Quick root searching method for resonances of dielectric optical microcavities with the boundary element method

In this paper, we developed an efficient method for searching the resonant eigenfrequency of dielectric optical microcavities by the boundary element method. By transforming the boundary integral equation to a general eigenvalue problem for arbitrary, symmetric, and multi-domain shaped optical microcavities, we analyzed the regular motion of the eigenvalues against the frequency. The new strategy can predict multiple resonances, increase the speed of convergence, and avoid non-physical spurious solutions. These advantages greatly reduce the computation time in the search process of the resonances. Moreover, this method is not only valuable for dielectric microcavities, but is also suitable for other photonic systems with dissipations, whose resonant eigenfrequencies are complex numbers.