Dispersion Engineering and Disorder in Photonic Crystals

The possibility of achieving higher accelerating gradients at higher frequencies with the reduction of the effect of HOMs, compared to conventional accelerating structures, is increasing interest in the possible use of Photonic Crystals (PC) for accelerator applications. In this paper we analyze how the properties of the lattice of a PC resonator can be engineered to give a specific band structure, and how by tailoring the properties of the lattice specific EM modes can either be confined or moved into the propagation band of the PC. We further go on to discuss the role of disorder in achieving mode confinement and how this can be used to optimize both the Q and the accelerating gradient of a PC based accelerating structure. We also examine the use of high disorder to give rise to Anderson Localization, which gives rise to exponential localization of an EM mode. Discussing the difference between the extended Bloch wave, which extends over the entire PC, and the Anderson localized mode.