Using aberrations for small waists and degenerate optical cavities

Optical resonators enable strong interactions between single photons and atoms. Despite their ubiquity in both classical and quantum optics, relatively little work has explored these resonators beyond their simplest description: paraxial, quadratic optics. That description is inadequate for cavities with high-finesse, small waist, and/or many degenerate modes. In this talk I will present new theoretical frameworks to describe optical cavities beyond this first approximation. I will show experimental data validating the aberrated spectra of a non-planar, 17 μm-waist degenerate resonator using intracavity lenses compatible with finesse over 10⁵. I will discuss the engineering of spectrum aberrations, including a paraxially unstable geometry stabilized by aberrations. This cavity will be used to explore fractional quantum Hall physics with Rydberg polaritons.