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
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
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
ATR (attenuated total reflection) coupler Excitation of SPs SP sensor
Experimental System Jones vectors 1 1 P= e 1 iω t 1 1 1 analyzer AN t = 1 1 0 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
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.10 344-348) 0.1cm.5cm Corning 1737 glass.5cm Plasmon resonance coupling in metallic nanocylinders (Kottmann etal, Optics Express Vol.8 No.1 P655 001, Sburlan etal, Physical Review B 73 035403 006) Nanowire-based enhancemant of flocalized li surface plasmon resonance for highly sensitive detection (K.Kim, Optics Express Vol.14, No.5, 1419 006) 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 P3-37 005)
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.
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
TM mode (p-wave) )field enhancement tis a function of cylinder dimension S.E. Sburlan Physical Review B 73. 035403 006
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
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
Cylinder array TM Mode 電場強強度 3.00.75.50.5.00 1.75 1.50 1.5 100 1.00 0.75 0 100 00 300 400 500 600 700 (nm) y x z TE Mode
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 0.0001 0 0.0nm 0.% 0.01 0 Prism 5 10 77 10 55 5 10 55 46 10 4.6 10 77 coupling Grating coupling 10 6 6 10 5 10 4 J. Homola, S.S.Yee and G.Gauglitz Surface plasma resonance sensors: Review Sens. Actuators B 54, 3-15 (1999)
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 5 1419 (006)
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 1.67 1.357 1.18 0.714 0.696 y 0.464 0.3 x 0.000 E in TE mode H in TE mode E in TM mode H in TM mode
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.