Nyström-method analysis of active spiral subwavelength 2-D microresonators

The lasing modes in the arbitrarily shaped active microcavity are considered as solutions to the 2-D linear eigenproblem for the Maxwell equations with exact boundary and radiation conditions. This problem can be reduced to the set of two coupled boundary integral equations with smooth or integrable kernels. Discrete form of these equations is built using the Nystrom-type algorithm and corresponding quadrature formulas. Then the search for the eigenvalues reduces to the calculation of the roots of determinantal equation that can be obtained with guaranteed accuracy. A numerical study of several modes in a ldquospiralrdquo microcavity is presented.