Lecture 9: Introduction to Metal Optics. 5 nm

Transcription

1 Lecture 9: Introuction to Metal Optics 5 nm

2 What happene at the previous lectures? Light interaction with small objects ( < λ) Insulators (Rayleigh Scattering, blue sky..) Semiconuctors (Size epenent absorption, fluorescence..) Metals Resonant absorption at ωsp Microparticles Particles with λ (λ-inepenent scattering, white clous) Particles with >> λ (Intuitive ray-picture useful) Dielectric photonic crystal Moling the flow of light

3 Metal Optics: An Introuction Majority of optical components base on ielectrics igh spee, high banwith (ω), but Does not scale well Problems Bening losses Neee for large scale integration Diffraction Limit n CLAD n COR Optical moe in waveguie > λ 0 /n COR Solutions? Some funamental problems Some: Photonic functionality base on metals? J. D. Joannopoulos, et al, Nature, vol.386, p (1997)

4 Plasmon-Polaritons What is a plasmon? Compare electron gas in a metal an real gas of molecules Metals are expecte to allow for electron ensity waves: plasmons Bulk plasmon Metals allow for M wave propagation above the plasma frequency Surface plasmon Dielectric They become transparent z Strong local fiel Metal Note: This is a TM wave I Sometimes calle a surface plasmon-polariton (strong coupling to M fiel)

5 Local Fiel Intensity Depens on Wavelength z z D << λ o I I Long wavelength Short wavelength Characteristics plasmon-polariton Strong localization of the M fiel igh local fiel intensities easy to obtain Applications: Guiing of light below the iffraction limit (near-fiel optics) Non-linear optics Sensitive optical stuies of surfaces an interfaces Bio-sensors Stuy film growth

6 Plasmon-Polariton Propagation in Au ro Laser excitation λ 53 nm 8.1 µm Au ro Light at the other en R.M. Dickson an L. A. Lyon, J. Phys. Chem. B 104, (000)

7 Plasmon-Polariton xcitation using a Launch Pa J.R. Krenn et al., urophys.lett. 60, (00)

8 50 nm Array of 50 nanometer iameter Au particles space by 75 nanometer Guies electromagnetic energy at optical frequency below the iffraction limit nables communication between nanoscale evices Information transport at spees an ensities exceeing current electronics M.L. Brongersma, et al., Phys. Rev. B 6, R16356 (000) S.A. Maier et al., Avance materials 13, 1501 (001)

9 Purue Near-Fiel Optical Microscope Nanonics MultiView 000 NSOM / AFM Tuning Fork Feeback Control Normal or Shear Force Aperture tips own to 50 nm AFM tips own to 30 nm Raiation Source 53 nm Picture taken from Nanonics

10 APD To Piezoelectrics V Source Filter Freq. Gen. Obj. Lens Fiber Tip Upper Piezo 53nm Source Lock-In Detector Lower Piezo Obj. Lens Tuning Fork Filter APD PID Controller Computer

11 nhance Metal Transmission optics will make through your Sub-λ reams Apertures come true. Ag film with a 440 nm iameter hole surroune by circular grooves Transmission enhancement of 10 x compare to a bare hole 3x more light than irectly impingent on hole Reason: xcitation of plasmon-polaritons T.Thio et al., Optics Letters 6, (001).

12 Optical Properties of an lectron Gas (Metal) Dielectric constant of a free electron gas (no interban transitions) Consier a time varying fiel: quation of motion electron (no amping) { } ( t) Re ( ) exp( " i t) r m e t Dipole moment electron p( t) er( t) { } armonic time epenence p( t) Re p( ) exp( " i t) Substitution p into q. of motion: " m p( ) e ( ) This can be manipulate into: The ielectric constant is: p e 1 m ( ) " ( ) ( ) ( ) 0 0 p m e t N Ne 1 " r 1 + # p 1 1 " $ " m $ p r p

13 Dispersion Relation for M Waves in lectron Gas Determination of ispersion relation for bulk plasmons The wave equation is given by: (, t) " r r # ( r, t) c " t r, t Re r, exp ik " r # i t { } Investigate solutions of the form: ( ) ( ) ( ) Dielectric constant: Dispersion relation: " " c k r p r 1# " # % & ' ( p % 1$ & $ p c k p + c k ck p Note1: Solutions lie above light line No allowe propagating moes (imaginary k) Note: Metals: ħω p 10 ev; Semiconuctors ħω p < 0.5 ev (epening on opant conc.) k

