Non paraxial resonator mode calculations in the small-waist limit: a local ray expansion for wave physics

The field of optical cavity QED has long relied on ABCD matrices to describe propagation, mode structure, and resonator stability. This works extremely well for low NA resonators with parabolic mirrors. Going to higher NA, or introducing non-quadratic optics, breaks this paradigm. In this talk, we present a local ray expansion that dramatically reduces the numerical complexity of mode calculations in the non-paraxial regime. By expanding the Huygen's integral about a ray-traced eikonal field, we arrive at a technique capable of fast mode calculations for not only beyond-paraxial resonators, but also for resonators with intracvity opticsc. We explore implications for near-concentric resonators, near degenerate resonators, cavities containing aspheric surfaces, axicon cavities, and more.