Photonic Bandgap (PBG) Concept Electron moving in crystal periodic potential Photon moving in periodic dielectric e energy 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: An eigen-problem, very similar to electrons in a crystal except vector operators, and vector solutions Two polarisations!

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

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.

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 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)

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) 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

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 S.Y. Lin et al, Nature 394 (1998) 251 W.L. Vos [AMOLF] 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