Optical modes in elliptical microcavities for single-photon sources

A theory of optical modes in an elliptical microcavity has been developed using Mathieu functions in elliptical coordinates. A key difference from the circular case is the splitting of doubly degenerate modes. Split optical modes have been numerically calculated and their symmetry has been determined. A method has been proposed to choose the parameters of a cavity for a certain wavelength. The difference between the energies of optical modes in the cavity with metallic walls and in the dielectric cavity is no more than $\sim$ 20%. The dispersion relations of optical modes show the possibility of degeneracy of modes with different symmetries, which allows the spectral and polarization filtering of radiation of single-photon sources and the fabrication of sources of multiply entangled states.