Nanophotonics
Class 4
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)