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Nanophotonics
Class 4
Photonic Crystals
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Definition:
A photonic crystal is a periodic arrangementof a dielectric materialthat 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 mirrorAntireflection coatings (Fresnel equations)
1D Photonic Crystals
Bragg’s law:
2naveragedcos() m
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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
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Bloch waves
modified slide from Rob Engelen
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modified slide from Rob Engelen
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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
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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
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Example
Dielectric mirror400 – 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 calculationby 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 calculationwith FEMLABby Aarts TUE.
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TM TE
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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Zijlstra, van der Drift, De Dood, and Polman (DIMES, FOM)
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Silicon-on-insulator (SOI)
Si
SiO2
Si neff 1.7
n 1.5
SiSiO2
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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
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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.
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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
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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, 035322 (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)