Po-Han Chen, and Bing-Hung Chen. Institute of Electronic Engineering,

Transcription

1 Simulation of EM wave propagating p g in a nanocylinder-base localized surface plasma resonance senor Po-Han Chen, and Bing-Hung Chen Institute of Electronic Engineering, National Dong Hwa University, Taiwan

2 Outlines Introduction of surface plasmon resonance Experimental setup electronic resonance in single or pair of cylinders Field enhancement in Cylinder array Sensitivity enhancement Magnetic resonance conclusions

3 Introduction Dispersion Relations of SPs P-polarized: Ex, Ez, Hy SPs at metal-dielectric interface From Maxwell s equations & E and H fields continuity relations Dispersion relation (DR) E = ± E0 exp[ + i ( k xx ± kzz ωt)] + for z 0, for z k z : imaginary z 0 Plasmon dispersive relation

4 ATR (attenuated total reflection) coupler Excitation of SPs SP sensor

5 Experimental System Jones vectors 1 1 P= e 1 iω t analyzer AN t = SPR= iφ i s 0 rs e φ p r e 0 p E=AN t t SPR EOP I=E t t Et 1 r p + rs I= +r r cos t+ - 4 ( ω φ φ ) t p s p s rp Erp Eip ρ = = = tanψ exp( iδ) r E E s rs is In general r =1 φs constant s ωtω t i e 0 EO= 0 e ωt -i

6 Mode Nanoscale cylinder array Interaction between localized and delocalized surface plasmaon polarition modes in a metal photonic crystal (A. Christ etal, Phys. Stat. sol. (b) 43. No ) 0.1cm.5cm Corning 1737 glass.5cm Plasmon resonance coupling in metallic nanocylinders (Kottmann etal, Optics Express Vol.8 No.1 P , Sburlan etal, Physical Review B ) Nanowire-based enhancemant of flocalized li surface plasmon resonance for highly sensitive detection (K.Kim, Optics Express Vol.14, No.5, ) BK7 prism Coring glass slide Dielectric (alalyte ) Nano-cylinder array Index match oil gold nano-cylinder Resonance light interaction with plasmonic nanocylinder system (ref: Viktor A. Podolskiy etal J. of Optics A 7 P )

7 Macroscopic permittivities Maxwell s equation in the metallic cylinder 4π 4πσ D=4 πρ= J= E ( ε E ) =0 i ω i ω ε ε 4πσ - i ω 1 3 iω iω 3 M = d rθ1( r) r J( r) - D( r) = - ε1 d rθ1( r) r E( r) cv 4π 8πc c B = ( k E ) = εμ ( ) -4 e e ek E μe H = μe B πm εe εe E ω μe -1 μe -1 ω p M = B= εμ e e ( ek E ) ε e ε 1-4π 4π ω -i ωγ Enhanced E-field make contribution εe, but μe limited.

8 Mathematic Description Single cylinder L>>a, λ>l, the standing waves are good approximation to the eigenstates: M 1 ( ) = -cos( ) ( + ) ( αρ ) E r k z q signm k k e J e M z z q M-q q=± 1 ( ) ( ) im +i +sin k z k k signm e J αρ e ϕ kz α kz k i M 0JM ( - ) imqϕ z = L ε, k ε 1, k 1 L z = 0 B.C. e ± ie ω E M = 0 at z = 0, L x y e ± 1, e0 ez; ki εi α, 1 1, i kz i = c = + = kl= nπ, z n= k z/ π, k z/ π + 1,... TM Mode TE Mode

9 TM mode (p-wave) )field enhancement tis a function of cylinder dimension S.E. Sburlan Physical Review B

10 Two cylinders ρ < a a ( ) = -cos( ) ( + ) ( αρ) E r k z q signm k k e J e M z z q M-q 1 q=± 1 ( - ) imqϕ L r R ( ) ( α ρ) im +sinkz α k k signm e J e ϕ z 1 z z M 1 ρ > a M ( ) = -cos( z ) ( + z ) qy M-q( αρ ) q=± 1 E r k z q signm k k e e ( ) ( α ρ ) im +sin k z α k k signm e Y e ϕ z z z M ( - ) imq ϕ

11 Coupled system has the same magnitude resonance as for the individual cylinder, but the coupling is much stronger and depends on the incident field Main resonance is red-shifted with decreasing distance d

12 Cylinder array TM Mode 電場強強度 (nm) y x z TE Mode

13 Local Surface Plasmon Enhance Sensitivity Sensitivity Definition: Mathematic formula s Resolution Present σ RI : σ = RI = Δh Δn Δn Δh σ σ : ins s Can reach ~ 10-7 for using heterodyne interferometer : : Refraction index variation Physical parameter variation (θ or λ) σ ins Instrument t Resolution Interrogation Angular Wave Intensit y Phase σ ins nm 0.% Prism coupling Grating coupling J. Homola, S.S.Yee and G.Gauglitz Surface plasma resonance sensors: Review Sens. Actuators B 54, 3-15 (1999)

14 Local surface plasma resonance is accompanied by the broadening in dispersion relation which increase the damping term γ * Surface plasmon resonance consists of gold thin film part and nanocylinder part, angular width is Im{ { ksp } γi + γ r Δ θsp = = ωp ' '' ω ω εe ε 1- = εca + iε ns cosθsp ns cosθ ω -iωγ sp c c Im { k sp } '' ε ' '' ω ε ε ε Au Au ε '' Au εca 0 c ε ε ε Au Metallic photonic ' ' Au ca ' ' Au + ca ' ( ) crystal ca ' ' '' εauε ε ca Δθsp= nscosθsp εau εca ε Au ' ' ' + ( Au ) ε ' Au ε ' ca * Kyujung Kim Optics Express Vol 14, No (006)

15 Magnetic Resonance TE Mode: Anti-symmetric polarition mode Anti-parallel current in the two cylinders induce magnetic dipole moment resonance TM Mode: Symmetric polarition will induce the electric resonance, but magnetic resonance is limited y x E in TE mode H in TE mode E in TM mode H in TM mode

16 Conclusions Significant sensitivity increase is associated with larger field enhance. Field enhancement is achieved by nanocylinder based localized plasmon resonance mediated by nanocylinder and their coupling. Coupling has more contribution on the field enhance. Significant magnetic field enhancement is happen in TE mode due to antisymmetric polarition mode.