPR shifts of 10 - 20 nm have been observed for LC-based modulation of plasmonic
nanoparticles.194,195,197,198 This is most likely due to strong anchoring of the LC
molecules at the surface of the nanoparticle, preventing the nanoparticles from
sensing the maximum refractive index change caused by electric field-induced LC
reorientation.46,199,205,206 It has also been demonstrated that nanoparticles with
anisotropic shapes can be completely solvated in a LC matrix and become aligned
with respect to the nematic director, which, if manipulated with an external voltage,
will physically rotate the orientation of the solvated nanoparticles.52,68,69 However, it
is a common problem that the solubility of most plasmonic nanoparticles is too low
to achieve a macroscopically useful optical response from these composite
materials.
Recently, we have introduced an approach to actively modulate the LSPR
scattering from individual gold nanorods via the electro-optical properties of the LC
5CB. The polarization of the longitudinal LSPR was reversibly rotated by 90o,
leading to complete intensity modulation with a low external voltage applied in the
sample plane using an interdigitated electrode configuration.31 The mechanism of
this unique orthogonal polarization switching was hypothesized to be due to a
45
transition of the LC nematic director alignment from a HN to a TN phase, as the
interdigitated electrodes are much thinner compared to the overall device thickness.
Our approach excludes the need to dissolve plasmonic nanoparticles in a LC matrix,
and, because of the electrode configuration and use of only one alignment layer,
does not have to overcome the LC surface anchoring energy. However, the effects of
different cell thicknesses and wavelengths of the LSPR maximum are not fully
understood yet.
Here, we examine the dependence of the orthogonal polarization switching
for LSPR scattering from single gold nanorods on cell thickness and LSPR
wavelength. In doing so, we test and expand upon the previously suggested
mechanism.31 Four distinct polarization switching trends are identified and
categorized as a function of thickness. Two of these trends yield robust orthogonal
polarization switching for all gold nanorod orientations, while maintaining a high
degree of polarization (DOP) for the output light – important for complete on/off
intensity modulation. Furthermore, we discuss deviations from perfect orthogonal
polarization switching in our devices based on experimental variations in both cell
thickness and LSPR wavelength, and found good agreement between experimental
results and theoretical calculations.
46
4.3. Results and Discussion
4.3.1. Description of Sample Geometry
Figure 4.1a demonstrates the geometry of the experiment, in which the
polarized scattering by the LSPR of single gold nanorods passes through the LC and
then an analyzer before being detected. The scattered light is initially linearly
polarized parallel to the gold nanorod’s long axis. However, the detected
polarization is altered by the birefringence of the LC. Figure 4.1b illustrates this
effect schematically. Light, incident from the left, propagates along the z-direction
with a certain linear polarization, φ, with respect to the microscope reference frame.
It passes through the LC cell and through an analyzer at angle θ to detect the output
polarization φ'. The incident light polarization is given by the physical orientation of
the gold nanorods, which act as randomly orientated dipole antennas.
47
Figure 4.1 – Scattering of individual gold nanorods in a LC device
(a) Scheme of the dark-field microscope where the arrows indicate the path of light,
which is focused onto the sample by a condenser and excites the LSPR of individual
gold nanorods. The LSPR scattering is collected by the objective and then passes
through an analyzer. The upper slide of the sample supports gold nanorods, which
are randomly isolated between photolithographically prepared gold electrodes
(smaller bars). The larger bars represent the 6 µm diameter silica beads that serve
as a spacer. The lower slide supports a PI alignment layer which was rubbed
unidirectionally, with the rubbing direction parallel to the electrodes. (b) Definition
of the coordinate system for a sample placed on the microscope: 1. The light
polarization (synonymous with the orientation of the gold nanorods) traveling
along the z-axis from left to right is given by the angle φ with respect to the x-axis; 2.
The first glass slide of the sample supporting the electrodes; 3. HN LC phase
between the glass slides in the voltage off state with the nematic director parallel to
the x-axis, defined as 0o; 4. Second glass slide supporting the PI layer; 5. Analyzer
orientation at an angle θ measures the polarization φ′ of the output light. (c,d,e,f)
Dark-field scattering images of three gold nanorods detected with the analyzer
angle set to 0 with Voff (c) and Von (d) as well as detected with the analyzer angle set
to 90 with Voff (e) and Von (f). (g) Scattering intensity of a single gold nanorod as a
function of analyzer angle in the isotropic LC phase (open circles), with Voff (solid
circles), and Von (squares). The lines are fits to the data, as discussed in the text.
Reprinted with permission from PCCP.
48
Applying a voltage to our LC devices reorients the LC molecules in the
electrode gaps and changes the LC birefringence and therefore the output
polarization. When observed at a fixed analyzer angle, the scattered light can be
modulated on/off, as can be seen in Figure 4.1c-f, which shows a selected area
where all three gold nanorods display a similar intensity modulation. Here, the left
and right scattering images present the Voff and Von cases, respectively. The white
arrows indicate the angle of the analyzer, which is set to either 0 (Figure 4.1c and
Figure 4.1d) or 90 (e and f). The scattering from the three gold nanorods is 'turned
off' when a voltage is applied, as the recorded intensity transitions from bright (c) to
dark (Figure 4.1d), while the opposite is seen when comparing Figure 4.1e to Figure
4.1f, which are recorded with the orthogonal analyzer orientation. These results
imply that the output polarization is rotated by 90° when applying a voltage. This
orthogonal polarization switching is universal to our LC samples and is independent
of the gold nanorod orientation, i.e. incident polarization, making our devices
unique. In particular, a regular half wave-plate only produces a 90° rotation of the
output light compared to the incident light if the incident polarization is aligned ±
45° with respect to the optical axis.
4.3.2. Theoretical Model Using Jones Calculus
We have previously hypothesized that the voltage-induced orthogonal
polarization switching is due to a transition between a HN and a TN phase of the LC
5CB.31 When a voltage is applied, the LC molecules in the gap between the
electrodes (at plane 2 in Figure 4.1b) are rotated by 90°, while the LC molecules at
49
the opposite device interface (at plane 4) remain aligned in their original orientation
as enforced by the PI rubbing direction. Thus, the LC undergoes a gradual 90° twist
of the nematic director between the two surfaces, which is well known as a TN
phase. This mechanism is based on the fact that the electrode thickness is only tens
of nm, which is much smaller than the overall thickness of the LC cell, typically 5 –
20 micrometers. In this paper, we explore this mechanism and study the effect of
cell thickness on both the HN and TN phases, as well as the difference between these
two phases, corresponding to the experimentally observed polarization change with
applied voltage. In addition, because the output polarization also depends on the
wavelength of the incident light, we analyze the effect of the gold nanorod aspect
ratio polydispersity, which determines the distribution of LSPR wavelength maxima
in our LC devices. Finally, we evaluate the DOP of the output light, as it determines
the intensity contrast for on/off modulation. Only if linear polarization is
maintained for both Voff and Von can we achieve complete on/off switching of the
scattered light intensity in these devices.
Experimentally, the polarization and the DOP of the output light are
determined for Voff and Von by analyzing the intensities of the detected light for each
single gold nanorod as a function of analyzer orientation, 𝜃, from the recorded
scattering images. As an example, Figure 4.1g shows the dependence of the
scattered light intensity for a single gold nanorod as a function of θ for the isotropic
(open circles), Voff (solid circles), and Von (solid squares) states. The measured and
local-background corrected intensity values are fitted to the function I = A cos2(𝜃 -
50
φ′) + c (lines in Figure 4.1g). The output polarization is given by φ′, as the highest
intensity occurs when the analyzer is parallel to the output polarization of the light.
Additional fit parameters include A, the normalization coefficient, and c, the offset.
The DOP is calculated as shown in Equation 4.1 using the maximum and minimum
intensities, Imax and Imin, from the fit. In Equation 4.1, DOP = 100% refers to light
with perfect linear polarization and 0% indicates that the light is either unpolarized
or circularly polarized:
𝐼
DOP = 𝑚𝑎𝑥
−𝐼𝑚𝑖𝑛
𝐼𝑚𝑎𝑥 +𝐼𝑚𝑖𝑛
Equation 4.1 – Degee of polarization
The polarization and DOP of the incident light are determined at the same
time by recording a series of polarized scattering images while the LC is in the
isotropic phase, induced by increasing the lamp power to cause heating of the LC
above its melting point. The isotropic phase is not birefringent and therefore does
not affect the polarization of the light as it passes through the LC cell. Correlated
SEM cannot be used to determine the actual gold nanorod orientation because the
electron beam has an undesirable effect on the alignment of the LC molecules,
presumably because it changes the surface properties of the glass substrate.
Because of the dipole-like scattering from individual gold nanorods, the DOP of the
incident light should be near 100% when the LC is in the isotropic phase. Single gold
nanorods were identified by a DOP equal to or higher than 85% when observed in
the isotropic LC. Small deviations are possible because we measure only in 30°
increments. Using this analysis procedure, the gold nanorod in Figure 4.1g has an
actual orientation of 5°, while its output polarization is 0° without (circles) and 81°
51
with (squares) an applied voltage. Applying a voltage therefore results in a change
of polarization by 81° in the case of this gold nanorod. The output polarizations are
linear as the DOP remains mostly unchanged (99% for Voff and 100% for Von in this
example).
The change in polarization by the birefringent LC depends on the cell
thickness, d, the incident/LSPR wavelength, λ, and the difference in the refractive
indices for the extraordinary and the ordinary axes of the nematic LC, Δn, which is
0.18 for 5CB.41 The phase retardation of the light passing through the LC, defined
as 𝜒 =
2 𝜋 Δ𝑛 𝑑
𝜆
, can be tuned with sample thickness for a certain batch of gold
nanorods having a relatively narrow distribution of LSPR maxima. The thickness of
our samples is determined by the variable size of the silica beads used as spacers to
prepare the LC cell. We find minor variations in thickness across a given cell, but
more significant differences between different samples are observed even though
the same silica beads are used, which we attribute to likely aggregation of the beads.
Therefore, we determine the average thickness of the active area of a sample by
taking an extinction spectrum and analyzing the interference pattern which arises
due to multiple reflections at the glass interfaces of the sample before it is filled with
the LC.171 It should be mentioned that χ is typically used to describe the behaviour of
optical wave plates. If 𝜒 takes an integer value of π a half wavelength retardation of
the incident light occurs between the two orthogonal polarization components
along the extraordinary and ordinary axes of the birefringent material if the incident
polarization is aligned at ± 45° to the optical axis, resulting in a half wave plate
52
behaviour. A quarter wave plate, which turns linearly polarized incident light into
circularly polarized light, is achieved if the value of 𝜒 is a half-integer of π as then
one polarization component is retarded by a quarter of a wavelength compared to
the other, again for linear polarization aligned at ± 45° to the optical axis, which in
the case of nematic LCs is the nematic director.
The first question to answer is how our LC device should behave, if it is
switching, as hypothesized, between well-aligned HN and TN phases, and how that
behaviour depends on the LC thickness. Applying Jones calculus, we therefore
calculate the output polarization for different linearly polarized incident light with
values of χ ranging from 0 to 10π. In doing so, we simultaneously probe the effect of
different thicknesses, the effect of different values of the LSPR maximum
wavelength, and the effect of using any LC, in addition to using 5CB. The transmitted
light intensities for the HN (THN) and TN (TTN) LC phases are calculated using the
following equations, which are functions of incident polarization and analyzer
orientation:7
𝑇𝐻𝑁 = (cos(𝜑) cos(𝜃) + sin(𝜑) sin(𝜃) cos(𝜒))2 + ( sin(𝜑) sin(𝜃) sin(𝜒))2
Equation 4.2 – Transmitted light intensity through HN LC
𝛼
𝛼
𝑇𝑇𝑁 = 𝑐𝑜𝑠 2 (𝜑 − 𝛽) − ( tan(𝛾) − tan(2𝜑)) ( tan(𝛾) + tan(2𝛽)) (𝑐𝑜𝑠 2 (𝛾) cos(2𝜑)cos(2𝛽))
𝛾
𝛾
Equation 4.3 – Transmitted light intensity through TN LC
These equations follow the same convention used earlier, where φ is the
angle of the incident linear polarization and 𝜃 is the angle of the analyzer. Also, β =
𝜒
(φ – α), γ = √𝛼 2 + ( 2 )2, and 𝛼 is the twist angle of the LC director from glass slides 2
53
to 4 in Figure 4.1b. 𝛼 = 90o for an ideally aligned TN LC phase. If the samples are not
perfectly assembled, so that the nematic director is not aligned exactly parallel to
the electrode array, the twist angle 𝛼 is reduced, but with knowledge of the
experimental value of 𝛼, the theoretical data can be adjusted to the same value of 𝛼
in Equation 4.3, to be appropriately compared. To obtain these equations, we use a
Jones vector to describe the electric field vector of the incident light, E:207
E=[
𝑐𝑜𝑠(𝜑)
]
𝑠𝑖𝑛(𝜑)
Equation 4.4 – Electric field vector for incident light
We can also describe the HN (Equation 4.5) or TN (Equation 4.6) LC phase as
a Jones matrix:207
1
MHN = [
0
0
]
𝑒 −𝑖𝜒
Equation 4.5 – Jones matrix for HN LC
𝑖𝛽𝑠𝑖𝑛(𝛾)
MTN =𝑒
−𝑖𝛽
cos(𝛼)
[
sin(𝛼)
− sin(𝛼) cos(𝛾) − 𝛾
][
𝛼𝑠𝑖𝑛(𝛾)
cos(𝛼)
−
𝛾
𝛼𝑠𝑖𝑛(𝛾)
𝛾
𝑐𝑜𝑠𝛾 +
𝑖𝛽𝑠𝑖𝑛(𝛾)
]
𝛾
Equation 4.6 – Jones matrix for TN LC
The electric field vector of the transmitted light, E', can then be calculated by the
following equation:
cos(𝜃)
E′ = [(
sin(𝜃)
−sin(𝜃) 1
)] [
cos(𝜃)
0
cos(𝜃)
0
] [(
0 −sin(𝜃)
sin(𝜃)
)] 𝑀𝐻𝑁,𝑇𝑁 𝐸
cos(𝜃)
Equation 4.7 – Electric field vector for transmitted light
Here, E is manipulated by the matrix describing the LC phase (MHN or MTN), and the
result is passed through an analyzer at angle 𝜃 to obtain E'. The transmitted light
intensity is then calculated by:7
54
2
𝑇 = | 𝐸𝑥′ | + | 𝐸𝑦′ |
2
Equation 4.8 – Generalized transmitted light intensity
These calculations provide theoretical values for the transmitted intensity at
a specific incident polarization, analyzer orientation, and value of χ. By holding φ
constant, we can obtain a series of curves for the transmitted light intensity vs.
