Thresholds of lasing and modal patterns of a limacon cavity analysed with Muller´s integral equations

We consider the lasing characteristics of the natural modes in a limacon active microcavity. The modes are the solutions to the two-dimensional (2-D) linear eigenproblem for the Maxwell equations with exact boundary conditions and radiation condition at infinity. This problem is reduced equivalently to the set of Muller´s integral equations of the Fredholm second kind and discretized using the exponentially convergent quadrature formulas. The numerical studies of lasing thresholds and modal field patterns of the whispering-gallery modes are presented. They demonstrate that the directionality of emission from a cavity deformed from the circle can be enhanced in several times using relatively small deformations. However this is achieved at the expense of higher threshold values.