Nanophotonics Class 3 Photonic Crystals

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

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

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

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

Bloch waves modified slide from Rob Engelen

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

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

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

1D “photonic crystal” waveguide Joannopoulos et al.

Morpho butterfly

Structure morpho butterfly wing Mode calculation by Gralak et al.

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

Photonic crystals in two dimensions

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

TMTE Bandstructure for two polarizations Photonic bandgap

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

Photonic crystal waveguides Joannopoulos et al.

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

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

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

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.

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

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

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

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

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

Fabrication of So woodpile crystal

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

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

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

Joannopoulos et al., Nature (1998)