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Nanophotonics Class 3 Photonic Crystals

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Definition: A photonic crystal is a periodic arrangement of a dielectric material that exhibits strong interaction with light

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Examples: 1D: Bragg Reflector 2D: Si pillar crystal 3D: colloidal crystal

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Bragg mirror Antireflection coatings (Fresnel equations) 1D Photonic Crystals Bragg’s law:

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n1n1 n2n2 n1n1 n1n1 n1n1 n2n2 n2n2 Dispersion relation n 1 : high index material n 2 : low index material bandgap frequency ω wave vector k 0π/a standing wave in n 1 standing wave in n 2

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Bloch waves modified slide from Rob Engelen

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frequency ω wave vector k 0π/a -π/a Bloch wave with wave vector k is equal to Bloch wave with wave vector k+m2/a: This is called the first Brillouin zone modified slide from Rob Engelen

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Band diagrams and group velocity of light A light pulse with a center frequency w propagates with group velocity v g, which is altered near the band gap

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Example Dielectric mirror 400 – 900 nm Examples from Thorlabs Dichroic filters

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1D “photonic crystal” waveguide Joannopoulos et al.

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Morpho butterfly

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Structure morpho butterfly wing Mode calculation by Gralak et al.

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Band gap: no propagation possible at that frequency: Density of optical states (DOS) is 0 Density of optical states in photonic crystals

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Photonic crystals in two dimensions

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Field propagation into 2D photonic crystal -M direction, TM polarization dielectric band inside bandgap air band Mode calculation with FEMLAB by Aarts TUE.

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TMTE Bandstructure for two polarizations Photonic bandgap

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2D Photonic Crystals Simulations on a 90° bend in a 2D photonic crystal waveguide. A.Mekis et al., PRL 77, 3787 (1996)

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Photonic crystal waveguides Joannopoulos et al.

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2D Silicon photonic crystal waveguide bend Zijlstra, van der Drift, De Dood, and Polman (DIMES, FOM)

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Silicon-on-insulator (SOI) Si SiO 2 Si n eff 1.7 n 1.5 Si SiO 2

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2D Photonic Crystal: holes in semiconductor dielectric H. Gersen et al., PRL 94, (2005) Kobus Kuipers group at AMOLF wavevector |k| (units 2 p /a) frequency w (units 2 p c/a) crystal modes waveguide modes

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Aperture: ~200 nm 500nm Phase sensitive near-field microscopy developed by Kobus Kuipers et al Balistreri et al., PRL (2000) Local measurement of amplitude AND phase.

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Scansize : x 8.1 m 2 pulses : 123 fs, = 1310 nm Time resolved motion through a W3 waveguide Group velocity < c/1000 PRL 94, (2005) photonic crystal waveguide Slow light Kobus Kuipers group at AMOLF

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3D Photonic Crystals Woodpile structures Colloidal crystals Inverse opals W.L. Vos [AMOLF] Photonic Bandgap: No propagation of light with frequencies within the bandgap for three directions ! Focused Ion Beam... S.Y. Lin et al, Nature 394 (1998) 251

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Infiltrated colloidal crystal: - silica colloidal crystal - infiltration with polystyrene - etching of silica Colvin, MRS Bulletin 26, (2001)

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Colloidal photonic crystals Colvin, MRS Bulletin 26, (2001)

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Three-dimensional Si photonic crystal Y. A. Vlasov et al., Nature 414, 289 (2001) S.-Y. Lin et al., Nature 394, 251 (1998)

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Fabrication of So woodpile crystal

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Superstructure in Si woodpile photonic crystal p-polarization, = 20° “zone-folding” M.J.A. de Dood et al. Phys. Rev. B 67, (2003)

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2d and 3D photonic crystals in III-V semiconductors Noda, MRS Bulletin 26, (2001) science fiction: lasers, modulators, bends, point defects integrated

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Noda, MRS Bulletin 26, (2001) Line defect and point defects in 2D photonic crystals: - photon trapping and emission Stoffer et al. Joannopoulos et al.

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Joannopoulos et al., Nature (1998)

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