analyzer angle, similar to the experimental data discussed in Figure 4.1g. This data
is fitted by the same equation used for the experimental data: I = A cos2(𝜃 -φ′) + c,
yielding the polarization direction of the transmitted light. By repeating this
procedure for incident polarizations varying from 0° to 180° in 1° steps, and values
of χ from 0π to 10π, the output polarizations of the HN and TN phases as well as the
difference between them can be mapped out for any device, as shown in Figure 4.2.
4.3.3. Theoretical Results
The results of these Jones calculus simulations performed in Matlab for the
HN and TN phases, presented in Figure 4.2a and b, illustrate a periodic dependence
of the output polarization on χ, similar to the above discussion on optical wave
plates. In fact, the effect of the HN phase (Figure 4.2a) on linearly polarized incident
light is simply that of either a half wave plate (integer π values of χ) or a quarter
wave plate (half integer π values of χ). Furthermore, odd and even integer π values
are easily distinguishable. At χ = 3π (and also 5π, 7π, and so on), the output
polarization decreases as the incident polarization increases, whereas the trend is
opposite for χ = 4π (and 6π, 8π and so on). Similarly, there are distinctly different
trends for half integer values of χ, namely χ = (3.5, 5.5, 7.5, ...)π and χ = (4.5, 6.5, 8.5,
55
...)π, which form sharp transitions in output polarization between the different
integer π values, as indicated by the sudden change of output polarization from 0o to
180o or 180o to 90o for incident polarizations away from 90o. A similar kind of
periodicity is apparent for the TN phase (Figure 4.2b), except that the TN phase
does not simply function as either a half or quarter wave plate for any value of χ.
From this periodicity in the two phases, we can group the samples into four
categories, which we refer to as χ = 3π, χ = 3.5π, χ = 4π, and χ = 4.5π trends.
56
Figure 4.2 - Simulations of the output polarizations of a LC device as a
function of χ (x-axis) and incident polarization (y-axis)
The output polarization is given by the colour scheme with the scale given to the
right of each panel. (a) HN LC phase (voltage off). (b) TN LC phase (voltage on). (c)
Absolute value of the difference in output polarizations between the HN and TN
phases. The dashed line at χ = 3π for each panel indicates a line section that is also
plotted in Figure 4.3. Reprinted with permission from PCCP.
The difference between the Voff and Von states determines the function of our
LC devices and is shown in Figure 4.2c. Remarkably, this simulation shows that the
57
majority of the parameter space is the same colour, indicating a 90° switching of the
output polarization when applying a voltage, nearly independent of the incident
polarization or the value of χ. This observation implies little dependence on the cell
thickness or wavelength of the incident light, as χ increases with increasing
thickness or decreasing wavelength. However, it would be an oversimplification to
conclude that cell thickness and wavelength do not matter. This is because there are
regions in Figure 4.2c (the points around half integer values of χ) where the
polarization difference is not 90°, but only for half-integer values of χ and
approximately at 45o and 135o incident polarizations. For 0o and 90o incident
polarizations the orthogonal polarization switching is universal and no longer
dependent on the cell thickness or incident wavelength, which we recently exploited
the on/off modulation of a polarized Fano resonance in an asymmetric plasmonic
cluster.77 Figure 4.2b and c clearly show non-periodic trend to the left of the dashed
line, which indicates a minimum value of χ to achieve robust 90 o polarization
switching. If the LC cell is too thin for a given wavelength, then neither component of
the light’s polarization can be sufficiently retarded. χ should have a minimum value
of approximately 3π corresponding to a minimum cell thickness of approximately 6
µm for an average LSPR wavelength of 730 nm.
The four identified trends are more clearly visualized when displayed as
cross sections from Figure 4.2 for a constant value of χ as indicated by the vertical
dashed line at χ = 3π. In Figure 4.3 the output polarization is plotted as thick lines
for the HN (left) and TN (middle) phases as well as the absolute value of the
58
difference between the Von and Voff cases (right) as a function of the incident
polarization for each of the four previously noted values of χ, i.e. χ = 3π (Figure
4.3a), 3.5π (Figure 4.3b), 4π (Figure 4.3c), and 4.5π (Figure 4.3d) clearly shows the
four different trends identified, which, judging by the voltage-induced switching
(right column), can be further split into two groups. These two groups are the
integer π values of χ (Figure 4.3a and c), for which nearly perfect orthogonal
polarization switching is achieved, and the half integer π values of χ (Figure 4.3b
and d), which show deviation from orthogonal polarization switching of the output
light at input polarizations other than 0° or 90°. These line sections suggest that our
LC devices can be optimized for a certain wavelength by choosing cell thicknesses
such that χ takes on an integer π value (Figure 4.3a or c). Figure 4.3a and c differ by
the slope of the output polarization as a function of incident polarization in the HN
and TN phases. Only the trends shown in Figure 4.3a (for χ = 3π) have been
reported previously.31 The χ = 4π case in Figure 4.3c has not been identified before,
but reveals that an equally robust orthogonal polarization switching performance is
possible for cell thicknesses that yield even integer π values of χ.
59
Figure 4.3 –Calculated output polarization of a device switched between HN
and TN LC alignments
Output polarization (thick lines, right y-axis) and DOP (thin lines, left y-axis) as a
function of incident polarization for the four identified trends of our LC device as
obtained from constant χ line sections taken for the data in Figure 4.2. (a) χ = 3π;
(b) χ = 3.5π; (c) χ = 4π; (d) χ = 4.5π. The left column shows the HN phase. The
center column shows the TN phase. The right column shows the absolute value of
the output polarizations for the difference between the HN and TN phases.
Reprinted with permission from PCCP.
Maintaining a high DOP is important to achieve complete on/off intensity
modulation. In Figure 4.3, the calculated DOP of the output light is given by the thin
lines associated with the y-axis scale on the left side for each of the four values of χ,
for the HN (left column) and TN (center column) LC phases. The DOP remains high
for the 3π- and 4π-type devices and displays only small variations as a function of
incident polarization, mostly in the TN phase (Figure 4.3a and c). In contrast, the
DOP of the output light is low in the 3.5π- and 4.5π-type devices near 45o incident
polarization for both HN and TN phases (Figure 4.3b and d). The combination of low
60
DOP and non-orthogonal polarization switching of the output light in these halfinteger of π type devices are less attractive for samples with randomly orientated
gold nanorods as were used in this study. We therefore concentrate for the
remainder of this paper on experimental investigation of a 3π- as well as a 4π-type
device, which has not been observed before. If the proposed mechanism of a HN to
TN transition is valid, then samples prepared with different cell thicknesses should
operate according to the trends predicted by the line sections in Figure 4.3.
4.3.4. Experimental Results
Figure 4.4 shows the experimental data collected from a LC device that
demonstrates the predicted 4π trend. The cell thickness is measured to be 8.5 ± 0.4
µm, which is the average thickness over the whole active area of the sample. Figure
4.4 illustrates the dependence of the output polarization on the gold nanorod
orientation (incident light polarization) for the HN (a) and TN (b) phases as well as
their difference (c). Each coloured symbol in Figure 4.4 represents the output
polarization of a single gold nanorod as a function of its orientation as identified in
the isotropic LC phase, and is associated with error bars representing the average
95% confidence interval for the fits to the gold nanorod orientations and output
polarizations in each subfigure. For simplicity the average error bar is shown for
only one gold nanorod in each panel, but is representative of all data points. The
solid lines represent the expected trends for an ideal 4π-type device. This device
shows mostly 90° polarization switching of the output polarization when an electric
61
field is applied between the interdigitated electrodes. Furthermore, the
experimental data for this sample matches the calculations and in particular the
positive slope associated with the 4π trend is apparent.
62
Figure 4.4 - Experimental characterization of a 4π-type device
(a) Output polarization, plotted as a function of the gold nanorod’s physical
orientation, for the HN LC phase.(b) Same as A for the TN LC phase. (c) Absolute
value of the difference between the HN and TN LC phases for the polarization of the
LSPR scattering from individual gold nanorods. In all panels, the points correspond
to the experimental measurements. The 95% confidence bounds were calculated for
63
each point, and the average bounds for the gold nanorod orientation and output
polarization are plotted for a single experimental point near 90o. The solid lines
represent the trend of an ideal χ = 4π device. The shaded area corresponds to the
expected error based on the possible variations in χ values and is prepared by
varying the cell thicknesses from 8.1 µm to 8.9 µm (0.05 µm intervals) and the LSPR
wavelength from 680 nm to 780 nm (10 nm intervals). Reprinted with permission
from PCCP.
The deviation of the experimental data points from the predicted trends
given by the solid lines in Figure 4.4 can be attributed to non-ideal 4π-type
behaviour and also variations in the local cell thickness and distribution of LSPR
maxima. With a thickness of 8.5 um and an average LSPR wavelength of 730 nm this
sample has an average χ value of 4.19π. To account for all these effects we calculate
the output polarization for a range of χ values, considering LSPR wavelengths
between 680 and 780 nm (10 nm intervals) and LC cell thicknesses from 8.1 µm to
8.9 µm (0.05 µm intervals). All possible values of χ which could arise from the
combination of these two sets of numbers are used in our calculations, and the
resulting output polarizations are plotted for each χ as the dotted lines in Figure 4.4,
effectively creating shaded areas that indicate the expected experimental values for
this sample. Most of the data points fall inside these areas, confirming that the main
sources of error are in fact the local cell thickness and the variation in LSPR
wavelength. It should be noted that the range of possible χ values based on this
error analysis is large enough to include both integer and half-integer trends.
Nevertheless, the characteristics of the device in Figure 4.4 resemble most closely
the predicted positively sloped 4π trend, which has been identified here for the first
time. These results have been verified with several other independent LC samples
64
that have cell thicknesses giving χ ~ 4π.
Figure 4.5 shows experimental results for a 3π-type device. The data points
represent measurements for individual gold nanorods, with the averaged 95%
confidence intervals on the fits shown for one gold nanorod at around 90o, while the
solid lines indicate the trends for an ideal device. The expected experimental
variations are again given by the dotted lines based on a cell thickness of 6.6 ± 0.3
µm. With this cell thickness and an average LSPR wavelength of 730 nm, this sample
has an average χ value of 3.25π. Again the experimental data points for individual
gold nanorods agree well with theory and our previous results.31 Importantly, the
negative slope for the output polarization as a function of gold nanorod orientation
is evident in the data for both HN (Figure 4.5a) and TN (b) LC phases and is
opposite, and hence distinctively different, from the 4π-type device discussed in
Figure 4.4.
65
Figure 4.5 - Experimental characterization of a 3π-type device
(a) Output polarization, plotted as a function of the gold nanorod’s physical
orientation, for the HN LC phase. (b) Same as A for the TN LC phase. (c) Absolute
value of the difference between the HN and TN LC phases for the polarization of the
LSPR scattering from individual gold nanorods. In all panels, the points correspond
to the experimental measurements, the averaged 95% confidence bounds are
66
shown for a single experimental data point near 90o, and the solid lines represent
the trend of an ideal χ = 3π device. The shaded area corresponds to the expected
error based on the possible variations in χ values and is prepared by varying the cell
thicknesses from 6.3 µm to 6.9 µm (0.05 µm intervals) and the LSPR wavelength
from 680 nm to 780 nm (10 nm intervals). Reprinted with permission from PCCP.
