The dependence of frequency and field on stochastic ordering in photonic band gap resonant structures

In recent years the application of 2-Dimensional (2D) metallic Photonic Crystal (PC) structures to high power microwave devices, such as particle accelerators and gyrotrons, has gained increased interest. The work presented here focuses on the effect disorder has on the resonant frequency and peak electric field in the defect site of a 2D PC structure. For disorders up to a maximum of 15% variation in position and radius, we found that disorder applied to the inner-most scatterers surrounding the defect site dominates in determining the peak field and resonant frequency of the structure. We also show that small disorder (~1%) can lead to an increase in peak field in certain cases. We find increasing levels of disorder lead to a decreasing average peak field for all structures. Whereas the mean resonant frequency remains constant for increasing disorder while the standard deviation increases. We then develop an understanding for this behaviour in terms of frequency detuning and mode confinement.