Tao Li taoli@nju.edu.cn Nat. Lab. of Solid State Microstructures Department of Materials Science and Engineering Nanjing University
Concepts Basic principles Surface Plasmon Metamaterial Summary
Light
SOLID, LIQUID, GAS atom or molecule PLASMA + + - + - - + - decoupled positive and - + negative charges free electron gas metal Positive charge background Jellium model Collective oscillation of free elctrons quanta hω q Plasmonics Plasmon
SOLID, CYSTAL atom METAMATERIAL artificial atom Notice: This artificial material (atom) is not exist naturally! meta is beyond The property is with respect to the EM wave, so a key point is the unit cell is sub-wavelength. Light cannot see the structure
Concepts Basic principles Surface Plasmon Metamaterial Summary
Objective: Electromagneitcs of Metals r D = ρ f r r B E = t r B = 0 r r H = j + f r D t D r = εε r 0E ε = ε ( ω ) r r B = μμ H μ = μ ( ω ) 0 r r j = σ E ω = ω( k ) Field distribution: E and H Media response: ε and μ
Commonly, magnetic response is neglected for the optical material μ = 1 Electric part can be described by D( r, t) dt' dr' ( r r', t t') E( r', t') = ε 0 ε J ( r, t ) = dt ' dr' σ ( r r', t t ') E ( r', t ') Taking Fourier Transformation DK (, ω) = εε( K, ω) EK (, ω) 0 JK (, ω ) = σ ( K, ω ) EK (, ω ) Fourier domain of k-ω space
According to Equations D = ε P 0 E+ P, J = t We get the dielectric function of metal (, ) (, ) 1 iσ K ε K ω = + ω εω For a spatially local response, ε ( K = 0, ω) = ε( ω) From wave equation K 0 2 = μ D E 0 2 t 2 ω = ε ( K, ω) 2 c Generic dispersion relation 2 ω
Dielectric function of free electron gas We have dynamic equation of an electron of plasma sea in an external E field m&& x+ mγ x& = ee Plasma frequency x e () t = () t 2 m( ω + iγω) E ω 2 2 Ne P εω ( ) = 1 ω p = 2 ε m ω + i γω 2 ne P = E 2 2 ω m( ω + iγω) P εω ( ) = 1 2 ωp D = ε 0 (1 ) E 2 ω + iγω 2 ω If neglecting the loss Drude Model 2 2 2 2 ω = ω P + Kc Dispersion of volume plasmons 2 0 0
Dispersion of light in free space and perfect metal
Considering the bound electron with resonance frequencyω 0 e.g. geometric boundary, interband transition, or other forces It is more popular case in real metallic system m&& x+ mγ x& + mω x = ee 2 ω P εω ( ) = 1+ ω ω iγω 2 2 0 0 Lorentz Model
Optical property p of medium refractive index n, extinction coefficient κ and ε = n κ, ε = 2nκ 2 2 1 2 1 n = ( ε + ( ε + ε ) ) 2 1 1 2 2 1 1 2 2 2 1 1 1 2 2 2 2 κ = ( ε1 + ( ε1 + ε2 ) ). 2 n% and ε% are not independent variable s r
Considering the plasmon 2 ω 2 ω P εω ( ) = 1 n% = ε r ω > ω, p ω = ω, ω p ω, p n is real n=0 n is imaginary < Plasma frequency Optical reflectivity R = ~ 2 2 2 n n~ 1 + 1 = ( n ( n 1) + 1) 2 + + κ κ 2.
Concepts Basic principles Surface Plasmon SPP at flat metal surfaces Optical excitation of SPP Localized Surface plasmon (LSP) Application of SPP Metamaterial Summary
From Maxwell s Eqs, we can get the wave equation Considering the waveguide modes in x direction, then For TE mode For TM mode
For TE case ε 2 Z>0 ε 1 Z<0 According to the continuity of H y and εe z at the interface No mode for TE wave
ε 2 For TM case Z>0 ε 1 Z<0 According to the continuity of H y and εe z at the interface A surface wave!