In addition to variations in output polarization, the samples discussed in
Figure 4.4 and Figure 4.5 show a reduction in the DOP. In Figure 4.6, we analyze the
DOP for the output light without (HN) and with (TN) an applied voltage for the 3π(Figure 4.6a, b) and 4π-type (c, d) devices as a function gold nanorod orientation.
The solid symbols represent experimental data points, the error bars on points near
90o show the average 95% confidence bounds for the DOP of the fits, the bold solid
lines correspond to the expected DOP values for ideal integer π value devices, and
the dotted lines correspond to the predicted variations within the sample, using the
same average values as discussed for the output polarization in Figure 4.4 and
Figure 4.5. This analysis can account for the deviations of many of the experimental
data points that do not fall within the shaded area. However, not all data points fall
inside the shaded area despite the larger experimental error for determining the
DOP. The model we used based on Jones calculus can account for variations in cell
thickness and LSPR wavelength, but it does not include imperfections in either the
HN and/or TN LC phases. We have also not included the significant line width of the
LSPR resonance (~50 nm) in these calculations. Further deviations from the
predicted trends are therefore likely due to local imperfections of the LC director
alignment, especially as the gold nanorods could create local defects in the
molecular LC order.208 Such LC defects might also be due to imperfect electrodes
67
causing a non-uniform electric field or due to a non-perfect PI alignment layer. In
addition, the lower than predicted values for the DOP make it more difficult to
accurately determine the polarization directions of the LSPR scattering for some
gold nanorods in Figure 4.4 and Figure 4.5. Significant improvements of the LC
device performance are expected to be possible by changing the gold nanorod
preparation and deposition process in order to exploit the more robust switching at
0o and 90o incident polarization. In particular, future experiments will include using
electron-beam lithography to prepare the gold nanorods, providing direct control
over gold nanorod aspect ratio, position, and orientation.
Figure 4.6 - DOP of the output polarization as a function of gold nanorod
orientation in the HN and TN LC phases for the 3π- and 4π-type devices
discussed in Figure 4.4 and Figure 4.5
The data points represent the measured DOP values for single gold nanorods, and
the averaged 95% confidence bounds are shown for a single experimental point in
each panel. The solid lines represent the theoretical DOPs of ideally aligned devices.
(a) 3π-type device in the HN LC phase. (b) 3π-type device in the TN LC phase. (c)
4π-type device in the HN LC phase. (d) 4π-type device in the TN LC phase. The
shaded areas represent the errors in the DOP based on variations in cell thickness
and LSPR maximum. Reprinted with permission from PCCP.
68
4.4. Conclusions
In summary, we have used a combination of simulations based on Jones
calculus and single particle spectroscopy to characterize the active control over the
polarization of light scattered by the LSPR of individual gold nanorods incorporated
into a novel LC device that operates based on an in-plane switching of the LC
director with an interdigitated electrode array. In particular, we have evaluated the
effects of the cell thickness and LSPR maximum on the output polarization in the
voltage off and on states. We have identified four distinct trends, two of which (χ =
3π and χ = 4π) yield highly robust 90o polarization switching while maintaining the
linearity of the transmitted light. The newly identified 4π-type device exhibits
improved DOP of its output signal, compared to the 3π-type device. Deviations of
the experimental data from the models, which assume ideally aligned LC phases, can
be explained by variations in the cell thickness and the distribution of LSPR maxima.
The good agreement between the simulations and the experimental results further
validates our proposed mechanism of a phase transition from a HN to a TN LC
alignment controlled by an external voltage. The unique ability to control the
polarization
from
individual
plasmonic
nanoparticles
will
enable
the
implementation of active plasmonic based components in photonic applications
such as tunable color displays and filters.
69
4.5. Acknowledgements
This work was funded by the Robert A. Welch Foundation (C-1664) and the
Office of Naval Research (N00014-10-0989). JO and DS acknowledge support from
the National Science Foundation through a Graduate Research Fellowship
(0940902), and PS thanks the Royal Thai Government for partial financial support.
70
Chapter 5
Vivid, Full-Color
Aluminum Plasmonic Pixels
5.1. Abstract
Aluminum is earth abundant, low in cost, CMOS manufacturing methods, and
capable of supporting tunable LSPR structures that span the entire visible spectrum.
However, the use of aluminum for color displays has been limited by its intrinsically
broad spectral features. Here we show that vivid, highly polarized, and broadly
tunable color pixels can be produced from periodic patterns of oriented aluminum
nanorods. While the nanorod longitudinal LSPR is largely responsible for pixel color,
far-field diffractive coupling is employed to narrow the plasmon linewidth, enabling
monochromatic coloration and significantly enhancing the far-field scattering
intensity of the individual nanorod elements. The bright coloration can be observed
with p-polarized optical excitation, consistent with the use of this approach in
71
display devices. The resulting color pixels are constructed with a simple design, are
compatible with scalable fabrication methods, and provide contrast ratios of at least
100:1. This work was originally published in the Proceedings of the National
Academy of the Sciences of the United States of America in 2014.32
5.2. Background and Motivation
Display technologies have been evolving towards vivid, full-color flat panel
displays with high resolution and/or small pixel sizes, higher energy efficiency, and
improved benefit/cost ratios. Some of the most popular current technologies are
LCDs, laser phosphor displays, also known as electroluminescent displays, and light
emitting diode LED based displays. A common characteristic of all color display
technologies is the incorporation of various color-producing media, which can be
inorganic, organic or polymeric materials, into the device. These chromatic
materials are chosen to produce the fundamental components of the color spectrum
in additive color schemes such as the standard Red-Green-Blue (sRGB), when
illuminated by an internal light source or when an electrical voltage is applied.
Inorganic chromatic materials have the potential to greatly extend the
durability and lifetime of color displays. Inorganic nanoparticles have recently
begun to be used in color displays in the form of quantum dot LEDs, which have
excellent display lifetimes and industry-scalable size-based and material-based
color.209–211 However, obtaining blue colors from quantum dots has been
challenging212 due to the requirement of synthesizing nanoparticles in the small size
72
range required to achieve optical transitions in this wavelength range. Au
nanoparticles can produce green and red colors based on their LSPRs,143 but shorter
wavelength hues are quenched because of interband transitions for wavelengths
below 520 nm.86 Ag has also been investigated for display applications,142,213 and
while spectral features can be achieved across the visible region, the material
readily oxidizes,179,214 requiring additional passivation layers.
Aluminum is potentially a highly attractive material for plasmon based fullspectrum displays. Aluminum is the third most abundant element in the earth’s
crust, behind silicon, another suitable nanophotonic display material.215 Aluminum
is low in cost, and compatible with mainstream manufacturing processes in the
electronics industry, and CMOS manufacturing in particular.22,136 Aluminum has
recently been identified as a highly promising chromatic material for color filters,
for instance using structures such as hole arrays,137–139 or arrays of aluminum
crosses.140 While the LSPRs of aluminum nanoparticles typically have been studied
in the UV region of the spectrum,216 they can also be tuned into the visible,106,217
exhibiting a similar sensitivity to size and shape as Au and Ag nanoparticles.147,218
The structural tuning of the aluminum LSPR into the visible yields excellent blue
colors, but as the resonance is red shifted across the visible spectrum its linewidth
broadens, primarily due to the interband transition of aluminum that occurs at
nominally 1.5 eV. The increased spectral broadening and damping in aluminum
results in complex and pastel chromaticities, not the vivid monochromatic colors
required by full-color display technologies.
73
In this chapter, we show that aluminum pixels composed of sparse arrays of
aluminum nanorods can be fabricated and provide strong, spectrally narrow, and
vivid colors ideal for full-color LCD displays. By combining the tunable LSPRs of
individual nanorods with diffractive coupling effects, we achieve strong and
sufficiently narrow optical resonances to produce vibrant RGB colors suitable for
additive color displays. The colors appear in p-polarized excitation, consistent with
illumination geometries used in display technologies. We demonstrate this effect
with pixel sizes of 5 μm x 5 μm – two orders of magnitude smaller than the pixel
area in most display technologies. The polarization-selective plasmon resonant
nanorods17,144,183,219 fabricated here represent a first step toward the fabrication of
active LC-based pixels. The enhanced intensities, tunable peak positions, and strong
polarization characteristics of these pixels make them immediately compatible with
LCD-based displays, without the need for color filters or multiple polarizers.
5.3. Results and Discussion
5.3.1. Coupled Dipole Model of Nanorod Arrays
The theoretical calculations are performed using a coupled dipole
model.126,220 Within this approach, the nanorods are described as point dipoles with
anisotropic polarizability 𝛼 = 𝛼xx 𝐱̂𝐱̂ + 𝛼yy 𝐲̂𝐲̂ + 𝛼zz 𝐳̂𝐳̂. This polarizability is obtained
through a finite element method simulation performed using the commercial
software COMSOL Multiphysics. When the ensemble is illuminated with an external
field 𝐄(𝐫), the dipole induced in each nanorod can be written as
74
𝐩𝑖 = 𝛼 (𝐄(𝐫𝑖 ) + ∑ 𝐆𝑖𝑗 𝐩𝑗 ).
𝑗
Equation 5.1 – Induced dipole within each nanorod in a finite array
Here, 𝐆𝑖𝑗 = [𝑘 2 + 𝑛−2 ∇∇] exp(𝑖𝑘𝑛|𝐫𝑖 − 𝐫𝑗 |)⁄|𝐫𝑖 − 𝐫𝑗 | is the dipole-dipole interaction
matrix, 𝐫𝑖 are the vectors with the nanorod positions, 𝑘 is the light wavevector in
vacuum, and 𝑛 is the refractive index surrounding the nanorod ensemble. The selfconsistent induced dipole can be obtained by solving this system of equations as
−1
𝐩𝑖 = ∑ 𝐌𝑖𝑗
𝛼𝐄(𝐫𝑗 ),
𝑗
Equation 5.2 – Self-consistent induced dipole in a finite array
where 𝐌𝑖𝑗 = [𝛿𝑖𝑗 − 𝛼𝐆𝑖𝑗 ]. Finally, the power scattered by the nanorod ensemble is
given by
𝑃=
𝑐𝑛𝑘 4
Re ∑ ∫ 𝑑Ωe𝑖𝑘𝑛(𝐫𝑗−𝐫𝑖 )∙𝐬̂ [𝐩𝑖 ∙ 𝐩∗𝑗 − (𝐩𝑖 ∙ 𝐬̂)(𝐩∗𝑗 ∙ 𝐬̂)].
2𝜋
𝑖,𝑗
Equation 5.3 – Power scattered by a finite array of nanorods
Here, 𝐬̂ is the unit vector in the radial direction, and the angular integral is
performed over the angles compatible with the numerical aperture of the detection
set up.
In order to test the accuracy of the coupled dipole model we have compared
it with the rigorous solution of Maxwell’s equations obtained through finite element
method simulations performed with the COMSOL Multiphysics software. The system
75
chosen for this test consists of an ensemble of 4 nanorods with 𝑙 = 95 nm, 𝑤 =
40 nm, and ℎ = 35 nm, separated by 𝐷𝑥 = 240 nm and 𝐷𝑦 = 290 nm, and embedded
in a medium with a refractive index 𝑛 = 1.55. Notice that this system, contrarily to
the ensembles considered in the main paper, is within the limits of what can be
simulated using finite element method. Figure 5.1 shows the scattering produced by
the ensemble when illuminated at normal incidence with an electric field polarized
along the long axis of the nanorods. The black line represents the results of the
coupled dipole method while the red curve corresponds to finite element method
simulations. As can be seen from Figure 5.1, there is a good agreement between both
methods, especially in the position of the resonance peak.
Scattering (a.u.)
1.2
0.8
0.4
Coupled dipole model
Finite element method
0.0
400
500
600
700
800
Wavelength (nm)
Figure 5.1 – Comparison between the scattering spectrum of a nanoparticle
using two different theoretical methods
The scattering spectrum calculated with the coupled dipole model (black line) and
the corresponding one obtained from the rigorous solution of Maxwell’s equations
with a finite element method simulation (red line). The system studied consists of
an ensemble of 4 nanorods with l = 95 nm, w = 40 nm, and h = 35 nm, separated by
Dx = 240 nm and Dy = 290 nm, and embedded in a medium with a refractive index n =
76
1.55. The incident field is normal to the sample plane and polarized along the long
axis of the nanorods. Reprinted with permission from PNAS.
