Download Powerpoint show - bio-page

Fundamentals &
applications of
Lecture 2/2
plasmonics
Svetlana V. Boriskina
Overview: lecture 2
• Recap of Lecture 1
• Refractive index sensing
• SP-induced nanoscale optical forces
– Optical trapping & manipulation of nano-objects
•
•
•
•
•
Fluorescence & Raman spectroscopy
Plasmonics for photovoltaics
Hydrodynamic design of plasmonic components
Magnetic effects
Thermal effects:
– Plasmonic heating
– Near-field heat transfer via SPP waves
• Plasmonic photosensitization of materials
• Further reading & software packages
• Omitted topics
S.V. Boriskina, 2012
Drude-Lorentz-Sommerfeld theory
Plasma
frequency
Drude
permittivity
function:
 p2  ne2  0me
 ( )  1 
 p2
Image credit: Wikipedia
( 2  i )
Collision
frequency
 1   v l
electron
velocity
S.V. Boriskina, 2012
mean free
path
Recap of Lecture 1: Propagating waves
Frequency
Plane
wave
transverse
Bulk
plasmon
longitudinal

photon
Dispersion equation
kx 

c
ω
d
p
p
plasmon
1  d
metals:
ne 2   10eV k    1  2   2 1 2
p 
p
x
p
c
 0 me semicond.:
 p  0.5eV
Surface
plasmon
p
TM:
E=(Ex,0,Ez)
1 d
S.V. Boriskina, 2012
(Quasi)
particle
polariton =

photon + k x       m d
c   m   d
plasmon
12



kx(ω)
High DOS,
high localization
Recap of Lecture 1: Localized plasmons
Scattering
response
quadrupole
E
dipole
Near-field
patterns
--+++
Lowest-energy modes
Movie: http://juluribk.com
dimer
heptamer
Plasmonic
molecules
Plasmonic
antenna
array
S.V. Boriskina, 2012
λ
High DOS, high localization
Plasmonic
atom
Schematic dipoles
Plasmons interactions with matter
• Optical
– Extreme light focusing/localization (sub-resolution imaging,
photovoltaics)
– Strong sensitivity to environmental changes (sensing)
– Amplification of weak molecular signals (fluorescence, Raman
scattering, absorption, circular dichroism)
• Electronic
– Enhancement of catalytic reactions
– Plasmonic photosensitization of materials
• Mechanical
– Mechanical manipulation of nanoobjects
• Thermal
– Selective heating of nanoscale areas
– Enhanced near-field heat transfer
S.V. Boriskina, 2012
SP-enhanced sensing
LSP sensors
SPP sensors
McFarland, A.D. & R.P. Van Duyne,
Nano Lett. 2003. 3(8): p. 1057-1062.
Sensor figure of merit (FoM):
Sensitivity
http://www.bio-sensors.net
Requirements:
• High sensitivity
• High spectral resolution
• Compact
S.V. Boriskina,
2012 design
FoM 
 n

Resonance linewidth

FOM enhancement & miniaturization
• Fano resonances in plasmonic molecules
Mirin, N.A., K. Bao, & P. Nordlander, J. Phys.
Chem. A, 2009. 113(16): p. 4028-4034.
S.V. Boriskina, 2012
Towards single-molecule sensitivity
Hybrid modes in optoplasmonic molecules:
S.V. Boriskina, 2012
Santiago-Cordoba, M.A. et al, Appl. Phys. Lett., 2011. 99: p. 073701. Also: Boriskina, S.V. & B.M.
Reinhard, Opt. Express, 2011. 19(22): 22305-22315; Ahn, W. et al, ACS Nano, 2012. 6(1): 951-960.
Raman spectroscopy
Rayleigh scattering
Dipole moment induced by light:
  E0 cos(0t )
polarizability tensor
   (q)   0   q  q
Raman scattering
vibrational coordinate
q  q0 cos(mt )
cos(0  m )t  
  
