Numerical modeling of on-threshold modes of eccentric-ring microcavity lasers using the Muller integral equations and the trigonometric Galerkin method

Abstract

We analyze on-threshold mode characteristics of eccentric-ring microcavity lasers, i.e. two-dimensional (2-D) models of thin circular disks made of gain material and pierced with circular air hole. As a tool of computational electromagnetics, we use the Muller boundary integral equations, discretized with trigonometric Galerkin method. This enables us to reduce the lasing eigenvalue problem to an infinite matrix equation with elements having explicit form as combinations of the cylindrical functions. Then the Fredholm second-kind nature of this equation guarantees the convergence of its eigenvalues, with greater matrix-truncation numbers, to exact values. Using the proposed algorithm, we calculate frequencies, threshold values of material gain index and directivities of emission of laser modes on threshold. Numerical experiments demonstrate that, by varying the location and size of the piercing hole, one can increase the directivity while preserving the threshold gain as low as in unperturbed circular cavity.