5.3.2. Sample Design
The aluminum nanorod array-based pixels were prepared using standard
electron beam lithography and metal evaporation techniques on a glass substrate
with a coating of ITO as schematically illustrated in Figure 5.4a. For the pixels
presented in this paper, the ITO thickness is approximately 120 nm, which is too
thin to act as a waveguide. The size of each pixel is 5 μm x 5 μm and consists of a
finite array of nanorods each having the same length, width, height, and edge-toedge spacing. Nanorods were chosen as the repeat unit because their LSPR is
strongly sensitive to changes in the nanorod length, and because their spectral
response is highly polarized in-plane. The use of more symmetric nanoparticles, for
example nanospheres, would yield a much weaker response to in-plane
polarization, even when Dy and Dx are reasonably dissimilar, as shown in Figure 5.2.
In the interest of color tunability, the aluminum nanorod’s length can be set to
control the LSPR, while diffractive coupling can be used to further tune the
response. The nanorods are patterned in an approximately hexagonal arrangement,
as shown in the SEM image in Figure 5.4b, with well-defined periods along the Dx
and Dy directions (Figure 5.4b inset). All nanorods have widths w = 40 nm and
heights h = 35 nm but lengths l varying from 85 nm to 155 nm depending on the
color of the pixel. The values of Dx and Dy were varied from 180 nm to 360 nm, and
from 220 nm to 470 nm, respectively. An approximately hexagonal array was
chosen because this geometry enhances the diffractive far-field coupling.128 The use
77
of different values for Dx and Dy provides an additional enhancement of the
coupling.145,221 Although the aluminum nanorods in a pixel form their own selfterminating oxide layer very quickly after fabrication,172,217,222 the sample is coated
with a 50 to 60 nm thick layer of PI for additional protection against further
oxidation in ambient air, as shown in Figure 5.3.
Figure 5.2 – Calculated scattering spectra of pixels composed of nanorods and
nanospheres
Nanorods were calculated using physical dimensions l = 95 nm, w = 40 nm, and h =
35 nm (a - c) and nanospheres with a diameter of 30 nm (d-f) collecting the
response to either the p-polarized excitation (black) or the s-polarized excitation
(red). Both (a) and (d) have Dy = 290 nm and Dx = 240 nm, representing values for
Dy/Dx found in the main text. The nanorod based pixel demonstrates stronger
response to different polarized excitation than spheres in this Dy/Dx regime. The
same behavior is also seen when Dy = 190 nm and Dx = 990 nm (b, e), and when Dy =
990 nm and Dx = 190 nm (c, f). We conclude that the spheres demonstrate very little
polarization dependence, regardless of the values chosen for Dy and Dx. These
calculations were performed with an average refractive index of n = 1.55, excitation
incident at 53° with p- (black lines) or s- (red lines) polarization. In all cases, the
field intensity is chosen to give the same in-plane amplitude. We assign the strong
polarization dependence to the anisotropic polarizability of the nanorods. Reprinted
with permission from PNAS.
78
Figure 5.3 – Thickness data for both PI and ITO layers of a sample substrate
(a) A section analysis of an atomic force microscope (AFM, Digital Instrument
Nanoscope IIIA) image (b) performed using tools in the AFM software. The AFM
image shows a scratch test of a sample slide with bare ITO on the left side and PI on
the right side. The striations are an effect of the 1st order flattening process
performed on this image using standard AFM software, and therefore two thickness
measurements were performed on the same image, showing similar measurements
of a PI thickness of 50 to 60 nm. AFM surface roughness measurements, provide
average surface roughness values for bare ITO (2.636 nm), PI on ITO (0.636 nm),
and PI on a lithographically prepared pixel (0.984 nm). Coating the plasmonic pixels
with PI hence reduces the surface roughness by 2 to 4 times. This improved
smoothness causes less background scattering and improves the signal to noise
ratio. (c) SEM image showing an edge section of an ITO coated slide with no PI. This
sample was mounted on a 70° tilted sample stage and imaged at 400,000 x
magnification at 10 mm working distance. The ITO thickness is approximately 120
nm, which is too thin to act as an efficient dielectric waveguide to excite the
aluminum pixels. Reprinted with permission from PNAS.
Plasmonic pixels were imaged and spectrally resolved using an inverted
microscope under p-polarized excitation conditions (Figure 5.4c). P-polarized light
was incident on the glass substrate side of the sample, where an equilateral prism
79
was used for coupling incident light into the pixel plane. While diffractive coupling
in nanoparticle arrays typically is studied using normal incidence,133,216,222,223 it can
also be achieved using the off-normal angles of incidence used here.97,145,224–226 Total
internal reflection does not occur at the substrate-PI interface, but at the PI-air
interface, and this allowed for the collection of the extremely low background
images shown in Figure 5.5a. Images were obtained by mounting a digital singlelens reflex (DSLR) camera into the eyepiece of the microscope; spectra were
obtained by directing the signal toward a CCD camera attached to a spectrograph.
80
Figure 5.4 – Design of an aluminum pixel
(a) Schematic showing the unit cell of a pixel. The physical parameters (length l,
width w, height h, and edge-to-edge spacing Γ) of the nanorods in an aluminum pixel
are shown. All nanorods in this study have the same width of 40 nm and height of 35
nm. (b) SEM image of a 5 μm x 5 μm plasmonic pixel with the inset illustrating a
high magnification image of the lower right corner. The unit cell of this design is
81
marked with a white dotted line, defining the periods in the Dx and Dy directions.
Pixel dimensions are: l = 80 nm, w = 40 nm, h = 35 nm, Dx = 270 nm, and Dy = 300
nm. (c) Schematic of the excitation geometry. P-polarized white light is coupled into
the sample using an equilateral triangular prism. The nanorods are excited by ppolarized light, with the light propagating along the yz plane. The PI-air interface has
a critical angle of θc ~ 40°. Reprinted with permission from PNAS.
In each pixel, the individual longitudinal nanorod LSPR, determined by l, is
shifted and enhanced through far-field diffractive coupling which is controlled by Dx
and Dy. As the length of the nanorods decreases (left to right in Figure 5.5a), the
color of the pixels blue shifts, showing a dependence on both nanorod length and
aspect ratio.219,227,228 As the edge-to-edge spacing, roughly Γ = Dx - w = Dy - l, is
increased (top to bottom in Figure 5.5a), the pixel color redshift. The dependence on
edge-to-edge spacing Γ reflects the dependence on Dy and Dx which are the
parameters controlling diffractive coupling. In the diffractive coupling regime, the
individual nanorod plasmon modes interact with the diffractive grating orders
defined by Dx and Dy, resulting in a shifting and narrowing of the resonance and an
increase of its intensity.97,125,128–130,229,230 The PI coating, in addition to protection
against sample degradation, surrounds the pixels with a relatively uniform
refractive index, further enhancing the effects of diffractive coupling.97 Furthermore,
the PI coating makes the substrate smoother, which reduces background scattering.
It is clear from the images in Figure 5.5 that vivid RGB colors can be achieved with
this pixel design and illumination geometry.
82
5.3.3. Experimental Results
Because nanorods, with their highly polarized optical response, are the
fundamental color element of these pixels, the color scattered by the pixels is highly
polarized along the longitudinal axis of the nanorods, yielding contrast ratios on the
order of 100:1. Figure 5.5a shows the 'on state' of an array of different pixels, which
is obtained by placing a polarizer oriented in the y-direction in the detection path of
the microscope. Figure 5.5b shows the 'off state' of the same array, with the
polarizer oriented in the x direction. Contrast ratios have been calculated for each
pixel by selecting the region of one aluminum pixel and adding together the
measured intensity values of the RGB channels. This RGB-based integrated intensity
for the on state is then divided by the integrated intensity for the off state to obtain a
contrast ratio. The average contrast ratio for the pixels shown in Figure 5.5 is 81:1,
though the highest contrast ratio obtained for a single pixel in this sample is 139:1.
Calculations for similar arrays of aluminum nanospheres confirm that sphere-based
pixels do not display the same sensitivity to different incident polarizations as the
present nanorod pixels, as shown in Figure 5.2.
The ratio Dy/Dx of the hexagonal lattice also affects pixel color and intensity.
In Figure 5.5c, an unpolarized, composite image of the pixels imaged in Figure 5.5a
is shown, with the pixels ordered according to nanorod length (vertical axis) and
Dy/Dx (horizontal axis). Higher values of Dy/Dx correspond to increased pixel
brightness. Because diffractive coupling also affects pixel color, different
combinations of nanorod length and Dy/Dx can yield similar colors: for example, the
83
pixels with l = 105 nm, Dy/Dx = 1.25 and l= 135 nm, Dy/Dx = 1.42 are both yellow,
while the pixels with l = 105 nm, Dy/Dx = 1.29 and l = 135, Dy/Dx = 1.50 are both
cyan. A recent study on the plasmonic response of 2D rectangular arrays of Au
nanorods reported that the strongest enhancement of the scattered field with
diffractive coupling occurred for 0.5 < Dy/Dx L< 1.145 Here we find that for aluminum,
larger Dy/Dx values of ~ 1.5 correspond to the strongest diffractive enhancements.
Figure 5.5 – Scattering DSLR camera images of aluminum pixels
(a) Polarized image of an array of 6 by 7 pixels with different nanorod lengths in
each column (varying from 85 nm at the right to 155 nm at the left) and different
values of Γ in each row (varying from 140 nm at the top to 320 nm at the bottom). A
polarizer in the y-direction is present in the detection path, showing the 'on state' of
the pixels. The highlighted pixels display red, green, and blue colorations with
corresponding spectra shown in Figure 5.6. (b) Image of the same region as in (a),
with the polarizer parallel to the x axis, showing the 'off state' of the pixels. (c) An
84
unpolarized, composite DSLR camera image of individual pixels plotted as a function
of Dy/Dx ratio and nanorod length l. Six aluminum pixels were omitted due to
chromatic redundancy. All three images were obtained using a 50x objective with
NA = 0.8, with ISO = 100 (lowest gain setting) and exposure times of 10 seconds (a,
b) and 5 seconds (c). Reprinted with permission from PNAS.
To confirm the overall importance of diffractive coupling, aluminum pixel
patterns were alternatively created with oriented nanorods having random,
aperiodic spacings with the same total number of nanorods as the periodic pixel
design. Some limited color tuning as a function of nanorod density was observed,
but these pixels lacked the strong enhancement observed when pixels are composed
of ordered nanorod arrays. In addition, we image the periodic arrays in Figure 5.4
and Figure 5.5 under direct reflectance where diffractive coupling is suppressed. In
this geometry the pixels here appear dim and with similar colors which now are
determined by the aspect ratio of the individual nanorods and are independent of
Dy/Dx.
The patterning of aluminum nanorods into oriented periodic arrays has three
main effects on the LSPR: 1) a substantial narrowing of the lineshape, overcoming
the intrinsic broadening characteristic of the aluminum dielectric function, 2) an
increase in the intensity of scattered light relative to the additive scattering of an
equal number of oriented but randomly spaced nanorods, and 3) a shifting of the
peak wavelength of the scattered light relative to that of the individual nanorods. To
examine these effects in greater detail, we compare experimental and theoretical
spectra obtained for the three RGB pixels highlighted in Figure 5.5. These pixels
85
were selected because their spectral peak positions correspond to the wavelengths
of standard RGB colors (Red = 635 nm, Green = 535 nm, and Blue = 435 nm).
The top left panel of Figure 5.6a shows the theoretical spectrum of a pixel
with identical physical parameters as the experimental system (solid line),
calculated using a coupled dipole method where the nanorods are described as
point dipoles with a polarizability obtained from finite element method
(COMSOL).126,220 This model is completely described in section 5.3.1. The
unpolarized spectrum of the red pixel (l = 135 nm, Dx = 270 nm, Dy = 360 nm,
containing 234 nanorods), obtained in a p-polarized excitation geometry, are shown
in the top right panel of Figure 5.6a. The experimental spectrum of the red pixel is
scaled to roughly the same peak scattering cross section as the theoretical spectrum,
and subsequent experimental spectra are plotted with scattering cross sections
relative to the experimental red pixel. The middle panels of Figure 5.6a correspond
to the green pixel (l = 95 nm, Dx = 240 nm, Dy = 290 nm, containing 340 nanorods),
and the bottom panels of Figure 5.6a to the blue pixel (l = 85 nm, Dx = 210 nm, Dy =
250 nm, containing 460 nanorods). Experimental spectra for every pixel in Figure
5.5 are plotted in Figure 5.7. Both the lineshape and relative scattering cross
sections of the theoretical spectra agree well with the experimental data. For
comparison, the individual nanorod spectra were also calculated for these
geometries, clearly showing that the spectral peaks and line shapes obtained are
largely controlled by diffractive coupling effects. While the pixel spectra show far
narrower line shapes than the individual nanorods, they are not as narrow as those
86
observed for square arrays of nanospheres or nanodisks.231,232 All simulations were
performed using experimental (non-adjustable) structural parameters. The incident
angle in the calculation was adjusted to 53° to account for the light passing through
the prism, silicon dioxide, ITO, and PI interfaces. The slight deviation from the
nominal 60° incident angle is consistent with the angular uncertainty of the incident
beam in the experimental setup.
87
Figure 5.6 - Unpolarized experimental and theoretical spectra of the
aluminum pixels from Figure 5.5, and corresponding chromaticity
calculations.