14 Dispersion Relation Surface-Plasmon Polaritons Solve Maxwell s equations with bounary conitions We are looking for solutions that look like: Dielectric Metal Mathematically: Maxwell s quations in meium i (i metal or ielectric): " # i 0 " 0 At the bounary: x, m x, z<0 z>0 "# $µ t 0 m zm zm ym z ( 0,,0) expi( k x k z t) + " y x z (,0, ) expi( k x k z t) + " x z x z ( 0,,0) expi( k x k z t) + " m ym xm zm (,0, ) expi( k x k z t) + " m xm zm xm zm y x #$ " i " t

15 Dispersion Relation Surface-Plasmon Polaritons Start with curl equation for in meium i (as we i for M waves in vacuum) where i #$ i " i " t 0,,0 expi k x + k z " t ( ) ( ) i yi xi zi (,0, ) expi( k x k z t) + " i xi zi xi zi $ # # zi yi # xi # # zi yi # % xi ' &, &, & (,0, &,0, ) # y # z # z # x # x # y * ( ikzi yi ikxi yi) ( i" ixi i" izi ) k #" k #" We will use that: zi yi i xi zm yi m xm k #" z y x // across bounary is continuous: x, m, x kzm k ym m z y // across bounary is continuous: ym y Combine with: kzm kz ym m y kzm k m z

16 Dispersion Relation Surface-Plasmon Polaritons Relations between k vectors Conition for SP s to exist: kzm k m z xample z k z k zm 1 " 1 m Relation for k x (Continuity //, // ) : kxm kx xample z Air true at any bounary SiO For any M wave: Both in the metal an ielectric: k + k " # $ % & ' c ( x zi i sp x " # $ i % zi k k & ' k ( c ) kzm k m z Dispersion relation k x homework " # $ m % & c m + ' ( 1/

17 Dispersion Relation Surface-Plasmon Polaritons Plot of the ispersion relation Last page: k x " # $ m % & c m + ' ( 1/ Plot ielectric constants r ielectric " p sp metal Low ω: k x 1/ " & m ' " lim ) * c m #$% m + c ( +, sp k " c At ω ω sp (when ε m -ε ): k x " Note: Solution lies below the light line k

18 Dispersion Relation Surface-Plasmon Polaritons Dispersion relation plasma moes an SPP SP, Air " SP, Metal/air Metal/ielectric with ε Note: igher inex meium on metal results in lower ω sp ω ω sp when: p " m 1# #" # #" p p 1 + " p 1+ "

19 xcitation Surface-Plasmon Polaritons with lectrons xcitation with electrons First experiments with high energy electrons Measurement: nergy loss Direction of e s: Whole ispersion relation can be investigate Low k s are har xample: 50 kev has a λ nm << λ light k electron >> k light Stringent requirement on ivergence e - beam

20 Operating spee (z) 1T 1G 1M 1k Nanophotonics with Plasmonics: A logical next step? The operating spee of ata transporting an processing systems Coaxial circuits Telephone DWDM WDM 1.8 µm 130 nm Transcontinental cable Telegraph (µm-scale structures ~ 1µm) (nm-scale structures) Photonics Plasmonics? CMOS lectronics Communication networks CMOS lectronics Plasmonics Time The ever-increasing nee for faster information processing an transport is uneniable lectronic components are running out of steam ue to issues with RC-elay times

21 Why not electronics? As ata rates AND component packing ensities INCRAS, electrical interconnects become progressively limite by RC-elay: L A R $ L / # B max A " % C $ A L L # B max (bit/s)( A << 1 $ RC L ) $ A L lectronics is aspect-ratio limite in spee

22 Why not photonics? The bit rate in optical communications is funamentally limite only by the carrier frequency: B max < f ~ 100 Tbit/s (), but light propagation is subjecte to iffraction: core a claing n core n cla + % n n + % n # V ' a ncore ncla & " ë a n% n well guie moe : V $ ' # a " & / n% n moe size :% n<< 1() Photonics is iffraction- limite in size

23 Why Plasmonics? ε > 0 ε m < 0 D λ sp k sp " # m # c # m + # Dispersion Relation for SPPs: optical ω nm-scale λ (") # $ (") m λ p ~ very small SP wavelengths can reach nanoscale at optical frequencies SPPs are x-ray waves with optical frequencies

24 Why nanophotonics nees plasmons? Courtesy of M. Brongersma