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Nanophotonics Class 2 Surface plasmon polaritons

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

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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:

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Dispersion relation: x-direction: Bound SP mode: k z imaginary: m + d < 0, k x real: m < 0 so: m < - d z-direction:

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

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

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Bound SP modes: m < - d bound SP mode: m < - d -d-d

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pp Re k x real k x real k z imaginary k x real k z real k x imaginary k z Bound modes Radiative modes Quasi-bound modes Surface plasmon dispersion relation: Dielectric: d Metal: m = m ' + m " x z ' m > 0) d < ' m < 0) ( ' m < d )

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Re k x Surface plasmons dispersion: large k small wavelength Ar laser: vac = 488 nm diel = 387 nm SP = 100 nm Ag/SiO eV (360 nm) X-ray wavelengths at optical frequencies

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

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

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

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Concentration of light in a plasmon taper: experiment Ewold Verhagen, Kobus Kuipers Au Er Al 2 O 3 λ = 1.5 μm

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

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

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

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Coaxial MIM plasmon waveguides

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

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Narrow channels show negative index Excitation above resonance, > sp 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

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Positive and negative index modes René de Waele, Stanley Burgos

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Plasmonic toolbox: , ( ), d - Engineer ( ) thin section Plasmonic concentrator Plasmonic lens Plasmonic multiplexer And much more ….. Plasmonic integrated circuits

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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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