Sensitivity analysis for photonic crystal microcavities

Resonant modes in photonic crystal microcavities with large quality factors and small mode volumes are important in many applications, but they are very sensitive to geometric and physical parameters of the structure. In this paper, we develop an efficient method for computing the partial derivatives of the complex resonant frequency with respect to parameters such as radii, refractive indices, and positions of the circular cylinders, for two-dimensional photonic crystal microcavities. Like the adjoint variable method for sensitivity analysis, our method is capable of rapidly calculating the partial derivatives with respect to a large number of geometric and material parameters. The method is efficient, since it takes advantage of the many identical unit cells in photonic crystal devices and the analytic solutions for circular cylindrical structures.