Optical Properties of Nanomaterials
David G. Stroud,
Department of Physics,
Ohio State University Columbus OH 43210
Work supported by NSF Grant DMR01-04987, the
Ohio Supercomputer Center, and BSF
OUTLINE
Linear Optical Properties of Nanocomposites
Nonlinear Optical Properties of Nanocomposites
Surface Plasmons in Nanoparticle Chains
Gold/DNA Nanocomposites
Conclusions
“Labors of the Months” (Norwich, England, ca. 1480).
(The ruby color is probably due to embedded
gold nanoparticles.)
What is the origin of the color?
Answer: ``surface plasmons’’
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An SP is a natural oscillation of the electron gas
inside a gold nanosphere.
If the sphere is small compared to a wavelength
of light, and the light has a frequency close to
that of the SP, then the SP will absorb energy.
The frequency of the SP depends on the
dielectric function of the gold, and the shape of
the nanoparticle. For a spherical particle, the
frequency is about 0.58 of the bulk plasma
frequency. Thus, although the bulk plasma
frequency is in the UV, the SP frequency is in the
visible (in fact, close to 520 nm)
Sphere in an applied electric field
Metallic sphere
Incident electric field
is E_0exp(-i w t)
EM wave
Surface plasmon is excited when a longwavelength electromagnetic wave is incident on a
metallic sphere
Calculation of SP Frequency
Effective conductivity of
a random metal-insulator composite in the
effective-medium approximation
Note the broad ``surface plasmon peak and the
narrow Drude peak above the percolation threshold.
[D. Stroud, Phys. Rev. B19, 1783 (1979)]
Effective conductivity of a composite of Drude metal and
insulator: dots, numerical; full curves, effective-medium
approximation. [From X. Zhang and Stroud,
PRB49, 944 (1994).]
Theory and experiment for transmission
through Ag/SiO2 films
Theory: Maxwell-Garnett approximation (MGA) and effective-medium
approximation (EMA) [D. Stroud,Phys. Rev. B19, 1783 (1979)] ;
Experiment [Priestley et al, Phys. Rev. B12, 2121 (1975)]. (f is the
volume fraction of Ag.)
Nonlinear optical properties of
nanomaterials
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Suppose we have a suspension of nanoparticles
in a host (or some other composite which is
structured on the nanoscale).
If an EM wave is applied, the local electric field
may be hugely enhanced near an SP resonance.
Ifso,one expects various nonlinear
susceptibilities, which depend on higher powers
of the electric field, to be enhanced even more.
The Kerr Susceptibility is
defined by
where D is the electric displacement, E is the electric
field, and epsilon and chi are the linear and nonlinear
electric susceptibilities.
If the electric field is locally large, as near an SP
resonance, then its cube is correspondingly larger.
Thus, near an SP resonance, one expects a huge
enhancement of the cubic nonlinear (Kerr) susceptibility.
Kerr susceptibility for a dilute
suspension of coated spheres
Cubic nonlinear (Kerr) susceptibility for a dilute suspension of coated
metal particles in a glass host, calculated in Maxwell-Garnett
approximation [X. Zhang, D. Stroud, Phys. Rev. B49, 944 (1994)].
Inset: linear dielectric function of same composite. Left and right
are for two coating dielectric constants.
Kerr enhancement factor for
metal-insulator composite
Kerr enhancement factor for a random metal-insulator
composite, assuming (left) metal and (right) insulator
is nonlinear. Calculation is carried out numerically, at
the metal-insulator percolation threshold.
Real and imaginary parts of the SHG susceptibility for a dilute
suspension of of metal spheres coated with a nonlinear dielectric
[Hui, Xu, and Stroud, Phys. Rev. B69, 014203 (2004)]
Left and right panels show susceptibility enhancement per
unit volume of nonlinear material for two different ratios of
coating thickness to metal particle radius.
Real and imaginary parts of the THG susceptibility for a
dilute suspension of coated metal spheres in a dielectric
host
Susceptility enhancement per unit volume for third-harmonic
generation (THG) for coated metal sphere suspension [from
Hui, Xu, and Stroud, PRB69, 014202 (2004)]
Faraday Rotation in Composites:
enhanced near SP resonance
Real and imaginary
parts of the Faraday
rotation angle in a
composite of Drude
metal and insulator
in a magnetic field
(Xia, Hui, Stroud, J.
Appl. Phys. 67, 2736
(1990)
Faraday rotation in granular
ferromagnets
Frequency-dependence of the real and imaginary parts of the
Faraday rotation angle for a dilute suspension of ferromagnet in an
insulator at two different temperatures below the Curie temperature
[Xia, Hui, and Stroud, J. Appl. Phys. 67, 2736 (1990)].
Nanoparticle chain
d
a
Surface plasmons can propagate along a periodic
chain of metallic nanoparticles (above)
Photon STM Image of a Chain of
Au nanoparticles [from Krenn et
al, PRL 82, 2590 (1999)]
Individual particles: 100x100x40 nm, separated by 100
nm and deposited on an ITO substrate
Calculation of SP modes in
nanoparticle chain
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In the dipole approximation, there are three SP modes
on each sphere, two polarized perpendicular to chain,
and one polarized parallel. The propagating waves are
linear combinations of these modes on different spheres.
In our calculation, we include all multipoles, not just
dipoles. Then there are a infinite number of branches,
but only lowest three travel with substantial group
velocity.
