Dielectric profile segmentation used to reduce computation effort of the Fourier-Bessel mode solving technique

The Fourier-Bessel space conversion of Maxwell's wave equations into an eigenvalue formulation is a useful numerical tool for computing the steady states of cylindrically symmetric dielectric structures. The relative dielectric profile, inverse (1/ε_r) present in wave equations, is split into a constant offset and corresponding spatially dependent residue and greatly reduces the matrix building time (and thus computation time) when alternate dielectric configurations are considered with identical spatial distributions. Such a process significantly speeds up the theoretical analysis of numerous optical designs, such as index of refraction sensors, hole infiltration sensors and resonator tuning. The theoretical steps involved are presented along with examples of the technique applied to the well-known Bragg resonator and central defect containing hexagonal array.