(a) Unpolarized theoretical (left) and
experimental (right) spectra. Top left panel
shows a theoretical spectrum of an aluminum pixel (solid line) with parameters : l =
135 nm, Dx = 270 nm, Dy = 360 nm. For comparison, a single nanorod spectrum
(dotted line) with l = 135 nm is shown. Top right panel shows the experimental
spectrum of a nanorod pixel with the same physical parameters (l = 135 nm, Dx =
270 nm, Dy = 360 nm). Middle panels show the same as the top two panels for the
green pixel with l = 95 nm, Dx = 240 nm, and Dy = 290 nm. The bottom two panels
show the same for the blue pixel with l = 85 nm, Dx = 210 nm, and Dy = 250 nm. (b)
Apparent colors of the theoretical individual nanorods (left) and pixel array
(middle) spectra when analyzed with the CIE 1931 color matching functions
compared to observed colors from experimental pixels (right). (c) CIE 1931
chromaticity diagram overlaid with the sRGB gamut outlined in gray, single nanorod
colors (circles) and pixel array colors (squares). The square for the blue pixel array
lies outside of the sRGB gamut. While it can be perceived by the human eye, it is
beyond the display range of standard display technologies. Reprinted with
permission from PNAS.
88
Figure 5.7 – Dark field spectra of all pixels shown in Figure 5.5
Seven pixels, with variable Dx and Dy, were prepared for each nanorod length. (a)
image of all 49 pixels, with lengths: (b) l = 155 nm, (c) l = 135 nm, (d) l = 105 nm,
(e) l = 95 nm, (f) l = 90 nm, (g) l = 85 nm. Indices 1 through 7 refer to Γ = 140 nm,
170 nm, 200 nm, 230 nm, 260 nm, 290 nm, and 320 nm, respectively. All spectra
were taken with an integration time of 40 seconds, and corrected by subtracting
89
background and dividing by a transmission spectrum of the excitation lamp. The full
spectrum from 430 nm to 800 nm is presented here. Importantly, the noise
increases on the left side of the spectra, toward 400 nm, primarily because of the
low lamp intensity in this region, though the efficiency of the detector is also
reduced in this region compared to longer wavelengths. Reprinted with permission
from PNAS.
The simulations shown in Figure 5.6a convincingly illustrate the effects of
diffractive coupling by comparing theoretical spectra for individual aluminum pixels
(solid lines) with individual aluminum nanorods (dotted lines). For the green pixel
(Figure 5.6a, middle panels), diffractive coupling blue-shifts the peak wavelength of
the pixel by ~ 35 nm relative to the single nanorod scattering spectrum, and
narrows the linewidth by over 100 nm. The scattering cross section of the aluminum
pixel consisting of 340 nanorods exceeds that of the sum of 340 isolated, noninteracting nanorods, making the observed enhancement of the scattering cross
section due to diffractive coupling a synergistic effect. By convolving the theoretical
individual nanorod and pixel array spectra with the CIE 1931 color matching
functions the apparent color of the two systems can be compared (Figure 5.6b). In
the case of an individual nanorod, the relatively large linewidth of the longitudinal
resonance results in a weak pastel color. The color determined by the peak
wavelength for each nanorod is muted by the contributions from the broad range of
wavelengths within the envelope of the resonance, making the perceived color more
pastel. The narrow spectral peak created by the pixel configuration minimizes the
contributions from these additional wavelengths, producing a much purer color.
These pixel colors are verified by imaging the corresponding experimental arrays
with a DSLR camera. In Figure 5.6c, the color of each single nanorod and array pixel
90
is plotted on the CIE 1931 chromaticity diagram labeled with the limits of the sRGB
color gamut. The colors of the single red, green, and blue nanorods (circles) are
weak pastels and bunch around the white point because of their broad linewidths.
The pure color of the pixel arrays (squares) lie far away from the white point
toward the limits of the sRGB gamut. The color of the blue pixel actually lies outside
the sRGB gamut, meaning it has such a saturated color that it cannot be duplicated
by standard display technologies. The spectrum of the green pixel is used as a
starting point (l = 95 nm, Dx = 240 nm, and Dy = 290 nm; circles and solid line). (A)
Pixel spectra with Dx = 240 nm and Dy = 290 nm
Both the experimental and theoretical spectra for the pixels shown in Figure
5.6 have asymmetric line shapes, which are controlled by specific combinations of
the nanorod length l, Dy, and Dx. Here we focus on the green pixel (Figure 5.6a,
middle) and examine the origin of this unusual lineshape by varying l, Dy, and Dx
independently (Figure 5.8). Changing only the nanorod length from 60 nm
(diamonds) to 120 nm (stars) while maintaining a constant array spacing (Figure
5.8a), we find that the spectral maxima initially red-shift as the nanorod length
increases. However, once a resonance wavelength of nominally 560 nm is reached,
no further shifts occur and the intensity decreases, with no observable plasmon
response beyond a cutoff wavelength of 600 nm. If instead Dx is varied from 180 nm
(diamonds) to 300 nm (stars) with constant values for l and Dy (Figure 5.8b), the
same general trend is seen with a similar cutoff wavelength as in Figure 5.8a, but the
intensity drop is significantly more pronounced. This larger intensity decrease is
91
due in part by the decrease in the number of nanorods when the periodicity is
increased for a constant pixel area (357 for Dx = 180 nm to 294 for Dx = 300 nm).
A much stronger effect is apparent when varying Dy (Figure 5.8c). This is
because for p-polarized light, the cutoff wavelength is controlled by Dy. Only
wavelengths on the blue side of the cutoff are diffracted at collection angles over
which constructive interference of the nanorod-scattered light occurs. As Dy is
increased (Figure 5.8c), the cutoff wavelength red shifts by approximately 60 nm for
every 30 nm increment of Dy. This behavior arises because the nanorods are excited
at an incident angle 𝜃i, and the scattered light is collected with a maximum collection
angle 𝜃o, defined by the NA of the collection objective. This geometry introduces a
phase difference in the light scattered from nanorods at different y positions, and
defines a maximum wavelength λmax above which no constructive interference can
occur:
𝜆𝑚𝑎𝑥 = 𝐷𝑦 𝑛(𝑠𝑖𝑛𝜃𝑖 + 𝑠𝑖𝑛𝜃𝑜 )
Equation 5.4 – Maximum wavelength exhibiting constructive
interference
Here, n is the refractive index, for which we assume an average value of n = 1.55,
because the nanorods are on an ITO coated glass substrate (n = 1.50) and
surrounded by PI (n = 1.65). Therefore, for pixels with Dy = 350 nm, 320 nm, 290
nm, 260 nm, and 230 nm, the λmax should occur at 704 nm, 644 nm, 583 nm, 523 nm,
and 462 nm, respectively. These values are in good agreement with the spectra in
92
Figure 5.8c, despite the fact that this simple equation assumes an infinite array of
nanorods, while the calculations are performed on a finite area. Larger arrays
approaching the infinite limit will produce a sharper intensity drop-off at the cutoff
wavelength, while smaller arrays will reduce the intensity more gradually.
93
Figure 5.8 – Simulations of pixel spectra with l, Dx, and Dy varied individually
(a) Pixel spectra with Dx = 240 and Dy = 290 nm held constant, while varying the
nanorod length, l = 60 nm (diamonds), 80 nm (squares), 95 nm (circles), 110 nm
94
(triangles), and 120 nm (stars). (b) Pixel spectra with l = 95 nm and Dy = 290 nm
held constant with Dx varying from 180 nm (diamonds), 210 nm (squares), 240 nm
(circles), 270 nm (triangles), to 300 nm (stars). (c) Pixel spectra with l = 95 nm and
Dx = 240 nm held constant with Dy varying from 350 nm (diamonds), 320 nm
(squares), 290 nm (circles), 260 nm (triangles), to 230 nm (stars). Reprinted with
permission from PNAS.
The wavelength cutoff (through its dependence on Dy) provides an excellent
tuning knob for controlling and fine tuning RGB colors and their intensities.
However, also the incident angle 𝜃i and maximum collection angle 𝜃o play a role.
These angles are related to the refractive index n, which determines the critical
angle for total internal reflection 𝜃c. The critical angle 𝜃c is approximately 40° for the
PI/air interface, and determines the maximum collection angle, i.e. 𝜃o ≤ 𝜃c, as well as
the minimum incident angle, i.e. 𝜃i ≥ 𝜃c. The maximum collection angle in this study,
limited by the objective, is close to the critical angle, as NA = 0.8 corresponds to a
30° angle. Objectives with different NAs can yield slightly different results,
according to Equation 5.4. Additionally, the use of a diffuser in front of the pixel
sufficiently mixes all diffracted angles, and makes these pixels capable of providing a
more spatially uniform viewing experience, as is discussed further in section 6.3.
Furthermore, the power scattered by the pixel can be easily calculated by taking the
product of the scattering cross section and the incident intensity, though an
experimental demonstration of this measurement is presented in section 6.3 as well.
95
5.4. Conclusions
Our results demonstrate that highly polarized, vivid colors in the visible
spectrum can be designed by arranging aluminum nanorods into well-ordered finite
arrays termed plasmonic pixels. The colors of these pixels are determined by
diffractive coupling and are tunable through a combination of nanorod length l, Dx,
and Dy, resulting in bright, vivid RGB pixels compatible with additive color schemes.
Because of the use of nanorods as the basic component, the signal is strongly
polarized, making these aluminum plasmonic pixels compatible with LC switching
technology.30,31,77 Additionally, careful choices of medium refractive index can be
used to tune both the single nanorod LSPR and the critical angle for total internal
reflection, which in turn affects the incident and collection angles 𝜃i and 𝜃o. For
display purposes, a viewing-angle dependent signal would be problematic but could
be remedied by placing a diffusing layer on top of the pixel layer. Although the
standard electron beam lithography methods used in this work are not currently
scalable to industrial requirements, nanorods of similar sizes have been produced
by extreme UV lithography147 which utilizes an interference mask, a coherent light
source, and otherwise standard lithography techniques. This combination of highly
tunable, vibrant RGB colors, a highly polarized response, and potential industrial
scalability suggests that the aluminum plasmonic pixel is a promising platform for
future display technologies in the not-so-distant future.
96
5.5. Acknowledgements
This work was funded by the Robert A. Welch Foundation (Grants C-1220, C1222, and C-1664) and the Office of Naval Research (N00014-10-0989). A. M.
acknowledges financial support from the Welch foundation through the J. Evans
Attwell-Welch Postdoctoral Fellowship Program of the Smalley Institute of Rice
University (Grant No. L-C-004). J. O. acknowledges support from the National
Science Foundation through a Graduate Research Fellowship (0940902).
97
Chapter 6
Enhanced Chromaticity in LCDCompatible Aluminum Plasmonic
Pixels
6.1. Abstract
Colorants and filters based on nanomaterials have benefitted significantly
from the addition of aluminum as a viable plasmonic material, producing colors that
span the visible region while remaining cost effective and compatible with the
semiconductor industry. The range of colors produced by aluminum displays based
on arrays of nanoparticles has been mostly muted and pigment-like because of the
reliance on the single nanoparticle LSPR, which is size and shape tunable but heavily
damped in the visible region. In this work, we present a series of rationally designed
aluminum plasmonic pixels capable of producing far more vibrant colors than have
been previously reported. These pixels are based on orientated nanorods with
98
highly polarized resonances and take advantage of the spectrum enhancing effects
caused by diffractive coupling. With optimized pixel parameters, we are able to
produce color gamuts with 100% of the number of colors of a standard color
definition display, with enhanced definition in the blue-green colors, as evidenced
by dark field microscopy measurements and calculations using a coupled dipole
model. The same pixels are also shown to be compatible with alternative excitation
geometries, switchable liquid crystal displays, and their sizes can be scaled up from
1 μm to greater than 1 mm without significant changes to the pixel color. This work
is in preparation for publication.
6.2. Background and Motivation
Metal nanostructure-based color production has become an increasingly
popular subject of research, aided by the spectral selectivity of the LSPR.233 The
plasmon resonance is a collective oscillation of the conduction band electrons, and is
highly sensitive to the shape, size, and material of the nanostructure.234–236
Semiconducting quantum dots have already been incorporated into existing
television displays because of their spectral tenability with size based on quantum
confinement,211,212but entirely new kinds of plasmonics-based color selectivity are
also being developed. Plasmonic gold,143 silver,29,142,213 and aluminum17,135,136,144,237
have all been demonstrated as very promising display materials. Aluminum
especially has increased in popularity because its plasmon resonance is tunable
across entire visible wavelength range and it is furthermore compatible with CMOS
99
manufacturing techniques.22,136 This CMOS compatibility, along with its much lower
cost among plasmonic materials, makes aluminum particularly versatile for various
technological applications, including incorporation into solar cells27,238 and as filters
for color imaging.138,139,239–241
Typically, the grouping of nanostructures into an array of finite size is
referred to as a plasmonic pixel.22,140,143 The introduction of more complicated
design choices beyond disk-shaped nanostructures and square arrays excited with
normal incident light, as utilized in most previous studies,142–144 can provide
significant benefits. Examples include incorporation of Fabry-Perot resonances
either within individual annular rings in an array240 or between layers of silver
metal with no structural patterning at all.239 The crystallinity of the aluminum itself
can also have a drastic effect on the material’s color.242 Even while maintaining a
simpler layout, differently shaped structural elements or the use of hexagonal as
opposed to square arrays provide additional parameters for designing color
filters.137,243 Stretchable substrates121,244 or liquid crystals245 can even contribute to
active control over the color of an array of nanoparticles. Taking advantage of
diffractive coupling, we have previously shown how specifically designed arrays of
aluminum nanorods can create resonances that are narrower than previously
reported32 and hence result in more vivid colors. Importantly, because of the
anisotropic nanorod shape the color generated by these aluminum pixels is strongly
polarized, providing a potential active color control mechanism if it could be
incorporated into a LCD.
