Nanophotonics class 2 - surface plasmon polaritons

Nanophotonics Class Surface plasmon polaritons Surface plasmon polariton: EM wave at metal-dielectric interface z x   i ( k x + k z −ωt ) E d ( x, z , t ) = E d , e x z   i ( k x − k z −ω t ) E m ( x, z , t ) = Em , e x z For propagating bound waves: - kx is real - kz is imaginary EM wave is coupled to the plasma oscillations of the surface charges Derivation of surface plasmon dispersion relation: k(ω) 2 2π ∂ Ed ,m 2 k= Wave equation: ∇ E d , m = µ µ d , mε 0ε d , m λ ∂t Substituting SP wave + boundary conditions leads to the Dispersion relation: x-direction: ω  ε mε d k x = k ' x +ik "x =  c  εm + εd  1/     ε (ω ) ω   k= ε Note: in regular dielectric:  c   2π k= λ Dispersion relation: x-direction: z-direction: ω  ε mε d k x = k ' x +ik "x =  c  εm + εd  k z ,m ω = k ' z , m +ik " z ,m =  c  εm + εd  εm 1/     1/     ε (ω ) Bound SP mode: kz imaginary: εm + εd < 0, kx real: εm < so: εm < -εd ω   ε k = c   Dielectric constant of metals Drude model: conduction electrons with damping: equation of motion d 2x dx m + mγ = eE0 e iωt dt dt no restoring force ω P Nex Ne ε = 1+ = 1+ = 1− = 1− 2 (ω − iωγ ) ε0E ε0E mε (ω − iωγ ) p with collision frequency γ and plasma frequency If γ ωsp • 25 nm-wide channel in Ag filled with GaP • Simulation shows negative phase velocity with respect to power flow • Negative refractive index of -2 René de Waele, Stanley Burgos Positive and negative index modes René de Waele, Stanley Burgos Plasmonic toolbox: ω, ε(ω), d - Engineer λ(ω) Plasmonic integrated circuits Plasmonic concentrator Plasmonic multiplexer Plasmonic lens thin section Y Axis Title 1.0 0.5 0.0 -0.5 -1.0 200 400 600 Distance (nm) 800 1000 And much more … Conclusions: surface plasmon polariton Surface plasmon: bound EM wave at metal-dielectric interface Dispersion: ω(k) diverges near the plasma resonance: large k, small λ Control dispersion: control ω(k), losses, concentration Manipulate light at length scales below the diffraction limit ... -? ?d 50 ε" ε -5 0 -1 00 -1 50 -? ?d Measured data: ε'' ε" ε'' Drude model: ε'' ε" bound SP mode: εm < -? ?d Modified Drude model: ε'' 20 0 400 600 800 1000 120 0 Wavelength (nm) 1400 1600 1800 ω  ε mε d Surface. .. concentrator Plasmonic multiplexer Plasmonic lens thin section Y Axis Title 1.0 0.5 0.0 -0 .5 -1 .0 20 0 400 600 Distance (nm) 800 1000 And much more … Conclusions: surface plasmon polariton Surface plasmon: ... bound waves: - kx is real - kz is imaginary EM wave is coupled to the plasma oscillations of the surface charges Derivation of surface plasmon dispersion relation: k(ω) 2? ?? 2? ? ∂ Ed ,m 2? ?? k= Wave