Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Support:
Nanoplasmonics:
Optical Properties of Plasmonic Nanosystems
Mark I. Stockman
Department of Physics and Astronomy, Georgia
State University, Atlanta, GA 30303, USA
Lecture 1:
Introduction to Nanoplasmonics.
Plasmon Polaritonics: Propagation of Surface
Plasmon Polaritons in Nanostructured Systems
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.1
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Meet the Author
in his natural
environment:
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.2
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
CONTENTS OF THE COURSE
• Lecture 1: Introduction to Nanoplasmonics. Plasmon Polaritonics:
Propagation of Surface Plasmon Polaritons in Nanostructured
Systems
•Lecture 2: Nanoplasmonics of Nanosystems: Localized Surface
Plasmon Resonances
•Lecture 3: Ultrafast, Nonlinear, and Quantum Nanoplasmonics
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.3
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
LECTURE 1
Introduction to Nanoplasmonics.
Plasmon Polaritonics: Propagation of Surface Plasmon Polaritons in
Nanostructured Systems
1. Introduction
Problem of nanolocalization of energy
Surface plasmons and enhanced optical fields
Applications of surface plasmonics
2. Surface plasmon polaritons as interface electromagnetic waves
Maxwell equations solution for metal-dielectric interface
Surface plasmon polaritons in layered media
3. Adiabatic energy concentration in tapered plasmonic waveguides: theory and
experiment
4. Negative refraction in nanoplasmonic waveguides (optional)
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.4
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
PROBLEMS IN NANOOPTICS
Macro- and
Microscale
Delivery of energy
to nanoscale:
Conversion of
propagating EM
wave to local fields
Lecture Course Nanoplasmonics
2015
Enhancement and
control of local
nanoscale fields.
Enhanced nearfield responses
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Ultrafast,
nonlinear, and
quantum
nanoplasmonics
(SPASER)
Lecture 1 p.5
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Concentration of optical (electromagnetic wave)
energy: Minimum extension of electromagnetic
wave in uniform space
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.6
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Nanoplasmonics in a nano-nutshell
Wavelength, ~1000 nm
Enhanced Local Fields in
Proximity of Metal
Nanoparticle are
Nanoscale-Localized
Mean free path, ~40 nm
Skin depth, ~25 nm
Nanoplasmonics: ~10 nm
vF ω Spatial dispersion/Nonlocality radius, ~1 nm
Field enhancement
Polarizability:
or Quality factor:
3 εm − εd
α= R
, ε m = −2ε d
− Re ε m
ε m + 2ε d
Q=
~ 10 − 100
Im ε m
Localized Surface Plasmon:
Lattice
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Electrons
Lecture 1 p.7
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
I. Freestone, N. Meeks, M.
Sax, and C. Higgitt, The
Lycurgus Cup - a Roman
Nanotechnology, Gold Bull.
40, 270-277 (2007)
© Trustees of British Museum
Nanoplasmonic colors are very
bright. Scattering and absorption
of light by them are very strong.
This is due to the fact that all of
the millions of electrons move in
unison in plasmonic oscillations
Nanoplasmonic colors are also
eternal: metal nanoparticles are
stable in glass: they do not
bleach and do not blink. Gold is
stable under biological
conditions and is not toxic in
vivo
Scanning electron microscopy
Dark field optical microscopy
W. A. Murray and W. L. Barnes,
Plasmonic Materials, Adv. Mater. 19,
3771-3782 (2007) [Scale bar: 300 nm]
C. Orendorff, T. Sau, and C. Murphy, ShapeDependent …, Small 2, 636-639 (2006)
Lecture Course Nanoplasmonics
http://www.phy-astr.gsu.edu/stockman
2015
E-mail: mstockman@gsu.edu
Lecture 1 p.8
7/12/2015 11:31 AM
Eternal
nanoplasmonic
(Notre Dame de Paris)
Department
of Physics colors
and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.9
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Lecture Course Nanoplasmonics
http://www.phy-astr.gsu.edu/stockman
Lecture 1
p.10
The most beautiful
colors of the world: La Sainte 7/12/2015
Chapelle,
Paris
2015 polychroic nanoplasmonic
E-mail: mstockman@gsu.edu
11:31
AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
REUBEN
Lecture Course Nanoplasmonics
2015
ASHER
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
DAN
Lecture 1 p.11
7/12/2015 11:31 AM
Department of Physics and Astronomy Plasmonic Hot Spots
Georgia State University
Happy 20th Anniversary!