  E0 cos(0t )   q0 E0 



cos
(



)
t

q


0
m


Rayleigh
IR ~
6
d
particle size

4
S.V. Boriskina, 2012
hν0
hν0
Raman (Stokes &
anti-Stokes)
hν0
νm - molecular fingerprint
excited
hν0
virtual
(induced
dipole)
hνm
3
I Ram ~ 10 I R
a very weak effect!
h(ν0 ± νm)
Rayleigh
vibrat.
ground
Stokes Raman
Raman – Nobel Prize in 1930
Surface enhanced Raman spectroscopy (SERS)
ERam ~  R  g  g   E0
E-field enhancement @ ν0
@ the molecule position!
E-field enhancement @ (ν0 –νm)
High field localization enables SERS fingerprinting of single molecules
R6G molecules on
Ag nanoparticles
Nie, S. & S.R. Emory, Science, 1997. 275(5303): 1102-1106.
Fleischman M,et al Chem. Phys. Lett. 1974; 26: 123.
S.V.
Boriskina,
Jeanmaire
DL, 2012
Duyne RPV. J. Electroanal. Chem. 1977; 84: 1.
Review: Moskovits, M., J. Raman Spectr., 2005.
36(6-7): p. 485-496 +references therein
Single molecule delivery to the SP hot spot
• super-hydrophobic delivery:
De Angelis, F., et al. Nat Photon. 5(11): p. 682-687.
S.V. Boriskina, 2012
Single molecule delivery to the SP hot spot
• Optical trapping:
Gradient
force
Dissipative force
F   U  FD 
I 0n
( ' G   " kG )
c 0
The probability to find
a molecule @ r :
Intensity
enhancement
P ( r,U ) µ P0 ( r) exp {- U(r) kBT }
Optical
potential
Stable trapping:
U (r) kBT  10
Review: Juan, M.L. et al, Nat Photon,
2011. 5(6): p. 349-356
S.V. Boriskina, 2012
L. Novotny, et al, Phys. Rev. Lett. 79 (4), 645 (1997); H.
Xu and M. Käll, Phys. Rev. Lett. 89 (24), 246802 (2002).
SP-enhanced fluorescence
Fluorescence
Fluorescence rate of a dipole with moment μ:
 f   exc   r ( r   nr )
excitation rate
radiative rate
Excitation rate:
 exc  μ  E(rm , exc )
2
hνexc
hνf
non-radiative
rate (resistive
heating)
Spacer is needed to avoid quenching
Fermi’s golden rule:
2 2
( r   nr ) 
μ  (rm , f )
3 0
Local density
of states
The emission intensity affected by both
the excitation & emission modification
S.V. Boriskina, 2012
Anger, P., P. Bharadwaj & L. Novotny,
Phys. Rev. Lett., 2006. 96(11): p. 113002
SP-enhanced fluorescence
( r   nr ) 
Single-molecule fluorescence
2 2
μ  (rm , f )
3 0
Emission spectrum shaping by the
high-LDOS nanoparticle resonances
Kinkhabwala, A., et al.
Nature Photon., 2009.
3(11): p. 654-657.
Russell, K.J., et al., Nat Photon, 2012.
advance online publication.
S.V. Boriskina, 2012
See also a review: Ming, T., et al., J. Phys.
Chem. Lett. 3(2): p. 191-202 (2012).
Plasmonic solar cells
optical absorption
c-Si: 250 - 700 μm
a-Si: 0.1 – 0.3 μm
charge carrier diffusion
H. Atwater & A. Polman, Nature Mater. 2010
Electronic/photonic lengths mismatch
S.V. Boriskina, 2012
Efficient nanoscale light trapping
increase of the local density of optical
states in a certain frequency range
Callahan et al, Nano Lett. 2012
scattering
field enhancement
waveguiding
Atwater & Polman, Nature Mater. 2010
S.V. Boriskina, 2012
How can a particle absorb more than the light
C.F. Bohren, Am J. Phys. 1983, 51(4), p.326
incident upon it?


