Modeling a convex–concave ultra-stable optical cavity

The current performance of the state-of-the-art Fabry–Pérot optical resonators is limited by thermal processes through an energy dissipation mechanism. The dominant source of noise in both long-range interferometers and table-top ultra-stable cavities is the µm thick layer of highly reflective Bragg mirrors. Depending on the material used in mirror substrates, reflective coatings, and cavity temperature, the dominant noises that limit the stability of the cavity include Brownian, thermoelastic, and thermo-optic noises. We propose enhancing the beam spot size on the mirror surface to overcome current thermal limitations by applying the convex–concave configuration. We present the theoretical investigations of the convex–concave mirrors design for ultra-stable cavity purposes and prove that this configuration can significantly reduce Brownian coating noise. We prove the feasibility of the proposed design by verifying its stability conditions.