Atlanta, GA 30303-3083
•D. P. Tsai et al., Phys. Rev. Lett. 72, 4149 (1994)
•M. I. Stockman et al., Phys. Rev. Lett. 75, 2450 (1995)
•M. I. Stockman, L. N. Pandey, and T. F. George, Phys. Rev.
B 53, 2183-2186 (1996)
L. Novotny and S. J. Stranick, Annual Rev.
Phys. Chem. 57, 303-331 (2006)
M. Rang et al., Nano Lett. 8, 3357 (2008)
•J. A. Fan et al., Science 328, 1135 (2010)
•M. Hentschel et al., Nano Lett. 10, 2721 (2010)
Lecture Course Nanoplasmonics
2015
K. Li, M. I. Stockman, and D. J. Bergman,
Phys. Rev. Lett. 91, 227402 (2003)
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
M. I. Stockman, Phys. Rev. Lett. 93,
137404 (2004)
Lecture 1 p.12
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
A. Kubo, K. Onda, H. Petek, Z. Sun, Y. S. Jung, and H. K. Kim, Femtosecond Imaging
of Surface Plasmon Dynamics in a Nanostructured Silver Film, Nano Lett. 5, 1123
PEEM Image as a Function of Delay (250 as per frame)
(2005).
200 nm
30 femtoseconds from life
of a nanoplasmonic
systems
Localized SP hot spots are
deeply subwavelength as
seen in PEEM
(photoemission electron
microscope)
1
Delay
0.5
-100
-50
50
100
150
200
-0.5
-1
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.13
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Applications of Nanoplasmonics:
1.
2.
3.
4.
5.
6.
7.
Ultrasensitive and express sensing and detection using both SPPs and SPs (LSPRs): see,e.g., J. N.
Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, Biosensing with Plasmonic
Nanosensors, Nature Materials 7, 442-453 (2008);
NSOM (SNOM)
Nanoantennas: Coupling of light to nanosystems. Extraction of light from LEDs and lasers [N. F. Yu, J.
Fan, Q. J. Wang, C. Pflugl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, SmallDivergence Semiconductor Lasers by Plasmonic Collimation, Nat. Phot. 2, 564-570 (2008)];
nanostructured antennas for photodetectors and solar cells; heat-assisted magnetic memory [W. A.
Challener et al., Nat. Photon. 3, 220 (2009)]
Photo- and chemically stable labels and probes for biomedical research and medicine
Nanoplasmonic-based immunoassays and tests. Home pregnancy test (dominating the market), PSA test
(clinic), troponin heart-attack test, and HIV tests (in trials)
Near perspective: Generation of EUV and XUV pulses
Thermal cancer therapy: L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E.
Price, J. D. Hazle, N. J. Halas, and J. L. West, Nanoshell-Mediated Near-Infrared Thermal Therapy of
Tumors under Magnetic Resonance Guidance, Proc. Natl. Acad. Sci. USA 100, 13549-13554 (2003). C.
Loo, A. Lowery, N. Halas, J. West, and R. Drezek, Immunotargeted Nanoshells for Integrated Cancer
Imaging and Therapy, Nano Lett. 5, 709-711 (2005)
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.14
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Surface plasmon
frequency shifts to red
upon molecules adhesion
Molecule
ω0 p
ωp =
εd
Nanosensors based on
enhanced local fields
•X. Zhang, M. A. Young, O.
Lyandres, and R. P. Van Duyne,
Rapid Detection of an Anthrax
Biomarker by Surface-Enhanced
Raman Spectroscopy, Journal of
American Chemical Society 127,
4484 (2005).
•C. R. Yonzon, C. L. Haynes, X. Y.
Zhang, J. T. Walsh, and R. P. Van
Duyne, A Glucose Biosensor Based
on Surface-Enhanced Raman
Scattering, Anal. Chem. 76, 78-85
(2004).
Metal
Nanoparticle
Lecture Course Nanoplasmonics
2015
Raman radiation (SERS),
fluorescence, quenching, …
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.15
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Use of Enhanced Local Fields for Nano-Microscopy
Metal tip
Nanoparticle
Enhanced Local
Optical Fields
Scattered
Light, SERS
Lecture Course Nanoplasmonics
2015
•L. Novotny and S. J. Stranick, NearField Optical Microscopy and
Spectroscopy with Pointed Probes,
Annual Rev. Phys. Chem. 57, 303-331
(2006).
•A. Hartschuh, E. J. Sanchez, X. S. Xie,
and L. Novotny, High-Resolution NearField Raman Microscopy of Single-Walled
Carbon Nanotubes, Phys. Rev. Lett. 90,
095503 -1-4 (2003).