S  1 2 Re E  H Poynting vector
determines electromagnetic power flow
W. Ahn, S.V. Boriskina, et al, Nano Lett. 12, 219-227 (2012)
extinction cross-section
S.V. Boriskina, 2012
powerflow saddle point
Optical energy flows in the direction of
the phase change
v g    k group velocity
phase saddle
phase vortex
flow saddle
flow vortex
Local topological features (sources, saddle
points, vortices & sinks) define phase
landscape
that governs optical power flow
S.V.
Boriskina, 2012
W. Ahn, et al, Nano Lett. 12, 219-227 (2012)
vortex nanogear transmission
Reconfigurable vortex transmissions
S.V. Boriskina, 2012
S.V. Boriskina & B.M. Reinhard,
Nanoscale, 4, 76-90, 2012
Reconfigurable vortex transmissions:
vortex nanogates
‘… the title is straight out of
Enterprise's engineering room’
NextBigFuture.com SciTech forum
S.V. Boriskina, 2012
Physical picture behind vortex nanogate
Hydrodynamic design of SP components
Electromagnetics
Fluid dynamics
?
Maxwell’s equations:
E   
H  0
Gauss’ law
Gauss’ law for magnetism
  E     H t
  H  J    Ε t
Faraday’s law
Ampere’s law
Navier-Stokes equations:
 t    ( v)  0
Continuity (mass conservation) equation
 v t  ( v  ) v  
 p    T  f
Momentum conservation equation
+ boundary conditions
S.V. Boriskina, 2012
fluid density
flow velocity
Hydrodynamic form of Maxwell’s equations
Madelung transformation:
 (r )  k02 (r )
E(r, t )  U(r) expi((r)  t )
‘Photon fluid’ density:
material loss or gain
‘mass’ conservation:
 (r)  I (r) | U(r) |2
 (r ) v(r )    (r )  (r )
‘Photon fluid’ velocity:
momentum conservation:
v   (r )
v(r)   v(r)  V (r)  Q(r)
convective term
• steady state flow
• local convective acceleration possible
• fluid flux (the momentum density):
S.V. Boriskina, 2012
S  1 (20)   (r)v(r)
external potential created
by the nanostructure
V (r)  k 02 2 1   (r)
S.V. Boriskina & B.M. Reinhard,
Nanoscale, 4, 76-90, 2012
Hydrodynamic form of Maxwell’s equations
Vortex generates a velocity field:
v(r)  v(r)  V (r)  Q(r)
S.V. Boriskina, 2012
S.V. Boriskina & B.M. Reinhard,
Nanoscale, 4, 76-90, 2012
Energy flows in plasmonic nanostructures
Stockman’s
nanolens:
Li, K., M.I. Stockman, &
D.J. Bergman, Phys. Rev.
Lett., 2003. 91(22): p.
227402.
S.V. Boriskina & Reinhard, Nanoscale, 4, 76-90, 2012
Surface
plasmon
polariton
wave:
S.V. Boriskina, 2012
Magnetic SP effects
coil magnet
Plasmonic nanostructures built from
nonmagnetic materials can exhibit
effective magnetic permeability
  E     H t
Split-ring resonator:
Image: http://www.ndt-ed.org/
double-negative metamaterials
effective permeability
Pendry, J.B. et al, IEEE Trans. Microw. Theory Tech.,
47(11), p.2075, 1999
rotating currents in the rings induce magnetic flux
S.V. Boriskina, 2012
Shelby, R.A., et al Science, 2001.
292(5514): p. 77-79.
Magnetic SP effects in nanoparticle clusters
  E     H t
Anti-ferromagnetic response:
charge density:
Magnetic dipole
induced magnetic moments:
Liu, N., et al., Nano Letters, 2011. 12(1): p. 364-369.
dx
dy
Ag
2r
k
Electric
z
yfield intensity:
x
E
Magnetic field distribution:
Fan, J.A., et al. Science, 2010.
328(5982): p. 1135-1138.
S.V. Boriskina, 2012
S.V. Boriskina, in Plasmonics in metal
nanostructures: Theory & applications
( Shahbazyan & Stockman eds.) Springer, 2012
Thermal SP effects
cancer treatment
Electric field to heat:
T t ~ j(r, t )  E(r, t )
temperature
dissipation of
optical energy
Chen, J., et al. Small, 2010. 6(7): p. 811-817.
nanopatterning
Govorov A.O. & Richardson, Nano Today, 2007. 2(1) 30-38
Atanasov, P.A., et al., Int. J.
Nanopart. 2010. 3(3): p. 206-219.
S.V. Boriskina, 2012
