Spectra, Thresholds, and Modal Fields of a Triangular Microcavity Laser

© 2018 IEEE. We study the modes of a triangular microcavity laser, namely the frequencies of emission, threshold values of gain, and mode field patterns, within the classical electro-magnetics approach. Our instrument is the accurate formalism of Lasing Eigenvalue Problem (LEP), i.e. boundary-value problem with full set of the boundary and radiation conditions. The LEP is reduced to a nonlinear eigenvalue problem for the Muller integral equation on the cavity's boundary. Discretizing it with a Nyström approximation of weakly singular integral operators, we obtain a characteristic equation for the mode frequencies and thresholds