Nanoscale
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.16
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
NSOM images of healthy human
dermal fibroblasts in liquid obtained in
transmission mode with a
Nanonics cantilevered tip with a gold
nanosphere
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.17
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.18
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Chirality Changes in Carbon Nanotubes Studied with Near-Field Raman
Spectroscopy
Neil Anderson, Achim Hartschuh, and Lukas Novotny
Nano Lett. 577 – 582 (2007); DOI: 10.1021/nl0622496
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.19
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Next generation of scanning
near-field optical microscopy
(SNOM) with chemical
mapping:
Adiabatic concentration of
optical energy and giant
surface-enhanced Raman
scattering (SERS); resolution 7
nm.s
(to be discussed in the course)
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.20
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.21
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.22
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
SP Sensing and Detection
1 – Antigen (hCG)
2 – Primary antibody
3 – Gold nanosphere
functionalized with
secondary antibody
1 – Substrate
2 – Gold nanofilm
3 – Latex nanospheres
4 – Gold nanolayer
5 – Antibodies
6 - Analyte molecules
Adapted from:
T. Endo et al., Anal.
Chem. 78, 6465
(2006).
J.N. Anker et al. , Nature Materials 7, 442 (2008)
Lecture Course Nanoplasmonics
2015
N. Liu et al., Nat. Mater. advance online
publication DOI: 10.1038/nmat3029 (2011)
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.23
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
M. I. Stockman, Nanoplasmonic Sensing and Detection, Science 348,
287-288 (2015).
Lecture Course Nanoplasmonics
2015
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E-mail: mstockman@gsu.edu
Lecture 1 p.24
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Lecture Course Nanoplasmonics
2015
http://www.phy-astr.gsu.edu/stockman
E-mail: mstockman@gsu.edu
Lecture 1 p.25
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
William L. Barnes, Alain Dereux &
Thomas W. Ebbesen, Nature 424,
824 (2003)
Lecture Course Nanoplasmonics
2015
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Lecture 1 p.26
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
SURFACE PLASMON POLARITONS
Assume that we have a plane interface and consider propagation in the
xy plane.
z
y
x
Lecture Course Nanoplasmonics
2015
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Lecture 1 p.27
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Maxwell Equations in the absence of the external currents and charges:
for E, H ∝ exp(-iωt )
1 ∂B
∇×E = −
c ∂t
1 ∂D
∇×H =
c ∂t
∇D = 0 ,
⇒
⇒
∇ × E = ik0 µH
∇ × H = −ik0εE, where k0 ≡
ω
c
e
∇H = 0 ; F = eE + [ v × B] Lorent z formuala
c
See, e.g., L. D. Landau and E. M. Lifshitz, Electrodynamics of
Continuous Media (Pergamon, Oxford and New York, 1984).
Lecture Course Nanoplasmonics
2015
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Lecture 1 p.28
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
∞
General type
of linear
response
D(r, t ) = ∫ ε (r − r′, t − t ′)E(r′, t ′) dt ′d 3 r ′
−∞
∞
B(r, t ) =
3
′
′
′
′
′
(
,
)
(
,
)
−
−
µ
r
r
t
t
H
r
t
d
t
d
r′
∫
−∞
∞
Local
response
D(r, t ) = ∫ ε (r, t − t ′)E(r, t ′)dt ′ ⇒ D(ω ) = ε (ω )E (ω )
−∞
∞
B(r , t ) =
