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.
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BibTeX
@misc{laeuger2026mathematical,
title = {{Mathematical framework for simulation of non-perturbative cavity optomechanics with plate-like dielectrics}},
author = {Andrew Laeuger and Nancy Aggarwal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17475},
eprint = {2610.17475},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17475},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Mathematical framework for simulation of non-perturbative cavity optomechanics with plate-like dielectrics
AU - Andrew Laeuger
AU - Nancy Aggarwal
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17475
UR - https://arxiv.org/abs/2610.17475
AB - 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.
ER -