Mathematical framework for simulation of non-perturbative cavity optomechanics with plate-like dielectrics

Abstract:Cavity optomechanical models typically treat a sensor either as a perturbative polarizable object in a pre-existing optical field, or solve the field at a fixed equilibrium and linearize in a fixed optical-mode basis. Neither self-consistently determines the spatially resolved cavity field, the optical force, the mechanical equilibrium, and the back-action when a finite-thickness dielectric plate intercepts the entire optical mode and restructures the intracavity field. In this companion paper to [1], we develop that treatment by extending the vacuum two-photon formalism to finite-thickness planar dielectrics, incorporating their Fresnel reflection, internal propagation, optical forces, and mechanical back-action directly into the field equations. We derive the carrier and sideband transfer functions needed to describe the coupled optical-mechanical system, including optomechanical cooling and the response to external perturbations. The result is a systematic starting point for calculating detector response and noise budgets for cavity experiments with intracavity dielectrics, including gravitational wave detectors deploying levitated sensors.

General Relativity and Quantum Cosmology (gr-qc); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Optics (physics.optics); Quantum Physics (quant-ph)

arXiv:2610.17475 [gr-qc]

(or arXiv:2610.17475v1 [gr-qc] for this version)

https://doi.org/10.48550/arXiv.2610.17475 arXiv-issued DOI via DataCite (pending registration)