∫ µ (r, t − t′)H(r, t′)dt′
⇒ B(ω ) = µ (ω )H (ω )
−∞
∞
∞
D(ω ) = ∫ D(t )e dt , D(t ) = ∫ D(ω )e −iωt
iωt
-∞
Lecture Course Nanoplasmonics
2015
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-∞
dω
,
2π
Lecture 1 p.29
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Relation between permittivity and conductivity (Optional)
∂ρ (t ) ∂j(t )
Continuity eq. :
+
=0 ⇒
∂t
∂r
∂P
∂ P( t )
ρ =⇒ j(t ) =
⇒ j(ω ) = −iωP(ω )
∂r
∂t
ε (ω ) − 1
D(ω ) = E(ω ) + 4πP(ω ) = ε (ω )E(ω ) ⇒ P(ω ) =
E(ω )
4π
ε (ω ) − 1
j(ω ) = −iω
E(ω )
4π
ε (ω ) − 1
⇒ σ (ω ) = −iω
j(ω ) = σ (ω )E(ω )
4π
4π
ε (ω ) = 1 + i σ (ω )
ω
Lecture Course Nanoplasmonics
2015
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Lecture 1 p.30
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Seeking for solution as a TM wave
H = (H x ( y, z , t ),0,0 )
E = (0, E y ( y, z , t ), E z ( y, z , t ) )
(To be confirmed by equations)
Spatio-temporal dependence:
H x ( y, z , t ) = H x ( z ) exp(iky − iωt )
Ei ( y, z , t ) = Ei ( z ) exp(iky − iωt ) , i = y, z
Wave equations are obtained by
Maxwell equations:
∇ 2 + k02εµ H = 0 ⇒
(
(∇
)
2
)
+ k02εµ E = 0
Lecture Course Nanoplasmonics
2015
⇒
applying curl operation to
 ∂2

2
2
 2 − k + k0 εµ  H x = 0
 ∂z

 ∂2

2
2
 2 − k + k0 εµ  E y , z = 0
 ∂z

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Lecture 1 p.31
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Seeking
H x ( z ) ∝ exp(±κz ), E y , z ( z ) ∝ exp(±κz )
From the wave equations: k02εµ = k 2 − κ 2 , k0 = ω ;
c
∇ × H = −ik0εE ⇒
x:
y:
z:
∂H z ∂H y
−
= −ik0εE x ⇒ E x = 0
∂y
∂z
∂H x ∂H z
iκ
Hx
= −ik0εE y ⇒ E y = ±
−
k 0ε
∂z
∂x
∂H y
∂H x
k
Hx
−
= −ik0εE z ⇒ E z =
k 0ε
∂x
∂y
Because we have already satisfied the wave equations, the second
Maxwell equation is the satisfied identically
Lecture Course Nanoplasmonics
2015
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Lecture 1 p.32
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Boundary conditions are continuity across the interface plane of
i ∂H x
H x and E y =
k0ε ∂z
For a planar layered medium, surface plasmon polariton (SPP) is a TM
wave where in an i-th medium layer at a point (y, z) for a wave
propagating in the y direction
H x (i, y, z ) = [Ai exp(κ i z ) + Bi exp(−κ i z )]exp(iky ),
iκ i
[Ai exp(κ i z ) − Bi exp(−κ i z )]exp(iky),
E y (i, y, z ) =
ε i k0
E z (i, y, z ) =
k
εi
H x (i, y, z );
k ≡ k y ; k εµ = k − κ , k0 =
2
0
Lecture Course Nanoplasmonics
2015
2
2
ω
c
; i = 1,2,... is layer number
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Lecture 1 p.33
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
For metal/dielectric interface
Boundary conditions :
H x (1, y, z ) = H x (2, y, z )
E y (1, y, z ) = E y (2, y, z )
κ1
κ2
=−
ε1
ε2
E y (1, y, z ) = −
iκ 1
B1 exp(−κ i z ) exp(iky ),
ε 1k 0
y
These conditions
reduce to :
B1 = A2
z H (1, y , z ) = B exp(−κ z ) exp(iky ),
1
1
x
x
Lecture Course Nanoplasmonics
2015
H x (2, y, z ) = A2 exp(κ 2 z ) exp(iky ),
iκ 2
E y (2, y, z ) =
A2 exp(κ 2 z ) exp(iky ).
ε 2 k0
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Lecture 1 p.34
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Boundary conditions :
κ1
κ2
=−
ε1
ε2
Wave equations :
k ε = k −κ
2
0 1
2
2
1
Definition :
k0 =
ω
c
k02ε 2 = k 2 − κ 22
Transforming :
Substituti ng : ⇓
κ12 κ 22
= 2
2
ε1 ε 2
k02ε 1 − k 2
⇒
ε
=
k02ε 2 − k 2
ε 22
εε
Algebraically solving for k 2 : k 2 = k02 1 2
ε1 + ε 2
2
1
ε 22
ε 12
2
2
Finding by substituti on : κ = − k
, κ 2 = − k0
.
