Numerical modeling of active microcavities with piercing holes using the Muller boundary integral equations and the Galerkin method

The current paper proposes a Galerkin method for calculating spectral characteristics of microcavity lasers with piercing holes. If boundaries of the cavity and holes are circles, then entries of the matrix have explicit expressions computed in the present work. Using the proposed algorithm, we calculate directivities, spectra, and thresholds of laser modes. Numerical experiments demonstrate that, by varying the location of the hole, we can increase the directivity, while the threshold gain stays low.