  Laser-driven acceleration holds great promise for significantly improving
accelerating gradient. However, scaling the conventional process of
structure-based acceleration in vacuum down to optical wavelengths requires a
substantially different kind of structure. We require an optical waveguide that
(1) is constructed out of dielectric materials, (2) has transverse size on the
order of a wavelength, and (3) supports a mode with speed-of-light phase
velocity in vacuum. Photonic crystals--structures whose electromagnetic
properties are spatially periodic--can meet these requirements.
  We discuss simulated photonic crystal accelerator structures and describe
their properties. We begin with a class of two-dimensional structures which
serves to illustrate the design considerations and trade-offs involved. We then
present a three-dimensional structure, and describe its performance in terms of
accelerating gradient and efficiency. We discuss particle beam dynamics in this
structure, demonstrating a method for keeping a beam confined to the waveguide.
  We also discuss material and fabrication considerations. Since accelerating
gradient is limited by optical damage to the structure, the damage threshold of
the dielectric is a critical parameter. We experimentally measure the damage
threshold of silicon for picosecond pulses in the infrared, and determine that
our structure is capable of sustaining an accelerating gradient of 300 MV/m at
1550 nm. Finally, we discuss possibilities for manufacturing these structures
using common microfabrication techniques.