ε1 + ε 2
ε1 + ε 2
2
1
Lecture Course Nanoplasmonics
2015
2
0
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Lecture 1 p.35
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Metal-Dielectric Interface
For a two-medium system, the SPP wave vector is found as a function of
frequency (dispersion relation):
k=
ω
c
ε 1ε 2
ε1 + ε 2
Evanescent decay exponents in these two media are found as
ω
ε 12
κ 1=
−
ε1 + ε 2
c
ω
ε 22
κ 2=
−
c
ε1 + ε 2
From these, it follows that for the existence of SPPs, it is necessary and
sufficient that ε 1 + ε 2 < 0 and ε 1ε 2 < 0
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Lecture 1 p.36
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Dielectric permittivity for silver and gold in optical region
P. B. Johnson and R. W. Christy, "Optical-Constants of NobleMetals," Physical Review B 6, 4370-4379 (1972).
1.24
λ[µ ] =
ω[eV]
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Lecture 1 p.37
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
ω p2
ε = ε0 −
ω (ω + iγ )
Drude formula:
Im ε ; γ = 0.02 eV
0
20
40
60
80
100
Im ε ; γ = 0.055 eV
8
1
2
3
4
5
Re ε ; ε 0 = 3.6; ω p = 9.1 eV
6
6
4
4
2
2
1
2
3
4
5
ω (eV)
Fit to near-ir
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1
2
3
4
ω (eV)
Fit to visible
Lecture 1 p.38
7/12/2015 11:31 AM
5

Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Surface plasmon dispersion and resonance for real silver [data of
Johnson and Christy, P. B. Johnson and R. W. Christy, OpticalConstants of Noble-Metals, Phys. Rev. B 6, 4370-4379 (1972)]
ω (eV) ε = 1
2
3.5
3
2.5
2
1.5
1
0.5
Re[ε m + ε d ] =
0
ε2 = 3
ω
ε mε d
k=
c εm + εd
20000 40000 60000 80000
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Rek (cm -1 )
[Inverse wavelength in cm]
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Surface Plasmon Polaritons and Sommerfeld-Zenneck Waves
(example for silver in vacuum)
k=
ω (eV)
6
ω
c
ε m (ω )
ε m (ω ) + 1
κ vacuum =
ε m (ω ) + 1
Light line
6
Zenneck
wave
4
c
−
1
ω (eV)
Light line
5
ω
5
4
3
Overdamped
SPP
2
1
Propagating
SPP
3
2
10000 20000 30000 40000 50000
10000
20000
-1
Rek (cm )
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30000
40000
50000
Imk (cm-1 )
Lecture 1 p.40
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Surface plasmon polariton fields
Metal
Metal
y
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2015
y
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Lecture 1 p.41
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Surface plasmon polaritons fields
Metal
Metal
y
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2015
y
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Lecture 1 p.42
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Topography of Surface Plasmon Polariton Electric Fields
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Lecture 1 p.43
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
SPP excitation in Kretschmann geometry and SPP sensing
Sensors: http://www.biacore.com/
ε1 sin θ K =
ε1 >
ε mε 2
, where θ K is Kretschmann angle
εm + ε2
ε mε 2
> ε2
εm + ε2
ε1 sin θTIR = ε 2 , where θTIR is total internal reflection angle
θ K > θTIR
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Three-Layer Systems
Dispersion relation (exact analytical expression), where d is the layer
thickness: defines the SPP wave vector k
u1 − u2 ) × ( u3 − u2 )
(
exp [ 2k0d ε 2u2 ] =
;
( u1 + u2 ) × ( u3 + u2 )
ui =
1
ω
k2
ε
;
−
=
k
i
0
k02
c
εi
Here ε i is dielectric permittivity of i -th layer
Another form:
u2 (u1 + u3 )
tanh[k0 dε 2u2 ] = −
u1u3 + u22
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Problem
Find quasistatic limit of the dispersion relation, which describes thin
metal nanofilms and graphene embedded between two dielectrics. Obtain
2
2
an explicit solution by applying the Drude formula ε 2 = −ω p / ω
.
Finally, express through Fermi energy EF of electrons (assuming a very
low temperature kBT<< EF ).
Hint: Consider limit k  k0
ε i while kd → 0
u2 ( u1 + u3 )
1 k2
ω
tanh [ k0d ε 2u2 ] =
; ui =2 − ε i ; k0 =
−
2
ε i k0
u1u3 + u2
c
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Solution
to Problem
Department of Physics
and Astronomy
Georgia State University
2
Atlanta, GA 30303-3083
2
1
3
i
0
2 2
2
2
i
1 3
2
0
u (u + u )
ω
1 k
tanh [ k d ε u ] =
; u = − ε i ; k0 =
−
ε k
uu +u
c

ε1 + ε 3
1k
1 k 
−
→0
; tanh  k0d ε 2
ui 

ε i k0
ε 2 k0 
ε2

Thus tanh can be expanded as tanh x  x yielding
ε1 + ε 3
.
k−
d ε 2 (ω )
Substituting ε 2 = −ω / ω , we obtain SPP dispersion relation:
2
p
2
ω ε1 + ε 3
kd
, or ω =ω p
k 2
ωp d
ε1 + ε 3
2
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Lecture 1 p.47
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
ω 2 m ε1 + ε 3
4π ne 2
=
For
3D metal, ω p =
, thus k
.