100
Display technologies seek to improve resolution via smaller pixel size. In
principle, a single nanoparticle could constitute a pixel. The scalability from these
single plasmonic pixels to a full display is still a major obstacle for nanofabrication
because of the small individual feature sizes necessary. The use of aluminum as the
plasmonic material, rather than gold or silver, drastically reduces materials costs of
a large-scale product, especially in high metal-content designs. To produce largescale displays, a fabrication technique other than the serialized e-beam lithography
must be considered. Interference lithography using lasers141,149,246 or UV light147,148
are viable options, as well as nanoimprint lithography.150,151,153,245,247–249 The
smallest feature sizes achievable with these methods are approximately 10 - 40 nm.
In addition to scaling up to macroscopic devices, displays based on plasmonic
pixels can even more readily be scaled down to dimensions where nanotechnology
is already at home. Nano-barcodes have been introduced and included random
groupings
of
nanowires,23,250
phase-changing
nanoparticles,251
multi-metal
microrods,252 and biomimetic silica-coated polymer fingerprints,253 just to name a
few examples. The fabrication process for nano-barcodes must be either
randomizable for individual product tracking, or sufficiently reproducible for
repeated labeling. While scale-up to a macroscopic display is less of a problem for
nano-barcodes, color control via reproducible, sharp plasmon resonance at the
individual pixel level is still important. Interestingly, although many different
nanotechnology-based approaches have been applied to either displays or nano-
101
barcodes, few have demonstrated the necessary versatility to be applied to both
large- and small-scale applications.
In this work, we show how an array of aluminum nanorods can produce
rationally designed vivid color pixels, and that the size of these pixels can range
from 1 micron up to at least several millimeters without significant changes to their
spectrum. The rational color design of these pixels relies both on the single nanorod
plasmon resonance, and on the inter-rod spacings in two directions within the
array, thereby enabling diffractive coupling and supporting additional Fano
resonances. Because the plasmonic pixels described here consist of parallel
nanorods, the polarization sensitivity of the single nanorod plasmon is transferred
to the whole pixel, as we demonstrate by incorporating a set of red, green, and blue
pixels into a liquid crystal display (LCD) and modulating their intensity on/off via an
applied voltage. Furthermore, although electron beam lithography produces
variations in the dimensions of the nanorods within a pixel, we find that the
variation from pixel to pixel is reduced for pixels containing as few as 9-nanorods.
6.3. Results and discussion
6.3.1. Theoretical Model
The model for a finite array of nanorods is the same as provided in section
5.3.1, and is explained again here for convenience. Theoretical calculations for this
work are performed using a coupled dipole model126,170,220,254. We describe the
102
nanorods as point dipoles with an anisotropic polarizability = 𝛼xx 𝐱̂𝐱̂ + 𝛼yy 𝐲̂𝐲̂ +
𝛼zz 𝐳̂𝐳̂ , which we obtain from a finite element method simulation performed using
the commercial software COMSOL Multiphysics. Upon illumination with an external
field, the dipole induced in each nanorod can be written as in Equation 5.1:
𝐩𝑖 = 𝛂 (𝐄(𝐫𝑖 ) + ∑ 𝐆𝑖𝑗 𝐩𝑗 ),
𝑗
Equation 5.1 – Induced dipole within each nanorod in a finite array
where 𝐆𝑖𝑗 = [𝑘 2 + 𝑛−2 ∇∇] exp(𝑖𝑘𝑛|𝐫𝑖 − 𝐫𝑗 |)⁄|𝐫𝑖 − 𝐫𝑗 | is the dipole-dipole interaction
tensor, 𝐫𝑖 are the vectors with the nanorod positions, 𝐄(𝐫) = 𝐄𝟎 𝑒 𝑖𝑛𝐤·𝐫 is the external
field with amplitude 𝐄𝟎 , 𝐤 is the light wavevector in vacuum, and 𝑛 is the refractive
index of the medium surrounding the nanorod array. The self-consistent induced
dipole can be obtained by solving this system of equations as in Equation 5.2:
−𝟏
𝐩𝒊 = ∑[𝜹𝒊𝒋 − 𝛂𝐆𝒊𝒋 ] 𝜶𝐄(𝐫𝒋 ),
𝒋
Equation 5.2 – Self-consistent induced dipole
Once the induced dipole is known, the power scattered by the array is given by
𝑃=
𝑐𝑛𝑘 4
Re ∑ ∫ 𝑑Ωe𝑖𝑘𝑛(𝐫𝑗−𝐫𝑖 )∙𝐬̂ [𝐩𝑖 ∙ 𝐩∗𝑗 − (𝐩𝑖 ∙ 𝐬̂)(𝐩∗𝑗 ∙ 𝐬̂)].
2𝜋
𝑖,𝑗
Equation 5.3 – Power scattered by a finite array of nanorods
103
Here, 𝐬̂ is the unit vector in the direction of emission, and the angular integral is
performed over the angles compatible with the numerical aperture of the detection
setup.
In addition to the finite array just described, we also study the case of an
infinite array to obtain deeper insight into the behavior of the plasmonic pixel.
Calculations for an infinite array require a slightly different approach. Specifically,
we write the dipole induced in each nanorod as
𝐩𝑖 = 𝐩𝐤∥ 𝑒 𝑖𝐤∥ ·𝐑𝑖 ,
Equation 6.1 – Induced dipole in each nanorod in an infinite array
where 𝐤 ∥ is the component of the wave vector of the incident field parallel to the
array, and 𝐑 𝑖 = (𝑥𝑖 , 𝑦𝑖 ) is the nanorod position on the array plane. Using this
expression, the dipole amplitude can be written as
𝐩𝐤∥ = 𝛂𝐄𝟎 + 𝛂𝓰(𝐤 ∥ )𝐩𝐤∥
Equation 6.2 – Dipole amplitude for an infinite array
where 𝓰(𝐤 ∥ ) = ∑𝑗≠𝑖 𝐆𝑖𝑗 𝑒 −𝑖𝐤∥ ·(𝐑𝑖 −𝐑𝑗) . This quantity, which is commonly known as the
lattice sum, contains the information of the response of the array and therefore
determines the existence and properties of the lattice resonances126,220,254. Indeed, a
lattice resonance exists whenever 𝓰(𝐤 ∥ ) diverges. The wavelength at which this
resonance condition happens is given by Equation 6.3.
104
𝜆 = 2𝜋𝑛/|𝐤 || − 𝐠|
Equation 6.3 – Wavelength of the lattice resonance
Here, 𝐤 || is the component of the wave vector of the incident light parallel to the
array plane, and 𝐠 is a reciprocal lattice vector. In this chapter, we will particularly
exploit the Fano dip associated with the reciprocal lattice vector:
𝐠 (1,0) = (2𝜋/𝐷𝑥 )𝐱̂ − (𝜋/𝐷𝑦 )𝐲̂
Equation 6.4 – Reciprocal lattice vector for (1,0) lattice resonance
Here, the unit vectors 𝐱̂ and 𝐲̂ lie parallel to the nanorods’ short and long axes,
respectively. In our particular geometry these vectors can be obtained from the
generalized version of Equation 6.4:
𝑖
𝑗
𝑖
𝐠 (𝑖,𝑗) = 2𝜋 [ 𝐱̂ + ( −
) 𝐲̂],
𝐷𝑥
𝐷𝑥 2𝐷𝑦
Equation 6.5 – General equation for the reciprocal lattice vector
and therefore the wavelength of the lattice resonances are
𝛌(𝑖,𝑗) =
−𝑏 + √𝑏 2 − 4𝑎𝑐
,
2𝑎
Equation 6.6 – Wavelength at which lattice resonance (i,j) occurs
with
a=
𝑖2
𝑗2
𝑖2
𝑖𝑗
+
+
+ 2,
2
2
2
𝐷𝑥 𝐷𝑦 4𝐷𝑦 𝐷𝑦
𝑖
𝑗
𝑖
b = −2𝑛sin𝜃𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 ( cos𝜙𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 +
sin𝜙𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 +
sin𝜙𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 ),
𝐷𝑥
𝐷𝑦
2𝐷𝑥
105
𝑐 = −𝑛2 cos 2 𝜃𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡
Equation 6.7 – Geometry dependent parameters for Equation 6.6
Finally, to calculate the scattering spectrum we solve the equation for the
dipole amplitude 𝐩𝐤∥ . This can be done as follows
𝐩𝐤∥ = [1 − 𝛂𝓰(𝐤 ∥ )]−1 𝛂𝐄𝟎 .
Equation 6.8 – Dipole amplitude for an infinite array reorganized
Once the induced dipole is known, the power scattered per nanorod is given by
𝑃 2𝜋𝑐 2
2
2
=
𝑘 ∑ [|𝐩𝐤∥ | − |𝐬̂ · 𝐩𝐤∥ | ],
𝑁
𝐴𝑛
𝐠
Equation 6.9 – Power scattered per nanorod in an infinite array
where 𝐴 is the area of the unit cell and the summation runs over reciprocal lattice
vectors for which 𝐬̂ = (𝐬̂∥ , 𝐬̂⊥ ) with 𝐬̂∥ = (𝐤 ∥ − 𝐠)⁄𝑛𝑘 , lies within the collection cone.
6.3.2. Experimental Results
The vivid colors generated by the plasmonic pixels described in this work are
produced by light scattering from an approximately hexagonal array of same-size,
co-oriented aluminum nanorods, as shown in Figure 6.1. The color-defining physical
parameters for each pixel are the distance between rows of nanorods in the y
direction (Dy), the distance between nanorods along the x direction (Dx), as well as
the length (l) and width (w) of each nanorod (Figure 6.1a top view). The height of
the nanorods is 35 nm for all pixels, and all nanorod widths are designed to be 40
nm for compatibility with scalable fabrication methods, such as nanoimprint
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lithography or EUV lithography. All samples are prepared via standard e-beam
lithography on an ITO coated glass substrate, followed by spin coating with a layer
of PI, as shown in the main portion of Figure 6.1a. After fabrication, the pixels are
then spectrally characterized using dark field excitation with p-polarized light that
is orientated along the nanorods’ long axes.
Figure 6.1 – Plasmonic pixel scheme
(a), Inset: top down view of the layout of a plasmonic pixel, indicating the length (l)
and width (w) of the nanorods and also the inter-rod (Dx) and inter-row (Dy)
spacing. The main panel of (a) shows the same pixel on an ITO-coated silica
substrate prepared via electron beam fabrication and then overcoated with a thin
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layer of PI. This sample is excited via p-polarized light in the pixel plane at an angle
of 53° normal to the glass surface, and the scattered light is collected from the top
surface of the sample. (b), (c), and (d) show high-resolution SEM images of a red (l =
153, Dx = 256, Dy = 410), green (l = 88.5, Dx = 272, Dy = 272), and blue (l = 81, Dx =
118, Dy = 227) pixel, respectively, with marker bars indicating 250 nm. The insets
show the color created by a pixel of dimensions shown in each respective SEM
image. All physical dimensions are in nm.
In general, longer nanorods and larger inter-rod distances produce redder
colors, while shorter nanorods and smaller inter-rod distances produce bluer colors.
Each individual pixel is designed to cover a footprint of 5 μm x 5 μm, unless
otherwise stated. Figure 6.1b is an SEM image showing a 1 μm region of a red pixel,
with nanorod length l = 153 nm, Dx = 256 nm, and Dy = 410 nm. The color produced
by this combination of physical parameters is orange-red (inset of Figure 6.1b),
when measured using the dark field microscope setup described in section 3.3.2.
Corresponding images for a green pixel (l = 89 nm, Dx = 202 nm, Dy = 272 nm) and a
blue pixel (l = 81 nm, Dx = 118 nm, Dy = 227 nm) are given in Figure 6.1c and Figure
6.1d, respectively.
