Dr. Tao Li

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1 Tao Li Nat. Lab. of Solid State Microstructures Department of Materials Science and Engineering Nanjing University

2 Concepts Basic principles Surface Plasmon Metamaterial Summary

3 Light

4 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

5 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

6 Concepts Basic principles Surface Plasmon Metamaterial Summary

7 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

8 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

9 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

10 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 ω = ω P + Kc Dispersion of volume plasmons 2 0 0

11 Dispersion of light in free space and perfect metal

12 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 Lorentz Model

13 Optical property p of medium refractive index n, extinction coefficient κ and ε = n κ, ε = 2nκ n = ( ε + ( ε + ε ) ) κ = ( ε1 + ( ε1 + ε2 ) ). 2 n% and ε% are not independent variable s r

14 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 = ~ n n~ = ( n ( n 1) + 1) κ κ 2.

15 Concepts Basic principles Surface Plasmon SPP at flat metal surfaces Optical excitation of SPP Localized Surface plasmon (LSP) Application of SPP Metamaterial Summary

16 From Maxwell s Eqs, we can get the wave equation Considering the waveguide modes in x direction, then For TE mode For TM mode

17 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

18 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!

19 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

20 Bulk Plasmon Light Forbidden band SPP SPP: k spp >k light k = k + k + k k 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

21 Electric field distribution of SPP E z δ d ~ 100 nm δ m ~ 10 nm z

22 Dispersions of true SPPs at a real system (silver/air and silver/silica interfaces)

23 IMI multilayer ε3 ε1 ε2

24 (1) at z=a Dispersion of coupled SPP (2) () at z=a (3)

25 If a, this dispersion degenerate to If ε2=ε3, this dispersion splits to two Eqs. Decoupled Coupled SPP modes

26 antisymmetric symmetric a= 50nm, large a= 4 nm, small

27 MIM multilayer case Still valid, with reverse of ε1 and ε2

28 Concepts Basic principles Surface Plasmon SPP at flat metal surfaces Optical excitation of SPP Localized Surface plasmon (LSP) Application of SPP Metamaterial Summary

29 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

30 (a) Prism coupling Kretschmann geometry ε prism >1 Otto geometry

31 (b) Grating coupling k sp k light G=2π/D Coming from the grating Polarization 1 TM 0 TE Reciprocal vectors

32 (b) Grating coupling Overlap of the dispersion

33 Grating image Detecting: SNOM SEM image SNOM image

34 (c) Near-field excitation SNOM

(c) Near-field excitation to detector NSOM in

Ag film Al-coating optical fiber aperture 50-80

beam 200 100 nm nm Near-field Scanning Optical

35 (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 nm Z X incident beam glass illuminatig i beam nm nm Near-field Scanning Optical Microscope (NSOM) in collection mode λ inc = 532 nm 20 µm

36 (d) Coupling with conventional Photonic elements e.g. fiber taper

37 (d) Others: e.g. charge impact, surface feature, surface roughness

38 Concepts Basic principles Surface Plasmon SPP at flat metal/insulator surfaces Optical excitation of SPP Localized Surface plasmon (LSP) Application of SPP Metamaterial Summary

39 Modes of Sub-wavelength metal particle Boundary condition polarizability Determine the resonance!

40 Klar et al Kuwata et al

41 Transverse mode Longitudinal mode Selective Switch

42 Concepts Basic principles Surface Plasmon SPP at flat metal surfaces Optical excitation of SPP Localized Surface plasmon (LSP) Application of SPP Metamaterial Summary

43 Modulating light: Extraordinary Optical Transmission (EOT) Ebbesen et al, Nature, PRB, (1998) Angle dispersion

44 Modulating light: Directional Beaming Lezec et al, Nature (2002)

45 Modulating light: Color Sorting

46 2 D Optics Plasmonic circuit SPP Brag reflector SPP lens

47 2 D Optics Plasmonic circuit SPP focusing Refracting SPP wave SPP Demultiplexer

48 2 D Optics Plasmonic circuit Subwavelength waveguide by grooves Plasmonic BG waveguides

49 Strongly localized field Enhanced detector Enhanced Raman Scattering

50 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

52 Concepts Basic principles Surface Plasmon Metamaterial AtifiilM Artificial Magnetism Negative Index Material (NIM) Transformation Optics Illumination Optics Summary

53 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

54 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

55 Circuit resoance at ω 0 = (LC) -1/2 Resonant Circuit

56 Array of metallic cylinder Out F μ = 1 1+ i 2 ρ / ωrμ 0 In magnetic Drude model

57 Array of metallic cylinder 2 f ω μ = ω ω + iγω 0 magnetic Lonretz model Negative μ -μ band gap

58 Swiss roll

59 SRR Split Resonant Ring μ = 1 2 f ω 2 2 ω0 ω + i Γ ω Strong dipole weak dipole quadruple

60 ~THz, 2001 NIR, 2005 ~100THz, 2004 VIS, 2007

61 Concepts Basic principles Surface Plasmon Metamaterial Artificial i Magnetism Negative Index Material (NIM) Transformation Optics Illumination Optics Summary

62 Diagram of Classification by ε and μ What we are interested metamaterial

63 SRR+wire

64 Simulation Experimental realizations

65 An obtuse angle cone for Cerenkov radiation Reversed Goos Hanchen shift

67 Effective media Prism 3D fishnet

68 Photonic Crystal Effective anisotropic media Negative dispersion waveguide

69 Concepts Basic principles Surface Plasmon Metamaterial Artificial i Magnetism Negative Index Material (NIM) Transformation Optics Illumination Optics Summary

70 Spatial transferred by parameters Optical Cloaking

74 X. Zhang Group, 2009

75 Concepts Basic principles Surface Plasmon Metamaterial Artificial i Magnetism Negative Index Material (NIM) Transformation Optics Illumination Optics Summary

76 C.T. Chan Group, 2009 Illusion Optics: The Optical Transformation of an Object into Another Object A further development of Transformation Optics

77 C.T. Chan Group, 2009

78 NIM MP waveguide fishnet

79 (a) Coupled metamaterial (b) Plasmonic electro-optics (c) SPP propagation modulation and integration

81 Thank you!

II Theory Of Surface Plasmon Resonance (SPR)

II Theory Of Surface Plasmon Resonance (SPR) II.1 Maxwell equations and dielectric constant of metals Surface Plasmons Polaritons (SPP) exist at the interface of a dielectric and a metal whose electrons