Bulk Plasmon Light The God close a door with a window open! ω P ω SP Forbidden band Forbidden band Surface Plasmon wh en k 2 ω p ε m ( ω ) = 1 = ε 2 ω ω p ω sp = 1 + ε d d
Bulk Plasmon Light Forbidden band SPP SPP: k spp >k light k = k + k + k k 2 2 2 2 0 x y z y = 0, for TM mode and k x > k 0 So k k is an 2, z < 0, z Im SPP is also an evanescent wave
Electric field distribution of SPP E z δ d ~ 100 nm δ m ~ 10 nm z
Dispersions of true SPPs at a real system (silver/air and silver/silica interfaces)
IMI multilayer ε3 ε1 ε2
(1) at z=a Dispersion of coupled SPP (2) () at z=a (3)
If a, this dispersion degenerate to If ε2=ε3, this dispersion splits to two Eqs. Decoupled Coupled SPP modes
antisymmetric symmetric a= 50nm, large a= 4 nm, small
MIM multilayer case Still valid, with reverse of ε1 and ε2
Concepts Basic principles Surface Plasmon SPP at flat metal surfaces Optical excitation of SPP Localized Surface plasmon (LSP) Application of SPP Metamaterial Summary
Bare light cannot couple to SPP, due to the mismatch of wave vectors If the light is not along surface and incident with an angle θ, Then Δ = Δ+(1-sinθ ( ) k light The mismatch is bigger ω klight Δ k spp To overcome this problem, there are several approaches
(a) Prism coupling Kretschmann geometry ε prism >1 Otto geometry
(b) Grating coupling k sp k light G=2π/D Coming from the grating Polarization 1 TM 0 TE Reciprocal vectors
(b) Grating coupling Overlap of the dispersion
Grating image Detecting: SNOM SEM image SNOM image
(c) Near-field excitation SNOM
(c) Near-field excitation to detector NSOM in collection mode k light E r trans E r SPP k r SPP Ag film Al-coating optical fiber aperture 50-80 nm @ 5 nm Z X incident beam glass illuminatig i beam 200 100 nm nm Near-field Scanning Optical Microscope (NSOM) in collection mode λ inc = 532 nm 20 µm
(d) Coupling with conventional Photonic elements e.g. fiber taper
(d) Others: e.g. charge impact, surface feature, surface roughness
Concepts Basic principles Surface Plasmon SPP at flat metal/insulator surfaces Optical excitation of SPP Localized Surface plasmon (LSP) Application of SPP Metamaterial Summary
Modes of Sub-wavelength metal particle Boundary condition polarizability Determine the resonance!
Klar et al Kuwata et al
Transverse mode Longitudinal mode Selective Switch
Concepts Basic principles Surface Plasmon SPP at flat metal surfaces Optical excitation of SPP Localized Surface plasmon (LSP) Application of SPP Metamaterial Summary
Modulating light: Extraordinary Optical Transmission (EOT) Ebbesen et al, Nature, PRB, (1998) Angle dispersion
Modulating light: Directional Beaming Lezec et al, Nature (2002)
Modulating light: Color Sorting
2 D Optics Plasmonic circuit SPP Brag reflector SPP lens
2 D Optics Plasmonic circuit SPP focusing Refracting SPP wave SPP Demultiplexer
2 D Optics Plasmonic circuit Subwavelength waveguide by grooves Plasmonic BG waveguides
Strongly localized field Enhanced detector Enhanced Raman Scattering
Enhance the light emission Strong field and enhanced DOS of SPP to improve the internal Quantum effeciency Reciprocal vectors to extract the light from LED to improve the external Quantum Effeciency 有望实现 LED 白光照明
Concepts Basic principles Surface Plasmon Metamaterial AtifiilM Artificial Magnetism Negative Index Material (NIM) Transformation Optics Illumination Optics Summary
Reconsider the plasma of metal n is the electron density it is fixed for a certain metal 1996, Pendry propose a dilute metal nanowire mesh Changes n to For example: Al ω p : 3.82e 12 GHz 8.2 GHz
r D r B r = εε 0E r = μμ H 0 Always be neglected for optical material Natural magnetism (μ) main comes from the spin, In dynamic system, spin response to the external alternative field, but frequency of the spin process is limited up to GHz! So at optical frequency, we regard μ=1 for almost all natural material It is also the right reason we usually do not consider μ in Maxwell s Equations
Circuit resoance at ω 0 = (LC) -1/2 Resonant Circuit
Array of metallic cylinder Out F μ = 1 1+ i 2 ρ / ωrμ 0 In magnetic Drude model
Array of metallic cylinder 2 f ω μ = 1 2 2 ω ω + iγω 0 magnetic Lonretz model Negative μ -μ band gap
Swiss roll
SRR Split Resonant Ring μ = 1 2 f ω 2 2 ω0 ω + i Γ ω Strong dipole weak dipole quadruple
~THz, 2001 NIR, 2005 ~100THz, 2004 VIS, 2007
Concepts Basic principles Surface Plasmon Metamaterial Artificial i Magnetism Negative Index Material (NIM) Transformation Optics Illumination Optics Summary
Diagram of Classification by ε and μ What we are interested metamaterial
SRR+wire
Simulation Experimental realizations
An obtuse angle cone for Cerenkov radiation Reversed Goos Hanchen shift
Effective media Prism 3D fishnet
Photonic Crystal Effective anisotropic media Negative dispersion waveguide
Concepts Basic principles Surface Plasmon Metamaterial Artificial i Magnetism Negative Index Material (NIM) Transformation Optics Illumination Optics Summary
Spatial transferred by parameters Optical Cloaking
X. Zhang Group, 2009
Concepts Basic principles Surface Plasmon Metamaterial Artificial i Magnetism Negative Index Material (NIM) Transformation Optics Illumination Optics Summary
C.T. Chan Group, 2009 Illusion Optics: The Optical Transformation of an Object into Another Object A further development of Transformation Optics
C.T. Chan Group, 2009
NIM MP waveguide fishnet
(a) Coupled metamaterial (b) Plasmonic electro-optics (c) SPP propagation modulation and integration
Thank you!