Nanophotonics

Class 3

Photonic Crystals

Definition:

A photonic crystal is a periodic arrangementof a dielectric materialthat exhibits strong interaction with light

Examples:

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

Bragg mirrorAntireflection coatings (Fresnel equations)

1D Photonic Crystals

Bragg’s law:

2naveragedcos() m

n1 n2 n1 n1 n1n2 n2

Dispersion relation

n1: high index materialn2: low index material

bandgap

freq

uen

cy ω

wave vector k0 π/a

standing wave in n1

standing wave in n2

n

ck

Bloch waves

modified slide from Rob Engelen

modified slide from Rob Engelen

frequ

ency

ω

wave vector k0 π/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 zonemodified slide from Rob Engelen

Band diagrams and group velocity of light

A light pulse with a center frequency w propagateswith group velocity vg, which is altered near the band gap

dk

dvg

Example

Dielectric mirror400 – 900 nm

Examples from Thorlabs

Dichroic filters

1D “photonic crystal” waveguide

Joannopoulos et al.

Morpho butterfly

Structure morpho butterfly wing

Mode calculationby 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 calculationwith FEMLABby Aarts TUE.

TM TE

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)

Zijlstra, van der Drift, De Dood, and Polman (DIMES, FOM)

Silicon-on-insulator (SOI)

Si

SiO2

Si neff 1.7

n 1.5

SiSiO2

2D Photonic Crystal: holes in semiconductor dielectric

H. Gersen et al., PRL 94, 073903 (2005)

Kobus Kuipers group at AMOLF

0 0.1 0.2 0.3 0.4 0.50.15

0.2

0.25

0.3

0.35

wavevector |k| (units 2

p/a)

frequ

ency

w (u

nit

s 2p

c/a) crystal

modes

crystalmodes

waveguidemodes

Aperture:~200 nm

500nm

Phase sensitive near-field microscopydeveloped by Kobus Kuipers et al

Balistreri et al., PRL 85 294 (2000)

Local measurement ofamplitude AND phase.

Scansize : 199.8 x 8.1 m2

pulses : 123 fs, = 1310 nm

• Time resolved motion through a W3 waveguide• Group velocity < c/1000

PRL 94, 073903 (2005)

photonic crystalwaveguide

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, 035322 (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)