Photonic crystals provide a method of confining a synchronous speed-of-light mode in an all-dielectric structure, likely a necessary feature in any optical accelerator. We explore computationally a class of photonic crystal structures with translational symmetry in a direction transverse to the electron beam. We demonstrate synchronous waveguide modes and discuss relevant parameters of such modes. We then explore how accelerator parameters vary as the geometry of the structure is changed and consider trade-offs inherent in the design of an accelerator of this type.
