Modified Gouy phase in optical resonators with mixed boundary conditions, via the Born-Oppenheimer method

We investigate near-paraxial modes of high-finesse, plano-concave microresonators without using the paraxial approximation. The goal is to develop an analytical approach which is able to incorporate not only the spatial shape of the resonator boundaries, but also the dependence of reflectivities on angle of incidence. It is shown that this can be achieved using the Born-Oppenheimer method, augmented by a local Bessel wave approximation. We discuss how this approach extends standard paraxial theory. It is found that the Gouy phase of paraxial theory, which is determined purely by ray-optics, is no longer the sole parameter governing transverse mode splittings. The additional determining factor is the sensitivity with which boundary reflection phases depend on incident angle.