High-accuracy numerical models of Brownian thermal noise in thin mirror coatings

TL;DR

This paper introduces a high-accuracy, open-source numerical modeling approach for Brownian thermal noise in mirror coatings, significantly improving precision and efficiency, and enabling the first detailed modeling of crystalline coating layers for gravitational-wave detectors.

Contribution

It presents a novel discontinuous Galerkin method implemented in SpECTRE, achieving higher accuracy at lower computational cost and modeling crystalline coatings for the first time.

Findings

SpECTRE outperforms previous models in accuracy and efficiency.

First numerical modeling of crystalline coating layers.

Potential to optimize mirror designs for gravitational-wave detection.

Abstract

Brownian coating thermal noise in detector test masses is limiting the sensitivity of current gravitational-wave detectors on Earth. Therefore, accurate numerical models can inform the ongoing effort to minimize Brownian coating thermal noise in current and future gravitational-wave detectors. Such numerical models typically require significant computational resources and time, and often involve closed-source commercial codes. In contrast, open-source codes give complete visibility and control of the simulated physics, enable direct assessment of the numerical accuracy, and support the reproducibility of results. In this article, we use the open-source SpECTRE numerical relativity code and adopt a novel discontinuous Galerkin numerical method to model Brownian coating thermal noise. We demonstrate that SpECTRE achieves significantly higher accuracy than a previous approach at a fraction of the computational cost. Furthermore, we numerically model Brownian coating thermal noise in multiple sub-wavelength crystalline coating layers for the first time. Our new numerical method has the potential to enable fast exploration of realistic mirror configurations, and hence to guide the search for optimal mirror geometries, beam shapes and coating materials for gravitational-wave detectors.