Lecture 9: Introduction to Metal Optics · Nanophotonics with Plasmonics: A logical next step? 1825...
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Transcript of Lecture 9: Introduction to Metal Optics · Nanophotonics with Plasmonics: A logical next step? 1825...
Lecture 9: Introduction to Metal Optics
5 nm
What happened at the previous lectures ?
Microparticles
• Particles with d ≈ λ (λ-independent scattering, white clouds)
• Insulators (Rayleigh Scattering, blue sky..)
• Semiconductors (Size dependent absorption, fluorescence..)
• Metals…Resonant absorption at ωsp
• Particles with d >> λ (Intuitive ray-picture useful)
Light interaction with small objects (d < λ)
Dielectric photonic crystal
• Molding the flow of light
What happened at the previous lectures ?
Metal Optics: An IntroductionMajority of optical components based on dielectrics
• High speed, high bandwidth (ω), but…
Some fundamental problems!
nCORE
nCLAD
Diffraction Limit
Optical mode in waveguide > λ0/2nCORE
• Does not scale well Needed for large scale integration
J. D. Joannopoulos, et al, Nature, vol.386, p.143-9 (1997)
ProblemsBending losses
Solutions ?
Some:Photonic functionality based on metals?!
Metal Optics: An Introduction
Plasmon-PolaritonsWhat is a plasmon ?
• Compare electron gas in a metal and real gas of molecules
• Metals are expected to allow for electron density waves: plasmons
Strong local field
Metal
Dielectric
z
I
E
HNote: This is a TM wave
• Sometimes called a surface plasmon-polariton (strong coupling to EM field)
Surface plasmon
Bulk plasmon• Metals allow for EM wave propagation above the plasma frequency
They become transparent!
Plasmon-Polaritons
Local Field Intensity Depends on Wavelength
Long wavelength Short wavelength
z
I
z
I
D << λo
Characteristics plasmon-polariton • Strong localization of the EM field• High local field intensities easy to obtain
Applications: • Guiding of light below the diffraction limit (near-field optics)• Non-linear optics• Sensitive optical studies of surfaces and interfaces• Bio-sensors• Study film growth• ……
Local Field Intensity Depends on Wavelength
R.M. Dickson and L. A. Lyon, J. Phys. Chem. B 104, 6095-6098 (2000)
Laser excitationλ = 532 nm
8.1 µm Au rod
Light at the other end
Plasmon-Polariton Propagation in Au rod
Plasmon-Polariton Propagation in Au rod
Plasmon-Polariton Excitation using a Launch Pad
J.R. Krenn et al., Europhys.Lett. 60, 663-669 (2002)
Plasmon-Polariton Excitation using a Launch Pad
50 nm
• Array of 50 nanometer diameter Au particles spaced by 75 nanometer
• Information transport at speeds and densities exceeding current electronics
• Enables communication between nanoscale devices
M.L. Brongersma, et al., Phys. Rev. B 62, R16356 (2000)S.A. Maier et al., Advanced materials 13, 1501 (2001)
• Guides electromagnetic energy at optical frequency below the diffraction limit
Purdue Near-Field Optical Microscope
• Nanonics MultiView 2000• NSOM / AFM• Tuning Fork Feedback
Control– Normal or Shear Force
• Aperture tips down to 50 nm• AFM tips down to 30 nm• Radiation Source
– 532 nmPicture taken from Nanonics
APD
APD
Computer
HV Source
Lock-In Detector
Freq. Gen.
532nm Source
PID Controller
To Piezoelectrics
Filter
Filter
Obj. Lens
Obj. LensUpper Piezo
Lower Piezo
Fiber Tip
Tuning Fork
Metal optics will make your dreams come true….Enhanced Transmission through Sub-λ Apertures
T.Thio et al., Optics Letters 26, 1972-1974 (2001).
• Ag film with a 440 nm diameter holesurrounded by circular grooves
• 3x more light than directly impingent on hole !
