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Nanophotonics Class 2 Surface plasmon polaritons

Nanophotonics Class 2 Surface plasmon polaritons. Surface plasmon polariton: EM wave at metal-dielectric interface. z. x. For propagating bound waves: - k x is real - k z is imaginary. EM wave is coupled to the plasma oscillations of the surface charges.

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Nanophotonics Class 2 Surface plasmon polaritons

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  1. Nanophotonics Class 2 Surface plasmon polaritons

  2. Surface plasmon polariton: EM wave at metal-dielectric interface z x For propagating bound waves:- kx is real- kz is imaginary EM wave is coupled to the plasma oscillations of the surface charges

  3. Derivation of surface plasmon dispersion relation: k() Wave equation: Substituting SP wave + boundary conditions leads to the Dispersion relation: x-direction: Note: in regular dielectric:

  4. Dispersion relation: x-direction: z-direction: Bound SP mode: kz imaginary: em + ed < 0, kx real: m < 0 so: m < -d

  5. Dielectric constant of metals Drude model: conduction electrons with damping: equation of motion with collision frequencyg and plasma frequency If g << wp, then: no restoring force

  6. Measured data and model for Ag: Drude model: Modified Drude model: Contribution of bound electrons Ag:

  7. Bound SP modes: m < -d -d bound SP mode:m< -d

  8. z x Dielectric: ed Metal: em = em' + em" Surface plasmon dispersion relation: w Radiative modes real kx real kz (e'm > 0) wp Quasi-bound modes imaginary kx real kz (-ed < e'm < 0) real kx imaginary kz Bound modes (e'm < -ed) Re kx

  9. Surface plasmons dispersion: w large k small wavelength 3.4 eV (360 nm) X-ray wavelengths at optical frequencies Ar laser: vac = 488 nm diel = 387 nm SP = 100 nm Ag/SiO2 Re kx

  10. Surface plasmon dispersion for thin films Drude model ε1(ω)=1-(ωp/ω) 2 Two modes appear Thinner film: Shorter SP wavelength Propagation lengths: cm !!! (infrared) Example: HeNe = 633 nm SP = 60 nm L- L+(asymm) L-(symm)

  11. E r z k Cylindrical metal waveguides E Fundamental SPP mode on cylinder: • Can this adiabatic coupling scheme be realized in practice? taper theory first demonstrated by Stockman, PRL 93, 137404 (2004)

  12. E + + + + + + + E |E| z 1 µm x k 1 µm Delivering light to the nanoscale nanoscale confinement Field symmetry at tip similar to SPP mode in conical waveguide Optics Express 16, 45 (2008) Ewold Verhagen, Kobus Kuipers

  13. λ = 1.5 μm Au Er Al2O3 Concentration of light in a plasmon taper: experiment Ewold Verhagen, Kobus Kuipers

  14. 1 µm Er3+ energy levels (1490 nm) Concentration of light in a plasmon taper: experiment 60 nmapex diam. transmission 10 µm PL Intensity (counts/s) lexc = 1490 nm Nano Lett. 7, 334 (2007) Ewold Verhagen, Kobus Kuipers

  15. E z x k Concentration of light in a plasmon taper: experiment • Detecting upconversion luminescence from the air side of the film (excitation of SPPs at substrate side) 550 nm 660 nm Plasmonic hot-spot Theory: Stockman, PRL 93, 137404 (2004) Optics Express 16, 45 (2008) Ewold Verhagen, Kobus Kuipers

  16. sym asym Et, H 1 µm E + + + tip + + + + start FDTD Simulation: nanofocussing to < 100 nm |E|2 z = -35 nm n1 = 1 1 µm n2 = 1.74 • Nanofocusing predicted: 100 x |E|2at 10 nm from tip • 3D subwavelength confinement: 1.5 µm light focused to 92 nm (/16) • limited by taper apex (r=30 nm) Optics Express 16, 45 (2008) Ewold Verhagen, Kobus Kuipers

  17. Coaxial MIM plasmon waveguides

  18. FIB milling of coaxial waveguides <w>=50 nm, L=485 nm <w>=100 nm, L=485 nm 100 nm 100 nm • Silica substrates with 250-500 nm thick Ag • Ring width: 50-100 nm • Two-step milling process • ~7° taper angle Nano Lett. 9,in press (2009) René de Waele, Stanley Burgos

  19. Narrow channels show negative index • Excitation above resonance, w>wsp • 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

  20. Positive and negative index modes René de Waele, Stanley Burgos

  21. Plasmonic toolbox: , (), d - Engineer () Plasmonic multiplexer Plasmonic integrated circuits Plasmonic lens Plasmonic concentrator thin section Andmuch more …..

  22. Conclusions: surface plasmon polariton Surface plasmon: bound EM wave at metal-dielectric interface Dispersion: (k) diverges near the plasma resonance: large k, small  Control dispersion: control (k), losses, concentration Manipulate light at length scales below the diffraction limit

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