Thermal SP effects
Heat to electric field:
E(r, )  i0  G(x, x' , )  j(x' , )dx'
V
~ DOS
fluctuating
currents
Near-field heat transfer:
(cold, T2)
d
(hot, T1)
High SPP-induced DOS results in the
near-field coherence
e.g., Narayanaswamy, A. & G. Chen, Appl. Phys. Lett.
2003. 82(20): p. 3544-3546; Fu, C.J. & W.C. Tan, J. Quant.
Spectr. Radiat. Transf. 2009. 110(12): p. 1027-1036;
Rousseau, E., et al. Nat Photon, 2009. 3(9): p. 514-517;
Volokitin, A.I. & B.N.J. Persson. Rev. Mod. Phys., 2007.
79(4): p. 1291-1329
S.V. Boriskina, 2012
Plasmonic photosensitization of semiconductors
Knight, M.W., et al., Science. 332(6030): p. 702-704.
• hot electrons can tunnel from metal nanoantennas into semiconductor
• photon detection at energies below the semiconductor band gap
Theoretical prediction: Shalaev, V.M., et al., Phys. Rev. B,
S.V. Boriskina, 2012 1996. 53(17): p. 11388-11402.
Plasmonic enhancement of photocurrent
in graphene:
in silicon:
Xu, G., et al (2012), Adv. Mater., 24: OP71–OP76
Mubeen, S., et al., Nano Letters. 11(12):
p. 5548-5552.
Echtermeyer, T.J.,
et al. 2012,
Nature Commun.
2: p. 458.
S.V. Boriskina, 2012
Books & review articles on plasmonics:
• Lal, S., S. Link, and N.J. Halas, Nano-optics from sensing to waveguiding. Nat
Photon, 2007. 1(11): p. 641-648
• Halas, N.J., et al., Plasmons in strongly coupled metallic nanostructures. Chem.
Rev., 2011. 111(6): p. 3913-3961
• Schuller, J.A., et al., Plasmonics for extreme light concentration and
manipulation. Nature Mater., 2010. 9(3): p. 193-204
• Stockman, M.I., Nanoplasmonics: past, present, and glimpse into future. Opt.
Express. 2011, 19(22): p. 22029-22106
• Maier, SA, Plasmonics: Fundamentals and Applications, Springer, NY, 2007
• Novotny, L., and B. Hecht. Principles of Nano-Optics, Cambridge University
Press, 2006
This list is by no means complete …
S.V. Boriskina, 2012
Commercial & free software
• Lumerical FDTD Solutions
http://www.lumerical.com/tcad-products/fdtd/
• COMSOL Multiphysics® (FEM)
http://www.comsol.com/products/multiphysics/
• MEEP (FDTD)
http://ab-initio.mit.edu/wiki/index.php/Meep
• DDSCAT (discrete dipole approximation)
http://www.astro.princeton.edu/~draine/DDSCAT.html
• A collection of free software (including Mie theory methods)
http://www.scattport.org/index.php/light-scattering-software
S.V. Boriskina, 2012
Topics I had to omit due to the lack of time
Plasmonic cloaking:
New Journal of Physics, Focus Issue on 'Cloaking and Transformation Optics',
Guest Editors: Ulf Leonhardt and David R. Smith, Vol. 10, Nov 2008.
Non-local response:
A.D. Boardman, Electromagnetic Surface Modes, Ch. Hydrodynamic Theory of
Plasmon–polaritons on Plane Surfaces, John Wiley & Sons Ltd., 1982.
Resonant energy transfer & ‘dark’ plasmonic nanocircuits:
Andrew, P. and W.L. Barnes, Energy Transfer Across a Metal Film Mediated by
Surface Plasmon Polaritons. Science, 2004. 306(5698): p. 1002-1005
Akimov, A.V., et al., Generation of single optical plasmons in metallic nanowires
coupled to quantum dots. Nature, 2007. 450(7168): p. 402-406.
Boriskina, S.V. and B.M. Reinhard, Spectrally and spatially configurable
superlenses for optoplasmonic nanocircuits. Proc. Natl. Acad. Sci. USA, 2011.
108(8): p. 3147-3151.
Spasers:
Stockman, M.I., Spasers explained. Nat Photon, 2008. 2(6): p. 327-329.
Plasmonic particles on demand:
Luther, J.M., et al., Localized surface plasmon resonances arising from free
carriers in doped quantum dots. Nat Mater, 2011. 10(5): p. 361-366.
finally, Metamaterials is a huge area in itself – could be a separate class
S.V. Boriskina, 2012