Transcript Photonic Crystals - Photonic Materials Group

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
1D Photonic Crystals
Bragg mirror
Antireflection coatings (Fresnel equations)
Bragg’s law:
2naverage d cos( )  m
Dispersion relation
n1: high index material
n2: low index material
frequency ω
standing wave in n2
bandgap
standing wave in n1
0
π/a
wave vector k
c
k
n
n1 n2 n1 n2 n1 n2 n1
Bloch waves
modified slide from Rob Engelen
modified slide from Rob Engelen
frequency ω
-π/a
0
π/a
wave vector k
This is called the first Brillouin zone
Bloch wave with
wave vector k is
equal to Bloch
wave with wave
vector k+m2p/a:
modified slide from Rob Engelen
Band diagrams and group velocity of light
A light pulse with a center frequency w propagates
with group velocity vg, which is altered near the band gap
d
vg 
dk
Example
Dielectric mirror
400 – 900 nm
Dichroic filters
Examples from Thorlabs
1D “photonic crystal” waveguide
Joannopoulos et al.
Morpho butterfly
Structure morpho butterfly wing
Mode calculation
by Gralak et al.
Density of optical states in photonic crystals
Band gap: no propagation possible at that frequency:
Density of optical states (DOS) is 0
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.
Bandstructure for two polarizations
TM
Photonic bandgap
TE
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
neff  1.7
n
 1.5
Si
Si
SiO2
2D Photonic Crystal: holes in semiconductor dielectric
frequency w (units 2pc/a)
0.35
crystal
modes
0.3
waveguide
modes
0.25
crystal
modes
0.2
0.15
0
0.1
0.2
0.3
0.4
0.5
wavevector |k| (unitsp/a)
2
H. Gersen et al., PRL 94, 073903 (2005)
Kobus Kuipers group at AMOLF
Phase sensitive near-field microscopy
developed by Kobus Kuipers et al
500nm
Aperture:
~200 nm
Local measurement of
amplitude AND phase.
Balistreri et al., PRL 85 294 (2000)
Slow light
photonic crystal
waveguide
Scansize : 199.8 x 8.1 mm2
pulses : 123 fs,  = 1310 nm
• Time resolved motion through a W3 waveguide
• Group velocity < c/1000
Kobus Kuipers group at AMOLF
PRL 94, 073903 (2005)
3D Photonic Crystals
•Woodpile structures
•Colloidal crystals
•Inverse opals
•Focused Ion Beam
•...
Photonic Bandgap: No propagation of light with frequencies within
the bandgap for three directions !
W.L. Vos [AMOLF]
1 mm
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
S.-Y. Lin et al., Nature 394, 251 (1998)
Y. A. Vlasov et al., Nature 414, 289 (2001)
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
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.
Noda, MRS Bulletin 26, (2001)
Joannopoulos et al.
Joannopoulos et al., Nature (1998)