Aberrated optical cavities

TL;DR

This paper develops a comprehensive theory of optical cavity aberrations, incorporating non-paraxial propagation and complex mirror geometries, enabling more accurate modeling of high-finesse, small-waist cavities in quantum science.

Contribution

It introduces a complete theoretical framework for optical cavity aberrations, extending prior models to include non-paraxial effects and arbitrary mirror shapes, validated by experimental comparisons.

Findings

Good quantitative agreement with experimental non-planar lens cavities

Reconciles previous conflicting reports on aberration presence

Enables design of cavities with smaller waists and more degenerate modes

Abstract

Optical cavities are an enabling technology of modern quantum science: from their essential role in the operation of lasers, to applications as fly-wheels in atomic clocks and interaction-enhancing components in quantum optics experiments, developing a quantitative understanding of the mode-shapes and energies of optical cavities has been crucial for the growth of the field. Nonetheless, the standard treatment using paraxial, quadratic optics fails to capture the influence of optical aberrations present in modern cavities with high finesse, small waist, and/or many degenerate modes. In this work, we compute the mode spectrum of optical resonators, allowing for both non-paraxial beam propagation and beyond-quadratic mirrors and lenses. Generalizing prior works [1-5], we develop a complete theory of resonator aberrations, including intracavity lenses, non-planar geometries, and arbitrary mirror forms. Harnessing these tools, we reconcile the near-absence of aberration in Ref. [6] with the strongly evident aberrations in the seemingly similar cavity of Ref. [7]. We further validate our approach by comparison to a family of non-planar lens cavities realized in the lab, finding good quantitative agreement. This work opens new prospects for cavities with smaller waists and more degenerate modes.