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Photonic Bandgap (PBG) Concept
• Electron moving in crystal
periodic potential
• Photon moving in periodic
dielectric
energy
e
bandgap
Natural PBG
• The bandgap effect can be found in nature, where bright
colors that are seen in butterfly wings and opals are the
result of naturally occurring periodic microstructures.
1D, 2D, 3D synthetic PBGs
1D: Bragg Reflector
2D: Si pillar crystal
3D: colloidal crystal
Intuitive picture of PBG, 1D
Reflected waves cancel incident wave (Bragg reflection)
means wave cannot propagate in medium
Yablonovitch, Scientific American Dec. 2001
Theory of photonic crystals
• Starting with Maxwell’s Equations
– Assuming linear low loss dielectrics
– Separating time dependence
– Wave Equation:
 1
  
  
  Hr     Hr 
  r 
 c
2
– An eigen-problem, very similar to electrons in a
crystal except vector operators, and vector solutions
– Two polarisations!
Dispersion relation
Zijlstra, van der Drift, De Dood, and Polman (DIMES, FOM)
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
n1 n2
n1 n2 n1 n2 n1
Frequency, 
1D Band Structures
Spatial frequency, k
• On-axis propagation shown for three different multilayer
films, all of which have layers of width 0.5a.
– Left: Each layer has the same dielectric constant. ε = 13.
– Center: Layers alternate between ε = 13 and ε = 12.
– Right: Layers alternate between ε = 13 and ε = 1.
• Gap increases as dielectric contrast increases.
1D PBG: commercial example
Dielectric mirror
400 – 900 nm
Dichroic filters
Examples from Thorlabs
2D Bandstructure square lattice
TM
TE
Photonic bandgap
PBG only for one polarisation
Defect in a 2D PBG Crystal
• Removing
cylinder = defect
• Leads to
localised mode
in the gap
– transmission
peak in the
forbidden band.
Joannopoulos, jdj.mit.edu/
Propagation along line defect
• high transmission, even
around 90 degree bend
light out
• light confined to plane by
usual index waveguiding
light in
Zijlstra, van der Drift, De Dood, and Polman (DIMES, FOM)
Photonic Crystal Fibre
• guiding by:
- effective index
- PBG
after Birks, Opt. Lett. 22, 961 (1997)
Preform Construction
Tubes are packed in a hexagonal shape with hollow,
solid, birefringent, doped or tubular core elements.
Small-core holey fiber
after Knight, Optics & Photonics News, March 2002
• High birefringence
• effective index of “cladding” is close to that of air (n=1)
• anomalous dispersion over wide  range (enables soliton
transmission)
• can tailor flat dispersion for phase-matching
Holey fiber with large hollow core
• high power transmission
without nonlinear optical
effects (light mostly in air)
• losses now ~1 dB/m (can be
lower than index-guiding
fiber, in principle)
after Knight, Optics & Photonics
News, March 2002
• small material dispersion
Special applications:
• guiding atoms in fiber by optical confinement
• nonlinear interactions in gas-filled air holes
First 3D PBG material: yablonovite
• Full Photonic Bandgap: No
propagation of light with
frequencies within the bandgap
for any direction
• First prediction of full PBG
– FCC symmetry (ABCABC
stacking)
– require n > 1.87
After Yablonivitch, www.ee.ucla.edu/~pbmuri/
3D Photonic Crystals
•Woodpile structures
•Inverse Opals
W.L. Vos [AMOLF]
1 m
S.Y. Lin et al, Nature 394 (1998) 251
www.photonicbandgaps.com for lots of information and more
Future? Tunable 3D Inverse Opal
Structure
• An inverse opal photonic crystal structure
partially infiltrated with liquid crystal molecules.
• Electro-optic tuning can cause the bandgap to
wink in and out of existence.
Applications of PBG
Advantages of Optical
Communications
• Immunity to electrical interference
– aircraft, military, security, chip to chip
interconnects
• Cable is lightweight, flexible, robust
– efficient use of space in conduits
• Higher data rates over longer distances
– more “bandwidth” for internet traffic