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arXiv · 2610.17475

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

Andrew Laeuger·Nancy Aggarwal
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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.

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Andrew Laeuger, Nancy Aggarwal. 2026-10-12. Mathematical framework for simulation of non-perturbative cavity optomechanics with plate-like dielectrics. https://arxiv.org/abs/2610.17475

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