Mathematical model of thermal shields for long-term stability optical resonators

TL;DR

This paper introduces an analytical model to efficiently evaluate and optimize passive thermal shields for optical resonators, enhancing long-term stability crucial for high-precision physics experiments.

Contribution

It presents a novel analytical approach to predict thermal shield performance, reducing reliance on complex numerical simulations and enabling faster design iterations.

Findings

Analytical model accurately predicts thermal shield behavior.

Identification of transfer function dips at specific frequencies.

Model validated against finite element numerical simulations.

Abstract

Modern experiments aiming at tests of fundamental physics, like measuring gravitational waves or testing Lorentz Invariance with unprecedented accuracy, require thermal environments that are highly stable over long times. To achieve such a stability, the experiment including typically an optical resonator is nested in a thermal enclosure, which passively attenuates external temperature fluctuations to acceptable levels. These thermal shields are usually designed using tedious numerical simulations or with simple analytical models. In this paper, we propose an accurate analytical method to estimate the performance of passive thermal shields in the frequency domain, which allows for fast evaluation and optimization. The model analysis has also unveil interesting properties of the shields, such as dips in the transfer function for some frequencies under certain combinations of materials and geometries. We validate the results by comparing them to numerical simulations performed with commercial software based on finite element methods.