2
m
4π ne
d
Substituting relation between density and Fermi energy EF ,
n
mEF
2 2 ε1 + ε 3
, we obtain k  ω
, or
=
2
2
4e E F
π d
ε1 + ε 3
k  ω (ω + iγ ) 2
with collision rate γ .
4e E F
For graphene in terms of EF , the SPP dispersion relation
can be shown to be exactly the same.
2
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
IMI Waveguide
Fast SPP root
(Long range SPP)
Slow SPP root
(Short range SPP)
Two roots for nano-thin silver in vacuum: Symmetric and
Antisymmetric SPPs. No cut-off for SPP as thickness tends to zero
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Dispersion Relations for Symmetric Systems
ε1 = ε 3
2u1u2
2 tanh x
− 2
tanh [ k0d ε 2u2 ] =
; using: tanh 2 x =
2
1 + tanh 2 x
u1 + u2
Parity (symmetry) is conventionally defined as that of the normal (z)
component of the electric field or the magnetic field (x-component)
Even (symmetric) mode
u1
1

tanh  k0 dε 2u2  = −
u2
2

Lecture Course Nanoplasmonics
2015
Odd (antisymmetric) mode
u2
1

tanh  k0 dε 2u2  = −
u1
2

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Lecture 1 p.50
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of Physics
and of
Astronomy
Dispersion Department
relations for
nanofilm
silver in vacuum (IMI structure):
Georgia State University
SymmetricAtlanta,
mode GA
(dashed)
and antisymmetric mode (solid line)
30303-3083
Negative refraction
branch
∂ω
vg =
<0
∂k
Decay exponent (Imk) for 30 nm silver layer
Symmetric mode
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2015
Antisymmetric mode
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Lecture 1 p.51
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Local electric
fields for 10 nm
silver layer in
vacuum at 2.2 eV
frequency
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7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Local fields for 10 nm layer
of silver in vacuum for a
high wave vector
Rek=5 105 cm-1
Antisymmetric mode: positive
refraction
Symmetric mode: negative
refraction, high loss
(practically, no propagation).
The sign of refraction is
determined by the sign of the
group velocity
v g = ∂ω
∂k
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Lecture 1 p.53
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
SPPs in Metal-Insulator-Metal Waveguides
ε m (ω)
εd
a
ε m (ω)
for odd (antisymmetric) mode:
for all modes:
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2015
Im ko ⋅ Re ko < 0
Re ko ≤ Im ko
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negative refraction
large dissipation
Lecture 1 p.54
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Radiative condition (other “causality”): Selecting one of the two solutions in
electrodynamics. Mandelstam-Veselago’s negative refraction
v pvg > 0
v pvg < 0
k
k
k ||
k ∂ω
kω
vg =
; vp =
k ∂k
k k
k ||
k′
k′
Universal negative refraction condition from causality : Im k ⋅ Re k < 0
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Lecture 1 p.55
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
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2015
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Lecture 1 p.56
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
General condition of negative refraction in isotropic medium (does not depend on choice of the
square root sign for n):
2
Im n < 0 or Im n ⋅ Re n < 0 or Im k ⋅ Re k < 0;
Im n 2 ≡ Re ε Im µ + Re µ Im ε .
Group velocity is the transfer of energy velocity only if loses are small enough.
If losses at the observation frequency are zero, then an exact causality relation is valid for
isotropic medium without spatial dispersion:
∞
c2
2 Im n 2 (ω1 )
= 1+ ∫
dω1 , where ω is the observation frequency
2
2
2
π 0 ω1 − ω
v pvg
(
)
Criterion of negative refraction without loss at the observation frequency is
∞
Im n 2 (ω1 )
∫ (ω
0
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2015
2
1
−ω
)
2 2
dω1 < -
π
2
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Lecture 1 p.57
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Lecture Course Nanoplasmonics
2015
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Lecture 1 p.58
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
CONCLUSIONS
1. In metal/dielectric layered systems there exist surface plasmon
polariton (SPP) modes of different symmetries
2. For a metal layer in a dielectric medium, there are two types of SPP:
symmetric (fast or long-range) SPP and antisymmetric (slow or
short-range) SPP
3. Slow SPP for a thin metal film is nanolocalized at the surface of the
film. It is useful to couple nanosystems to laser sources.
