Designing photonic bandgap fibers for particle acceleration

Photonic bandgap (PBG) fibers with hollow core defects have been suggested for use as laser driven accelerator structures. The modes of a photonic crystal fiber lie in a set of allowed bands. A fiber with a central vacuum defect can support so-called defect modes with frequencies in the bandgap and electromagnetic fields confined spatially near the defect. A defect mode suitable for relativistic particle acceleration must have a longitudinal electric field in the central defect and a phase velocity at the speed of light (SOL). We explore the design of the defect geometry to support well confined accelerating modes in such PBG fibers. The dispersion diagram of an accelerating mode must cross the SOL line, and such modes form a special class of defect modes known as surface modes, which are lattice modes of the original PBG crystal that have been perturbed into the bandgap. The details of the surface boundary separating the defect from the surrounding PBG matrix are found to be the critical ingredients for optimizing the accelerator mode properties.