• Reason: Excitation of plasmon-polaritons
• Transmission enhancement of 10 xcompared to a bare hole
Enhanced Transmission through Sub-λ Apertures
Optical Properties of an Electron Gas (Metal)Dielectric constant of a free electron gas (no interband transitions)
( ) ( ) ( ){ }Re expt i t! != "E E• Consider a time varying field:
• Equation of motion electron (no damping)2
2
dm edt
= !r
E
• Harmonic time dependence ( ) ( ) ( ){ }Re expt i t! != "p p
• Substitution p into Eq. of motion: ( ) ( )2 2m e! ! !" =p E
( ) ( )2
2
1e
m! !
!= "p E• This can be manipulated into:
• The dielectric constant is:
• Dipole moment electron ( ) ( )t e t= !p r
2
2
2
dm edt
=p
E
( )( )
22
2 2
0 0
11 1 1
p
r
N Ne
m
!!" #
" ! " ! != + = = $ = $
p
E
!
r!
p!
Optical Properties of an Electron Gas (Metal)
Dispersion Relation for EM Waves in Electron GasDetermination of dispersion relation for bulk plasmons
( )( )
2
2
2 2
,,r
tt
c
! "=#
"
E rE r
t
• The wave equation is given by:
• Investigate solutions of the form: ( ) ( ) ( ){ }, Re , expt i i t! != " #E r E r k r
2 2 2
rc k! " =2
21
p
r
!"
!= #• Dielectric constant:
2
2 2 2 2 2
21
p
p c k!
! ! !!
" #$ = $ =% &% &
' (
!
k
p!
No allowed propagating modes (imaginary k)
ck! =
2 2 2
p c k! != +• Dispersion relation:
Note1: Solutions lie above light lineNote2: Metals: ħωp ≈ 10 eV; Semiconductors ħωp < 0.5 eV (depending on dopant conc.)
Dispersion Relation for EM Waves in Electron Gas
Dispersion Relation Surface-Plasmon PolaritonsSolve Maxwell’s equations with boundary conditions
• Maxwell’s Equations in medium i (i = metal or dielectric):
0i!" # =E 0!" =H
0µ!
"# = $!
HE
ti!"
#$ ="
EH
t
• At the boundary:
Metal
DielectriczE
H
, ,x m x dE E=
x
ym ydH H=m zm d zmE E! !=
• We are looking for solutions that look like:
( ) ( )0, ,0 expm ym xm zmH i k x k z t!= + "H
( ) ( ),0, expm xm zm xm zm
E E i k x k z t!= + "E
( ) ( )0, ,0 expd yd xd zdH i k x k z t!= + "H
( ) ( ),0, expd xd zd xd zd
E E i k x k z t!= + "E
• Mathematically: z<0
z>0
Dispersion Relation Surface-Plasmon Polaritons
i
i i!"
#$ ="
EH
t
Dispersion Relation Surface-Plasmon Polaritons
• Start with curl equation for H in medium i (as we did for EM waves in vacuum)
( ) ( )0, ,0 expi yi xi ziH i k x k z t!= + "Hwhere
( ) ( ),0, expi xi zi xi zi
E E i k x k z t!= + "E
( ) ( ), , ,0, ,0,yi yizi xi zi xi
zi yi xi yi i xi i zi
H HH H H Hik H ik H i E i E
y z z x x y!" !"
# #$ %# # # #& & & = = &' (
# # # # # #) *
zi yi i xik H E!"= #• We will use that:zm yi m xmk H E!"= #
zd yd d xdk H E!"= #
• E// across boundary is continuous: , ,x m x d
E E=
zm zdym yd
m d
k kH H
! !=
• H// across boundary is continuous: ym ydH H=
Combine with: zm zdym yd
m d
k kH H
! !=
zm zd
m d
k k
! !=
Dispersion Relation Surface-Plasmon Polaritons
Dispersion Relation Surface-Plasmon Polaritons
Relations between k vectors
• Condition for SP’s to exist: zm zd
m d
k k
! !=
• Relation for kx (Continuity E//, H//) : xm xdk k=
• For any EM wave:
zdk
zmk
Example1
m! = "
1d! =z
z
2
2 2
x zi ik k
c
!"# $
+ = % &' (
2
2
sp x i zik k kc
!"# $
= = %& '( )
• Both in the metal and dielectric:
zm zd
m d
k k
! !=
1/ 2
m d
x
m d
kc
! !"