4. There is no cut-off as SPP wavelength tends to infinity.
5. Losses of negative refraction (back-propagating SPP) are very large
6. To have negative refraction without loss at an observation frequency,
there must be loss in the adjacent region of negative refraction
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2015
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Lecture 1 p.59
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Adiabatic Nano-Optics
Conventional (non-adiabatic) conversion to the near zone (direct excitation of
local, near-zone fields by far-zone radiation) is very energy-inefficient, though can
generate high local fields.
Both aperture and aperturless methods lead to loss of the major fraction of energy.
If one could focus optical radiation from the far zone to nanoscale region, then the
problem of the energy-efficient excitation of the local fields would have been
solved. However, it is commonly known that it is impossible
Is it? We show that this common wisdom is wrong.
Using adiabatic transformation, one can transfer energy
from the far zone to near field without major losses, with a
high efficiency, limited only by absorption in plasmonic
waveguides.
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2015
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Lecture 1 p.60
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Adiabatic Nanofocusing of Surface Plasmon Polaritons
M. I. Stockman, Nanofocusing of Optical Energy in Tapered
Plasmonic Waveguides, Phys. Rev. Lett. 93, 137404-1-4
(2004).
Waveguide geometry
Lecture Course Nanoplasmonics
2015
Propagation direction
z
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Lecture 1 p.61
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
For Cylindrical Plasmonic
Waveguide
Electric field of SPP wave for TM0 mode (magnetic field is tangential
to the surface, normal to the axis; axially-symmetric solution of the
Maxwell curl equations)
r < R : E z = I 0 (κ m r ) exp( ikz)
I 0 (κ m R )
r > R : Ez =
K 0 (κ d r ) exp( ikz)
K 0 (κ d R )
ik
r < R : Er =
I1 (κ m r ) exp(ikz )
κm
ik I 0 (κ m R )
r > R : Er =
K1 (κ d r ) exp(ikz )
κ d K 0 (κ d R )
Continuity of displacement at the surface:
Lecture Course Nanoplasmonics
2015
εm
ε d I 0 (κ m R )
I1 (κ m R ) =
K1 (κ d R )
κm
κ d K 0 (κ d R )
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Lecture 1 p.62
7/12/2015 11:31 AM
L. Novotny and C. Hafner, Light Propagation in a
Department of Physics and Astronomy
Cylindrical Waveguide with a Complex, Metallic,
Georgia State University
Dielectric Function, Phys. Rev. E 50, 4094-4106
Atlanta, GA 30303-3083
(1994)
For TM0 mode (magnetic field is tangential to the surface, normal to the
axis; axially-symmetric solution), dispersion relation is
ε m I1 ( k 0 R k 2 − ε m )
k 2 − ε m I 0 (k0 R k 2 − ε m )
k0 =
ω
c
There is single root:
=−
ε d K1 ( k 0 R k 2 − ε d )
k 2 − ε d K 0 (k0 R k 2 − ε d )
10
7.5
5
2.5
Slow SPP. There is no cutoff as -2.5
-5
its wavelength tends to zero (or
-7.5
wavevector tends to infinity)
-10
Lecture Course Nanoplasmonics
2015
0.5 1 1.5 2 2.5 3
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k / k0
Lecture 1 p.63
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
k = nω c
Introduce effective index:
Close to the tip (R  0), this effective index diverges as 1/R:
1
n( R ) ≈
k0 R
4ε d
1
, γ ≈ 0.57721
−ε m log −4ε m − γ
εd
This describes slowing down and asymptotic stopping of SPP. Important,
the time to travel to the tip (singularity) of the conic waveguide
logarithmically diverges,
R
1
t = ∫ n(r )dr ~ − ln( k0 R) → ∞
c Rmax
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2015
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Lecture 1 p.64
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Adiabatic parameter: δ = R′ d ( R)
dR
dR( z )
where R′ =
is the waveguide grading
dz
For a plasmonic (TM0) mode, close to the tip
Thus, adiabatic parameter stays finite everywhere, including the tip.
Correspondingly, the adiabatic (eikonal or WKB) approximation is
applicable uniformly over the entire tip.
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2015
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Lecture 1 p.65
7/12/2015 11:31 AM
Adiabatic
Department of Physics and
Astronomy Nanofocusing in Tapered
Georgia State University
Atlanta, GA 30303-3083Nanoplasmonic Waveguides
Propagation direction
103
Intensity of Local Fields at the Surface of Tapered Plasmonic Waveguide
(Conic Silver Wire)
I
0
z
10
100
20
Coordinate s are in the units of  ≈ 100 nm
2 0 2
x
M. I. Stockman, Nanofocusing of Optical Energy in Tapered Plasmonic
Waveguides, Phys. Rev. Lett. 93, 137404-1-4 (2004).
