# Photonic crystal

Original Entry: Ian Bruce Burgess Fall 2009

## Definition

A photonic crystal is a dielectric superlattice whose refractive index varies periodically in three dimensions. The simplest type of photonic crystal is a single-component dielectric with high refractive-index which has a periodic lattice of air holes. With sufficiently high refractive index-contrast, the lattice forbids the propagation of light in all direction over a specific frequency range. This range is called the photonic crystal's band gap. The band-gap arises due to interference from periodic scattering and is a 3D extension of the concept of a Bragg mirror. In a 1D Bragg mirror of infinite length, the center-frequency of the band-gap is determined by the quarter-wave condition and the bandgap width or Bragg mirror strength is determined by the refractive-index contrast, which determines the strength of scattering from a single interface. In multi-dimensional photonic crystals, a complete bandgap exists if there is sufficient symmetry and index contrast such that the stop-bands in each direction have a common overlap region. Increased isotropy in the crystal brings the center-gap frequencies for each direction together, thus requiring smaller index contrast (gap width) to open up a complete bandgap. For example, an fcc structure requires a minimum index contrast of ~2.8:1 while a diamond lattice requires only ~2.0:1.

## References

1. Y.A. Vlasov, X.-Z. Bo, J.C. Sturm, D.J. Norris, *Nature* **414**, 289-293 (2001).

2. A. Blanco et al., *Nature* **405**, 437-440 (2000).

3. Y.A. Vlasov et al. *Phys. Rev. E* **61**, 5784 (2000).