Optimizing the topology of photonic crystals

The performance of photonic crystal devices can depend strongly on their geometry. Alas, their fundamental physics ofiers relatively little by way of pointers in terms of optimum shapes, so numerical design search techniques must be used in an attempt to determine high performance layouts. We discuss strategies for solving this type of optimization problem, the main challenge of which is the con∞ict between the enormous size of the space of potentially useful designs and the relatively high computational cost of evaluating the performance of putative shapes. The optimization technique proposed here operates over increasing levels of fldelity, both in terms of the resolution of its non-parametric shape deflnition and in terms of the resolution of the numerical analysis of the performance of putative designs. This is a generic method, potentially applicable to any type of electromagnetic device shape design problem. We also consider a methodology for assessing the robustness of the optima generated through this process, investigating