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.
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