  Photonic crystals have great potential for use as laser-driven accelerator
structures. A photonic crystal is a dielectric structure arranged in a periodic
geometry. Like a crystalline solid with its electronic band structure, the
modes of a photonic crystal lie in a set of allowed photonic bands. Similarly,
it is possible for a photonic crystal to exhibit one or more photonic band
gaps, with frequencies in the gap unable to propagate in the crystal. Thus
photonic crystals can confine an optical mode in an all-dielectric structure,
eliminating the need for metals and their characteristic losses at optical
frequencies.
  We discuss several geometries of photonic crystal accelerator structures.
Photonic crystal fibers (PCFs) are optical fibers which can confine a
speed-of-light optical mode in vacuum. Planar structures, both two- and
three-dimensional, can also confine such a mode, and have the additional
advantage that they can be manufactured using common microfabrication
techniques such as those used for integrated circuits. This allows for a
variety of possible materials, so that dielectrics with desirable optical and
radiation-hardness properties can be chosen. We discuss examples of simulated
photonic crystal structures to demonstrate the scaling laws and trade-offs
involved, and touch on potential fabrication processes.
