1. Photonic Bandgap (PBG) Concept
Electron moving in crystal periodic potential
Photon moving in periodic dielectric e
energy
bandgap

2. 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.

3. 1D, 2D, 3D synthetic PBGs
1D: Bragg Reflector D: Si pillar crystal D: colloidal crystal

4. Intuitive picture of PBG, 1D
Reflected waves cancel incident wave (Bragg reflection) means wave cannot propagate in medium
Yablonovitch, Scientific American Dec. 2001

5. Theory of photonic crystals
Starting with Maxwell’s Equations
Assuming linear low loss dielectrics
Separating time dependence
Wave Equation:
An eigen-problem, very similar to electrons in a crystal except vector operators, and vector solutions
Two polarisations!

6. Dispersion relation n1: high index material n2: low index material
Zijlstra, van der Drift, De Dood, and Polman (DIMES, FOM)
n1: high index material
n2: low index material
standing wave in n2 n1 n2 n1 n2 n1 n2 n1
frequency ω
bandgap
standing wave in n1
π/a
wave vector k

7. 1D Band Structures
Frequency, w
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.

8. 1D PBG: commercial example
Dielectric mirror
400 – 900 nm
Dichroic filters
Examples from Thorlabs

9. 2D Bandstructure square latticeTM TE
Photonic bandgap
PBG only for one polarisation

10. 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/

11. Propagation along line defect
light in
light out
after Mekis et al., Phys. Rev. Lett. 77, 3787 (1996)
high transmission, even around 90 degree bend
light confined to plane by usual index waveguiding
Zijlstra, van der Drift, De Dood, and Polman (DIMES, FOM)

12. Photonic Crystal Fibre
guiding by:
effective index
PBG
after Birks, Opt. Lett. 22, 961 (1997)

13. Preform Construction
Tubes are packed in a hexagonal shape with hollow, solid, birefringent, doped or tubular core elements.

14. 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

15. 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)
small material dispersion
after Knight, Optics & Photonics News, March 2002
Special applications:
guiding atoms in fiber by optical confinement
nonlinear interactions in gas-filled air holes

16. 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,

17. 3D Photonic Crystals Woodpile structures Inverse Opals
S.Y. Lin et al, Nature 394 (1998) 251
W.L. Vos [AMOLF]
for lots of information and more

18. 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.

19. Applications of PBG

20. 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