Nystrom-type technique for numerical analysis of lasing spectra and thresholds in arbitrary-shaped active 2-D microcavities

The lasing modes in the arbitrarily shaped microcavity are considered as solutions to the 2-D linear eigenproblem for the Maxwell equations with exact boundary and radiation conditions. The gain is introduced into the cavity material within the active region via the ldquoactiverdquo imaginary part of the refractive index, and the modal frequencies and threshold values of gain are sought as the eigenvalues. 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 exponentially convergent Nystrom-type algorithm. Then the search for the eigenvalues reduces to the calculation of the roots of determinantal equation that can be obtained with guaranteed accuracy.