The color of a plasmonic pixel is rationally designed through theoretical
considerations and simulated spectra based on the coupled dipole model, where all
physical parameters of the experiment are explicitly considered (see section 6.3.1
for further details). This rational design process begins with the selection of a
desired color and spectral shape, followed by optimization of Dy to produce an
appropriate threshold on the red side of the spectrum. Each pixel can be
approximated by an array of point dipoles, and therefore behaves analogously to a
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grating that is excited at a non-normal angle of incidence by a spectrum of light. The
threshold on the red side of the spectrum can then be described by Equation 5.4,
which is reprinted here for convenience:32
𝜆𝑚𝑎𝑥 = 𝐷𝑦 𝑛(𝑠𝑖𝑛𝜃𝑖 + 𝑠𝑖𝑛𝜃𝑜 )
Equation 5.4 – Maximum wavelength exhibiting constructive
interference
Again, λmax is the maximum wavelength above which no constructive
interference for the scattering by the pixel can be observed. The average refractive
index n is 1.55, 𝜃i is the angle at which the light is incident on the pixels, and 𝜃o is the
half-angle of the objective collecting the light. The incident light is coupled into the
sample using a 60° prism, and passes through the layers of glass, ITO, and PI, and
therefore 𝜃i = 53° inside the PI where the pixel is located, based on Snell’s law. For
an objective with NA = 0.8, the observation angle is 30° inside the PI. These
excitation and collection conditions apply for all spectra and images that are
reported here for measurements taken with a dark field microscope, and are
directly considered in the corresponding calculations. Figure 6.2a shows a series of
simulated spectra for pixels with l = 85 nm and Dx = 280 nm as Dy is increased from
200 nm through 340 nm, with the dashed line indicating the calculated location of
λmax based on Equation 5.4 for each simulated spectrum. The analytical expression
(Equation 5.4) and the simulated spectra are in excellent agreement, and
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demonstrate that the threshold wavelength, above which destructive interference
suppresses scattering into the far field, increases linearly with Dy.
Figure 6.2 – Theoretical basis for the three-step color design method
Calculated spectra are shown with intensity (color) as a function of wavelength
(vertical axis). (a), A series of spectra plotted as a function of Dy varying over 200
nm to 340 nm in 10 nm increments. The dashed line shows the positive linear
relationship between the diffractive coupling threshold and the value of Dy,
according to eq. (1). (b), A series of spectra plotted as a function of Dx varying over
200 nm to 340 nm in 10 nm increments. The dashed line shows the positive linear
relationship between the (1,0) grating resonance and the value of Dx, with Dy held
constant, according to Equation 6.4. (c), A series of spectra plotted as a function of
nanorod length varying over 60 to 135 nm in 5 nm increments. The dashed line
shows the relationship between the pixel peak intensity and the length of the
nanorod.
The second step in the rational design of the plasmonic pixel color is to select
Dx such that the combination of Dx and Dy together will produce one or more Fano
resonances in the spectrum at desirable locations. In the simplest case, the spectral
intensity dip associated with these resonances will act as a threshold on the blue
side of the scattering spectrum. These Fano resonances are a known
phenomenon220,254,255, which originate from the coupling between the broad dipole
resonance of the single nanorod and the sharp lattice resonances of the array.
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Therefore, we can choose the spectral positions of the different Fano dips by
selecting the appropriate wavelength of the corresponding lattice resonances, which
are given by Equation 6.3.
Figure 6.2b shows simulated spectra as Dx varies from 200 nm to 340 nm for
pixels with constant values of l = 85 nm, and Dy = 280 nm. The dashed line indicates
the position of the (1,0) lattice resonance calculated with Equation 6.4. A linear redshift with Dx is clearly visible from both simulated spectra and Equation 6.4. Pixel
colors can certainly be designed without the deliberate incorporation of the Fano
resonance to improve color control. However, care should still be taken to choose Dx
such that no lattice resonances overlap the intended spectrum, leading to undesired
Fano dips within the main resonance responsible for the color of the pixel.
The third step in the rational design of a plasmonic pixel is to select a
nanorod aspect ratio that will produce a peak in the pixel’s spectrum at the desired
location between the two thresholds imposed by Dy and Dx. The simulated spectra in
Figure 6.2c show how the peak intensity of a pixel with Dx = 280 nm, Dy = 280 nm
redshift with increasing nanorod length, as indicated by the dashed line. Rather than
continuing to increase, however, the wavelength of the peak intensity is limited by
the threshold imposed by Dy. In particular for these pixels, the redshift ceases at
approximately l = 85 nm, caused by the red-wavelength threshold at 563 nm
imposed by Dy. As the nanorod length is further increased, the scattering intensity is
reduced.
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This 3-step rational design method leads to intensely vivid colors that span
the whole visible region, as shown in Figure 6.3. The colors and spectra reported in
Figure 6.3 originate from scattering by 5 μm x 5 μm plasmonic pixels with optimized
structural parameters, recorded under dark field excitation in an optical microscope
(more details in section 3.3). In Figure 6.3a, a color space diagram, based on the
1931 CIE standard observer, illustrates the range of colors visible to the human eye
inside the colored region. The curved axis indicates the wavelengths in nm that
correspond to each color, where the most vivid colors lie along the edge of the graph
while pastel colors lie closer to the white point at (0.33,0.33). The white triangles
represent the red, green, and blue tristimulus values common to all sRGB displays.
The white line connecting the sRGB values encloses the sRGB color gamut, the area
of which correlates to the number of colors that can be produced by such a display.
Standard displays incorporate only red, green, and blue pixels while all other
displayed colors result from the summation of these three colors in different
amounts. The three white squares that are circled in Figure 6.3a represent colors
produced by aluminum pixels where the rational design goal has been to generate
colors comparable to the sRGB values. The colors shown are calculated from
measured dark field scattering spectra, which are plotted in Figure 6.3b with black
arrows indicating the corresponding data. This set of aluminum pixels can be used
to produce an aluminum plasmonic pixel color gamut with 59% of the area of the
sRGB color gamut.
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Figure 6.3 – Color range of plasmonic pixels
(a), The CIE color diagram, with color associated with every (x,y) color coordinate
pair plotted in the background of the figure. The color space is bounded by a curved
axis denoting the wavelength of light (in nm). The sRGB color gamut tristimulus
values (white triangles) are connected with white lines bounding the sRGB color
gamut. Several white squares show the (x,y) color coordinates achieved by
aluminum plasmonic pixels of different physical parameters. From blue to red, exact
physical parameters measured in nm are (l = 116, w = 70, Dx = 297, Dy = 348), (l =
85, w = 47, Dx = 210, Dy = 212), (l = 95, w = 54, Dx = 128, Dy = 237), (l = 180, w = 49,
Dx = 288, Dy = 322), (l = 176, w = 44, Dx = 22, Dy = 323), (l = 100, w = 43, Dx = 272, Dy
= 271). The respective (x,y) coordinates are (0.44,0.50), (0.12,0.36), (0.12,0.12),
(0.53,0.41), (0.16,0.55), (0.30,0.58), respectively. The three circled points indicate a
possible tristimulus-based color gamut using aluminum plasmonic pixels. The black
square shows the (x,y) color coordinates (0.64,0.34) achieved by a gold plasmonic
pixel of physical parameters in nm (l = 57, w = 30, Dx = 346, Dy = 335). (b), Spectra
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used to produce the calculated color coordinates in (a). The three black arrows
indicate the three spectra associated with the red, green, and blue tristimulus pixels
for the aluminum pixels.
The introduction of additional plasmonic materials or multistimulus gamuts
can further increase the color gamut of these plasmonic pixels. If a gold nanorod is
used as the fundamental building block, a more vivid red plasmonic pixel can be
achieved (black square in Figure 6.3a, dashed red line in Figure 6.3b). This gold pixel
overlaps completely with the sRGB red tristimulus value. Considering the blue and
green aluminum pixels and the red gold pixel we can realize at least 88% of the
sRGB gamut area. If a multi-stimulus color gamut is defined to include other
experimental aluminum pixels with colors outside the sRGB gamut area (two other
white squares in Figure 6.3a and correspondingly color-coded spectra in Figure
6.3b), the gamut increases to at least 92% of the sRGB color gamut and even
becomes 102% with the gold-based pixel included. Under this gamut definition, the
blue-green region of the color gamut is enhanced beyond the capabilities of sRGB
displays while maintaining most of the shared red and violet region.
Although the 5 μm x 5 μm pixels discussed so far are smaller than the human
eye can see, they can be tiled to cover a mm-scale area to produce colors bright
enough to be seen easily by the naked eye, while maintaining the same vivid color.
Figure 6.4a shows a composite digital camera photograph of large area (1.5 x1.5
mm) red, green, and blue pixels taken outside the microscope under edgeillumination by shining polarized white light into the edge of the slide, as illustrated
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in Figure 6.4b. Similarly to the dark field microscopy measurements, the excitation
light propagates roughly parallel to the long axis of the nanorods making up the
pixels with the electric field orientated mainly perpendicular to the pixel plane. The
excitation angle is, however, approximately normal to the narrow edge of the slide.
As opposed to 53° in the dark field experiments, the excitation angle is roughly 90
degrees due to total internal reflection inside the glass slide. According to Equation
5.4, an increase in 𝜃i for these pixels will result in a red shift in the wavelengths that
can be collected over the collection cone defined by 𝜃o. Therefore, for ideal color
production, these pixels should be tailored to the excitation geometry under which
they will be utilized. Equation 5.4 further indicates that the color of the pixels should
be viewing angle dependent, which can be mitigated with the help of a diffuser as
Figure 6.5 clearly verifies. With no diffuser (Figure 6.5a-g) the color of a single pixel
can range from violet to red, depending on the angle at which one views the pixels, with
the brightest intensity viewed at roughly 30° in this case. However, with the application
of an 80° optical diffuser (Figure 6.5h-n), the color does not significantly change over
the same range of viewing angles.
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Figure 6.4 – Break-down of large area pixels into 5-μm subpixels
(a), Photograph of three 1.5 mm x 1.5 mm pixels as viewed outside the microscope.
To most accurately represent the colors as viewed by the human eye, the pixels are
shown in a composite image consisting of two images: the red and blue pixels are
shown at 1/10 s exposure, while the green pixel is shown at 1/30 s exposure. These
pixels are fabricated by e-beam lithography according to the scheme in (b). (b),
Large pixels with footprints on the order of square mm are illuminated from the
side via p-polarized light, with the light traveling along the nanorods’ long axes. The
light is carried by a fiber with a rectangular output, passed through a polarizer to
produce p-polarized light, and illuminated on the 1 mm edge of the glass slide
approximately normal to the edge surface. Each large colored region is composed of
a tiling of 5 μm pixels in the following layout. The 1.5 x 1.5 mm area (top left)
contains 8x8 sub regions; each of these sub regions (top center) is approximately
100 μm x 100 μm, and contains 15 x 15 of the standard 5 μm pixels (top right). The
marker bars, from left to right, represent 100 μm, 10 μm, and 1 μm. These SEM
images have been contrast-enhanced.
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Figure 6.5 – Viewing angle dependence of a single macroscopic plasmonic
pixel
Subfigures (a-g) are show a 1.5 mm x 1.5 mm pixel imaged over viewing angles 0°
through 80°, respectively. Subfigures (h-n) show the same pixel as in a-g imaged over
the same angles, with an 80° optical diffuser film placed on top of the pixel.
Each of these 1.5 x1.5 mm color pixels in Figure 6.4a is composed of a tiling
of smaller 5 μm x 5 μm pixels as illustrated with the large-area red pixel in Figure
6.4b. The 1.5 mm x 1.5 mm region is formed from 8x8 sub-regions, and each of those
100 μm-wide sub-regions contains a 15 x 15 array of the originally designed 5 μm x
5 μm pixels. The fundamental 5 μm x 5 μm building blocks are the same as shown in
the SEM images in Figure 6.1b-d. These results demonstrate both that plasmonic
pixels can be fabricated over large areas (total patterned footprint in Figure 6.4a is
6.75 mm2), and that they are compatible with multiple excitation methods, while
still producing the same colors. The nanorods that comprise the plasmonic pixels
impart their polarization sensitivity to the entire patterned region, allowing the
same pixels from Figure 6.4a to be incorporated into an LCD for complete on/off
switching without significant loss of intensity and vividness or change in color,
based on visual inspection. Figure 6.6a shows a photograph of large-area red, green,
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and blue pixels incorporated into an LCD, which is prepared by placing the pixel
substrate face to face with a similar substrate without pixels, where the ITO/PI
surfaces are separated by approximately 6 μm of liquid crystal. The liquid crystal
5CB is aligned in a TN configuration, causing the scattered light from the pixels to be
rotated by 90° as it passes through the liquid crystal. A polarizer placed before the
digital camera is orientated so that in this voltage-off state the pixels can be seen
(Figure 6.6b, top). When a voltage is applied across the 6 μm gap, the anisotropic
liquid crystal molecules realign parallel to the electric field and hence parallel to the
direction of light propagation through the LCD. In this voltage-on state, the liquid
crystal does not appreciably rotate the polarization of the light scattered by the
pixels, and the polarizer then blocks the light so that the pixels become invisible
(Figure 6.6b, bottom).
