Numerically efficient multipole method for photonic molecules

A novel and numerically efficient multipole formulation for the calculation of resonances of photonic molecules is presented. Photonic molecules are often modeled as two dimensional coupled dielectric disks. We use the multipole expansion of the individual fields and formulate the boundary conditions in terms of a generalized eigenvalue problem. The complex root search is simplified by studying the flow of the eigenvalues, where we argue that the motion of the eigenvalues in the complex plane is analytic with respect to a two parameter family. Based on this analytic behavior we present a numerical algorithm to compute a range of photonic molecule resonances and field distributions using only two diagonalizations.