Going beyond Gaussian beams in optical resonators with mixed boundary conditions

Optical microresonators find application in many fields of physics and engineering, from quantum optics to photonic engineering. Small size, unconventional geometry and the use of new material systems make these devices different from macroscopic resonators. In particular one encounters the limits of the paraxial approximation, a workhorse of optics that gives rise to the well-known Gaussian beams. Motivated by recent experimental progress, we have performed numerical simulations of dome-shaped microcavities, allowing for the effects of different mirror materials and geometries. We encounter spectral and spatial mode structure that falls outside of standard Gaussian-beam theory, such as an optical analogue of spin-orbit coupling where the polarization-dependent reflectivity of a realistic boundary plays an important role. This has prompted us to look for approximate analytical methods that can explain our numerical observations. In the process, we also gain an improved understanding of the paraxial approximation and its limitations.