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Figure 6.6 – LC-based on/off switching of large scale plasmonic pixels
(a), Digital camera image of the large-scale red, green, and blue large scale pixels in
a prepared LCD, held in-hand under white light edge-illumination with relevant
components indicated in the figure. Marker bar indicates 2.5 cm. (b), Close view of
the on/off switching of pixels in the LCD. In both the top and bottom of (b), a
polarizing filter was placed in the excitation path (out of plane in this image) and
also in front of the camera lens, with the polarizer set perpendicular to the nanorod
long axis (nanorod long axis is horizontal in this image). The top image is shown
with no voltage applied, and the bottom image is shown with 20 V, 10 kHz square
wave AC voltage applied. As in Figure 4a, the top image is a composite with the same
exposure times as given for Figure 4a. The exposure time for the bottom image is
1/10 s. The marker bar represents 2 mm, and applies to both images in (b).
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So far, we have demonstrated that our plasmonic pixels are bright, produce
vivid colors, and can be manipulated via liquid crystal technology when their
footprints range from microns to millimeters, but even much smaller 9-nanorod
pixels can benefit from diffractive coupling to enhance their color. Figure 6.7a shows
the green portion of the color space diagram comparing the average color of
seventeen 1-nanorod pixels (white marker), seven 9-nanorod pixels (black marker),
fourteen 100-nanorod pixels (pink marker), and six 3969-nanorod pixels (blue
marker). In each case, the average color of the four pixel sizes is located at the
center of each crosshair, and the standard deviation in color coordinates x and y are
plotted as the arm lengths of each crosshair, with all individual data points given in
Figure 6.8. The average length of the nanorods for all samples is l = 85 nm with Dx =
317 nm and Dy = 317 nm for the pixels containing more than one nanorod. The 9nanorod pixels, as well as even larger pixels, display significantly less variation in
color compared to the 1-nanorod pixels. The length and width of the e-beam
lithographically prepared nanorods deviates from particle to particle by
approximately 5%, causing the aspect ratio to vary between 1.9 and 2.3. This
variation drastically affects the color scattered by a single nanorod. When several
nanorods are grouped into a pixel, these fluctuations due to size variations become
less pronounced and diffractive coupling furthermore shapes the collective
scattering spectrum. Surprisingly, it takes very few nanorods to be arranged in a
pixel to obtain reproducible colors. Already the 9-nanorod pixel’s spectrum is very
similar from sample to sample. These 9-nanorod pixels have a footprint of only
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about 1 μm x 1 μm. Larger pixels further benefit from this averaging effect as well as
the thresholds for the red- and blue-sides of the spectrum.
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Figure 6.7 – Color control over various pixel sizes
(a), CIE diagram focusing on the green region of the visible color space. Seventeen
single nanorods of average length 85 nm and average width 43 nm were measured
under dark field excitation, with a white cross centered at the average (x,y)
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coordinate and the standard deviation over those seventeen measurements shown
as the length of the crosshair in x and y. Seven 3x3-nanorod pixels of the same sized
nanorods with (Dx = 317 nm, Dy = 317 nm) (black cross), fourteen 10x10 nanorod
pixels (pink cross), and six 63x63-nanorod pixels (blue cross) are also plotted. For
reference, the sRGB color gamut in this region is also plotted. (b), Normalized
scattering intensity per nanorod is plotted for pixels of increasing sizes, from a
single nanorod to 65 x 65 nanorods per pixel. The same was also calculated for a
pixel composed of infinite nanorods. Theoretical values are plotted in squares (l =
85, w = 40, Dx = 317, Dy = 317), while experimental data points are plotted in circles
(l = 85, w = 43, Dx = 317, Dy = 317) in nm, with error bars indicating the standard
deviation over the same number of pixels as listed for (a). A dashed line indicates
the point on the intensity axis that corresponds to 90% of the maximum plotted
intensity. (c), Series of four scattering cross sections corresponding to green
squares in (b). Green dotted line represents a pixel containing 100 nanorods, blue
dashed-dotted line indicates a pixel of 400 nanorods, and pink dashed indicates a
pixel of 2500 nanorods. The black solid line represents a pixel with an infinite
number of nanorods. The two black dashed lines point to the wavelength at which
the (1,1) and (1,0) grating resonances occur; 425.5 nm, and 464.5 nm, respectively.
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Figure 6.8 – Complete color coordinate dataset of pixels of increasing size
Pixels range from to 632 according to the labels in the figures. The white squares indicate
a single pixel for each of the four sizes (a), single-nanorod pixels, (b), 9-nanorod pixels,
(c), 100-nanorod pixels, and (d), 3969-nanorod pixels. All pixels have the same average
nanorod dimensions of w = 43 nm and l = 85 nm, and panels b-d show data for pixels
with interred spacing of Dx = 317 nm and Dy = 317 nm.
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The thresholds for the red- and blue-sides of the spectrum imposed by array
spacing play a significant role in the color control of these plasmonic pixels, but the
pixel does not need to cover a large area for these array-based effects to exert
sufficient influence. A pixel need only contain 10 x 10 nanorods – an average
footprint of 4.5 microns – to reach 90% of the pixel’s maximum intensity per
nanorod. We compare in Figure 6.7b the integrated spectral intensities of pixels of
increasing size: 1 nanorod through 65 x 65 nanorods. Experimentally, the integrated
intensity was measured by imaging each pixel on a CCD camera and finding the total
intensity of the pixel’s image. Theoretically, the sum of the spectral intensities was
performed. The dashed line in Figure 6.7b indicates 90% of the normalized
integrated scattering intensity per nanorod. This value is already reached for a pixel
of 10 x 10 nanorods. In addition, it is not the ideal, infinitely large pixel that provides
the greatest intensity per nanorod; pixels of finite size yield a greater integrated
intensity per nanorod than an infinite pixel, as also seen from Figure 6.7b, where the
calculated values for an infinite pixel are plotted after the axis break. The infinite
pixel produces an integrated intensity per nanorod roughly equal to that of the 10 x
10 nanorod pixel.
The dark field scattering spectra of several simulated pixels from Figure 6.7b
are plotted in Figure 6.7c. The spectra display Fano resonances located at 426 nm
caused by the (1,1) lattice resonance, and at 465 nm caused by the (1,0) lattice
resonance. Both lattice resonances are indicated via dashed lines in Figure 6.7c.
Intuitively, as the number of nanorods per pixel increases from 102 to 502 nanorods,
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the total intensity of the pixel increases. As expected, an increase in the number of
nanorods in the array produces sharper features at the Fano resonances and at the
Dy-imposed threshold at 639 nm. However, the infinite pixel does not exhibit the
greatest scattering cross section per nanorod, as already demonstrated by the data
in Figure 6.7c. A likely possible explanation is that the nanorods at the edges of
finitely-sized pixels scatter light more efficiently to the far-field, contributing
significantly to the signal in smaller sized pixels. Therefore, the best choice for largearea printing of plasmonic pixels is to tile the smallest pixels that still exhibit strong
diffractive coupling, as we have done in Figure 6.4. In doing so, we ensure that the
lineshape is sufficiently controlled while allowing edge effects to significantly
contribute to the scattered intensity.
6.4. Conclusions
These results show that our aluminum nanorod-based plasmonic pixels are
capable of making a versatile impact on display technologies by providing an ultrathin vivid-color and highly polarized scattering source compatible with multiple
excitation geometries and LCD on/off switching. These pixels also push the
boundaries of the smallest display resolution, with near optimal pixel sizes of
approximately 5 μm, compatible with near-eye displays.11 The significant color
control of these pixels even at smaller pixel sizes lend themselves for use as nanobarcodes.256 Our aluminum plasmonic pixel color gamut is furthermore comparable
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to that of the sRGB color gamut, with blue and green colors even outside the sRGB
gamut.
6.5. Acknowledgements
This work was funded by Robert A. Welch Foundation Grants C-1220, C1222, and C-1664 and Office of Naval Research Grant N00014-10-0989. A.M.
acknowledges financial support from the Welch foundation through the J. Evans
Attwell-Welch Postdoctoral Fellowship Program of the Smalley Institute of Rice
University (Grant L-C-004). J.O. acknowledges support from the National Science
Foundation through Graduate Research Fellowship 0940902.
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Chapter 7
Conclusions and Outlook
This thesis describes a significant advancement to the body of research
focusing on nanomaterials for actively responsive, color- and spectrum-based
applications. In particular, a novel LC switching mechanism capable of orthogonally
rotating the polarization of single nanorod plasmons, regardless of their physical
orientation, has been elucidated. This unique result has yet to be combined with the
outstandingly vividly colored, highly polarized plasmonic pixels, also described
herein. These plasmonic pixels are certainly compatible with the HN-TN LCD
described in Chapter 4, but our ability to faithfully reproduce the necessary sample
thickness and alignment from sample to sample is reduced by the available
fabrication methods. Therefore, that work will be left to the professionals of the
display industry. However, as a demonstration of the immediate compatibility of our
plasmonic pixels with LCD technology, Chapter 6 includes the combination of
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macroscopic aluminum pixels with a standard TN-LCD as is common in many
computer screens and televisions today.
The plasmonic displays depicted in this thesis have been demonstrated to be
extremely versatile in the range of display applications with which they can be
combined, by virtue of their vivid color, polarization sensitivity, CMOS compatibility,
and fabrication scalability. To aid in the rapid incorporation of these pixels into
industrial applications, we defined a 3-step color-control method for the fabrication
of the plasmonic pixels. This 3-step process relies on diffractive coupling of
nanorods within the array, so that both geometrical diffraction grating effects (redthreshold) and Fano-resonances between the lattice resonances and the single
nanorod LSPR (blue-threshold) play a role. Furthermore, we provide generalized
information for how others can tailor their fabrication process to obtain desired
colors under conditions that differ from what we have presented. The significant
reproducibility of color in our structures was reported for footprints as small as a
few μm, so possible applications range from full-scale displays with at least sRGB
quality color definition down to nano-barcodes with direct-write encodable
information. Such barcodes could be faithfully reproduced from sample to sample,
providing relevant information rather than forcing manufacturers to rely on random
pattern generation merely for identification purposes.
One unique application to which our small-scale plasmonic pixels are
particularly well suited is near-eye displays, perhaps via combination with LCoS
technology. Near-eye displays necessitate higher resolution displays than standard
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televisions or computer screens. As mentioned in the introduction of this thesis,
LCoS technology relies on the placement of a liquid crystal layer on top of a silicon
back reflector. Because of their CMOS compatibility, aluminum plasmonic pixels
could provide significant benefits to LCoS technology by replacing the multicolor
light source and reflector, thereby eliminating convergence issues.
Alternatively, a tangential application that has not yet been mentioned: these
plasmonic pixels could serve as a near-eye version of digital light processing
technology by virtue of the color’s variation with viewing angle. This viewing-angle
dependence can be side-stepped with the aid of a diffuser as was demonstrated in
this thesis, but it can also be harnessed by display engineers who have the expertise
necessary to exploit it. One possible way may include a single-direction white light
source incident on an array of plasmonic pixels, each of which is supported by an
actuator, and the color of each pixel can be defined by the relative angle of the pixel
to the viewer. This mechanism would eliminate the use of sub-pixels, naturally
increasing the total resolution of the display. We did not explore in the direction of
this highly relevant and exciting application because we lack the apparatus to study
the sample at multiple angles with spectroscopic detail.
Regardless of the kind of display these pixels are combined with, more
drastic improvements to the color of the pixels could come from the use of gold or
silver nanorods as the plasmonic elements. The remarkably narrow linewidths (for
aluminum LSPRs) presented in this thesis rely mostly on the superiority of the
single nanorod to disks in this regard. There is also additional control imparted by
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the diffractive coupling described in detail in Chapter 5 and Chapter 6. The use of
these more traditional plasmonic metals, as was briefly demonstrated in a single
sample in Chapter 6, may significantly improve the vividness of the pixel color
because of reduced damping in the metal. This benefit would come at the cost of the
ease with which aluminum – but not gold or silver – can be combined with CMOS
technology. This change is not likely to be cost-prohibitive in industrial-scale
fabrication, because of the small percentage of the footprint that is actually covered
by the plasmonic material. In fact, the “empty” space between the nanorods is just as
important as the nanorods themselves in controlling the color of the pixels.
These advancements in both LC technology and plasmonics-based color
production have provided the research community as well as commercial
companies new insights into what can be achieved with the help of active
plasmonics. The versatility of the nanomaterials described herein is already strong,
and that versatility is not limited to the applications that have already been
described. Future improvements in LC alignment and control techniques, new and
scalable nano-fabrication methods, and novel plasmonic materials will only serve to
improve the usefulness of these plasmonic pixels. Future displays are slated to shift
toward what we would consider “non-traditional”, and these aluminum plasmonic
pixels will hopefully have helped to ensure nanotechnology’s place in that future.
131
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