A fast and accurate method is developed to compute the natural frequencies and scattering characteristics of arbitrary-shape two-dimensional dielectric resonators. The problem is formulated in terms of a uniquely solvable set of second-kind boundary integral equations and discretized by the Galerkin method with angular exponents as global test and trial functions. The log-singular term is extracted from one of the kernels, and closed-form expressions are derived for the main parts of all the integral operators. The resulting discrete scheme has a very high convergence rate. The method is used in the simulation of several optical microcavities for modern dense wavelength-division-multiplexed systems.
© 2004 Optical Society of America
(000.3860) General : Mathematical methods in physics
(140.4780) Lasers and laser optics : Optical resonators
(230.5750) Optical devices : Resonators
(260.2110) Physical optics : Electromagnetic optics
(290.0290) Scattering : Scattering
Svetlana V. Boriskina, Phillip Sewell, Trevor M. Benson, and Alexander I. Nosich, "Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization," J. Opt. Soc. Am. A 21, 393-402 (2004)