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2015
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Lecture 1 p.66
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Phase velocity of surface plasmon polaritons
Group velocity of surface plasmon polaritons
Adiabatic parameter (scaled by 10)
k ( R) ≈
1
R
2ε d
1
− ε m 1 log − 4ε m − γ
2
εd
−1
−1
k
 ∂k 
v p=   ∝ R , vg= 
 ∝R
ω 
 ∂ω 
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2015
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Lecture 1 p.67
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Local Electric Fields at Surface of Plasmonic
Tapered Waveguide
Transverse field
40
20
-25 -20 -15 -10
-20
-40
Longitudinal field
z

20
10
-25 -20 -15 -10
-10
-20
 ≈ 100 nm
Lecture Course Nanoplasmonics
2015
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Lecture 1 p.68
7/12/2015 11:31 AM
z

Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Local Electric Fields in Cross Section of System
Transverse electric field
Longitudinal electric field
20
10
Ex 0
20
20
10
z
Ez 0
10
2
0x
20
10
z
2
0
x
0 2
0 2
Coordinate s are in the units of  ≈ 100 nm
Lecture Course Nanoplasmonics
2015
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Lecture 1 p.69
7/12/2015 11:31 AM
Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Vector of optical electric field for TM0 plasmonic mode of conic
waveguide made of silver
z
35
Spatial scales are
in units of 100 nm
Lecture Course Nanoplasmonics
2015
-1
-2
-3
-4
-5
-2-1 0 1 2 1
x
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Lecture 1 p.70
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Problem
Analytically estimate field at the apex as a function of the distance to the
apex.
Hint: Neglect losses and use energy conservation along the SPP
propagation length.
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2015
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Solution to Problem
Distance to the apex z and local radius R are proportional, z ∝ R.
SPP wave vector is k ∝ R −1.
The field localization radius is ∆r ∝ k −1 ∝ R ∝ z.
The SPP group velocity is vg ∝ R ∝ z.
Conservation of energy flux is E 2v g R 2 ∝ 1, or
E 2 z 3 ∝ 1. Correspondingly, E 2 ∝ z −3 is the field scaling.
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2015
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Lecture 1 p.72
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Nano Lett. 7, 334-337 (2007)
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2015
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Latest: E. Verhagen, A. Polman,
and L.
Kuipers, Nanofocusing in Laterally
Tapered Plasmonic Waveguides, Opt.
Express 16, 45-57 (2008)
Lecture Course Nanoplasmonics
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Lecture Course Nanoplasmonics
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Nano Lett. 7, 27842788 (2007).
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Georgia State University
Atlanta, GA 30303-3083
Lecture Course Nanoplasmonics
2015
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p.77
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Department of Physics and Astronomy
Georgia State University
Atlanta, GA 30303-3083
Lecture Course Nanoplasmonics
2015
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E-mail: mstockman@gsu.edu
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p.78
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Georgia State University
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Di Fabrizio, E., et. al, Italian patent n. TO2008A000693 23.09.2008
5 nm radius
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εm
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Surface plasmon polaritons propagate along the adiabatic plasmonic taper, nanofocus at
the tip, and decay due to Landau damping, producing a nanosource of hot electrons at
the tip, which forms a Schottky diode with the substrate
Laser beam
Lecture Course Nanoplasmonics
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Geometry and principle of adiabatic-plasmonic hot-electron
Schottky nanoscopy
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2015
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Department of Physics and Astronomy
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Nano Lett. 11, 4309-4313
Atlanta, GA 30303-3083
(2011)
Doi: 10.1021/nl2023299
Nearly transformlimited 16-fs pulse
at the apex
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Adiabatic Nanofocusing Conclusions
•Due to adiabaticity, the back reflection and 3D scattering of SPP is minimal.
•The high wave vector of the TM0 SPP makes them dark (no coupling to the far field
radiation).
•The velocity of SPP tends to zero proportionally to R as they approach the tip:
adiabatic slowing down and asymptotic stopping.
•This leads to the accumulation of the SPP near the tip and their adiabatic
nanofocusing.
•Under realistic conditions it is possible to transfer to the tip vicinity ~50% of the initial
energy flux, that along with adiabatic stopping leads to the local field-intensity
enhancement by three orders of magnitude
•The energy and optical field concentration at the tip of a taper is usable to excite a
high-sensitivity, low-background SERS from a few molecules
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END LECTURE 1
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&
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