! !
# $= % &
+' (
Dispersion relation
homework
Example Air
SiO2true at any boundary
Dispersion Relation Surface-Plasmon Polaritons
Dispersion Relation Surface-Plasmon Polaritons
1/ 2
m d
x
m d
kc
! !"
! !
# $= % &
+' (
Plot of the dispersion relation
• Last page:
• Plot dielectric constants
• Low ω: 1/ 2
limm
m d
x d
m d
kc c!
! !" "!
! !#$%
& '= () *
++ ,
• At ω = ωsp (when εm = -εd):
!
r!
p!
sp!
d!"
d! dielectric
metal
xk !"
!
k
sp!
dk
c
!"=
• Note: Solution lies below the light line
Dispersion Relation Surface-Plasmon Polaritons
Dispersion Relation Surface-Plasmon Polaritons
Dispersion relation plasma modes and SPP
• Note: Higher index medium on metal results in lower ωsp2
21
p
m d
!" "
!= # = # 2 2 2
p d! ! " !# = #
2
2
1
p
d
!!
"=
+ω = ωsp when:
Metal/air
Metal/dielectric with εd
1
p
d
!!
"=
+
,SP Air!
, dSP !"
Dispersion Relation Surface-Plasmon Polaritons
Excitation Surface-Plasmon Polaritons with Electrons
Excitation with electrons
• First experiments with high energy electrons
• Whole dispersion relation can be investigated
• Measurement: Energy lossDirection of e’s:
• Low k’s are hard!
Example: 50 keV has a λ = 0.005 nm << λlight
kelectron >> klight
Stringent requirement on divergence e- beam
Excitation Surface-Plasmon Polaritons with Electrons
• The operating speed of data transporting and processing systems
The ever-increasing need for faster information processing and transport is undeniable
Electronic components are running out of steam due to issues with RC-delay times
Nanophotonics with Plasmonics: Alogical next step?
1825 1850 1875 1900 1925 1950 1975 2000 2025 20501
1k
1M
1G
1T
130 nm
1.8 µm
DWDMWDM
Coaxial circuits
Telephone
Transcontinental cable
Telegraph
Opera
ting s
peed (
Hz)
Time
Plasmonics?
CMOS Electronics
Photonics
Time
Communication networks
CMOS Electronics
Plasmonics
(µm-scale structures ~ 1µm)(nm-scale structures)
Nanophotonics with Plasmonics: A logical next step?
)!()bit/s(10
1/
2
2
15
max
2max
LAL
AB
L
A
RCBLCALR
<<!"#
$$#$%$
Electronics is aspect-ratio limited in speed!
As data rates AND component packing densities INCREASE,
electrical interconnects become progressively limited by RC-delay:
L
A
Why not electronics?
Why not electronics?
The bit rate in optical communications is fundamentally limited
only by the carrier frequency: Bmax < f ~ 100 Tbit/s (!),
but light propagation is subjected to diffraction:
cladding
core
a
)!(1 :size mode22/:modeguidedwell
2aë
2!2 22
<<!"#$!
"!=#+=+=
nnnaV
nnnnaVnnnnncladcorecladcore
%%&'
%&
'%%
Photonics is diffraction- limited in size!
Why not photonics?
Why not photonics?
( ) ( )m d! " ! "# $
!
ksp ="
c
#m#d
#m + #d
Dispersion Relation for SPPs:
λp ~ very small
Why Plasmonics?
optical ωnm-scale λ
- - -+ + + - - - + + +
E
H
Dλsp
εd > 0εm < 0
SP wavelengths can reach nanoscale at optical frequencies!SPPs are “x-ray waves” with optical frequencies
Why Plasmonics?
Why nanophotonics needs plasmons?
Courtesy of M. Brongersma