Can be compared to nanoplasmonic experiments, as
discussed by Brongersma et al [Phys. Rev. B62, 16356
(2000) and S. A. Maier et al [Nature Materials 2, 229
(2003)]
Surface plasmon dispersion
relations, nanoparticle chain
Calculated surface plasmon dispersion relations (left) and group
velocity of energy for the lowest two bands in a metal nanoparticle
chain. Solid curves: L modes; dotted curves: T modes. Light
curves; dipole approximation; dark curves, including all multipoles.
a/d=0.45 [from S. Y. Park and D. Stroud , Phys. Rev. B (in press);
a= particle radius; d= particle separation]
Composites of Au nanoparticles and
DNA strands
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Suppose we put Au nanoparticles and DNA
strands in an acqueous suspension.
Certain DNA strands (capped with thiol groups)
can attach to Au.
At high T, Au particles float in suspension, with
DNA strands attached.
At low T, strands on different grains react to
form links. Particles agglomerate to form a gellike structure.
This behavior is easily detected optically.
Methodology
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To determine structure, we calculate the probability that
any two bonds on different Au particles form a link,
using an equilibrium condition from simple chemical
reaction theory.
Structure determined by two different models: (i)
Percolation model; (ii) More elaborate model involving
reaction-limited cluster-cluster aggregation (RLCA)
To treat optical properties (for any given structure) use
the ``Discrete Dipole Approximation’’ (multiple
scattering approach).
References: S. Y. Park and D. Stroud, Phys. Rev. B67,
212202 (2003); B68, 224201 (2003).
Au/DNA suspension in liquid state
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At high T, Au particles float around in aqueous suspension. Single
strands of DNA capped with thiol groups are attached.
Melting of Au/DNA cluster, two
different models
(a), (b) and (c) are a percolation model: all particles on a cubic
lattice. (a): all bonds present; (b) 50% of bonds present; (c)
20% of bonds present. (d) Low temperature cluster formed by
reaction-limited cluster-cluster aggregation (RLCA)
Extinction coefficient, dilute
suspension
Calculated (full curves) and measured (dashed curves) extinction
coefficient for a dilute Au suspension, plotted versus wavelength
Extinction coefficient for compact
Au/DNA clusters
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Extinction coefficient per unit volume, plotted versus wavelength (in
nm) for LxLxL compact clusters, as calculated using the Discrete
Dipole Approximation (DDA) (from Park and Stroud, 2003)
Calculated extinction coefficient,
RLCA clusters
Calculated extinction coefficient versus wavelength for RLCA
clusters with number of monomers varying from 1 to 343.
Extinction coefficient versus
wavelength, percolation model
Extinction coefficient versus wavelength for different fractions p of Au
nanoparticles on a 10 x 10 x 10 simple cubic lattice. ``p=0’’
represents an isolated Au particle. Inset: C, B, and A are isolated
particles, compact clusters, and RLCA clusters. Melting more closely
resembles a transition from C to A in experiments.
Observed absorptance:
comparison of unlinked and
aggregated Au nanoparticles
Absorptance of unlinked and aggregated Au nanoparticles, as
measured by Storhoff et al
[J. Am. Chem. Soc. 120, 1959 (1998)]
Calculated extinction coefficients
versus temperature at 520 nm
Normalized extinction coefficient at wavelength 520 nm, calculated for two
different models, plotted vs. temperature in C. Full curves: percolation model
(3 diff. Monomer numbers). Open circles: RLCA model.
Extinction coefficient vs. T at 520
nm for different particle sizes
Calculated extinction coefficient versus T at wavelength 520 nm for
particle radius 5, 10, and 20 nm. Inset: comparison of extinction
for percolation model (open circles) and RLCA model (squares). Full
line in inset is probability that a given link is broken at T.
Measured extinction at fixed
wavelength vs. temperature
(left) extinction of an aggregate (full curve) and isolated particles
(dashed) at 260nm.
[Storhoff et al, JACS 122, 4640 (2000)]. (right) extinction of an
aggregate at 260 nm made from Au particles of three different
diameters [C. H. Kiang, Physica A321, 164 (2003)]
DNA/Au nanocomposite system
Linker DNA
1. Expected phase diagram
Gel-sol
transition
0
gel
R. Elghanian, et. al.,
Science 277, 1078 (1997).
2. Morpologies from a structural
model
melting
transition
sol
T
Ind. particles
3. DDA calculation (left) of extinction
cross section (S. Y. Park and D.
Stroud, Phys. Rev. B68 (224201 (2003)
Experiment
gel
sol
melting
transition
Gel-sol
transition
near melting
transition
R. Jin, et. al, J. Am. Chem. Soc. 125, 1643 (2003).
Work in Progress
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More realistic model for gold/DNA
nanocomposites
Selective detection of organic molecules, using
gold nanoparticles
SP dispersion relations in other nanoparticle
geometries
Diffuse and coherent SHG and THG generation
Control of SP resonances using liquid crystals.
Current Collaborators
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Dr. Sung Yong Park, Prof. Pak-Ming Hui,
Kwangmoo Kim, Ivan Tornes, Dr. Ha Youn Lee,
Prof. Brad Trees, Prof. David J. Bergman, Prof. Y.
M. Strelniker, Dr. W. A. Al-Saidi, D. ValdezBalderas, Ivan Tornes, K. Kobayashi
Work Supported by the U. S. National Science
Foundation, U. S.-Israel Binational Science
Foundation, and Ohio Supercomputer Center.