Coating thermal noise for arbitrary shaped beams

TL;DR

This paper derives a simple integral formula to quantify how different beam shapes affect coating thermal noise in gravitational wave detectors, enabling comparison of noise performance for various beam profiles.

Contribution

It introduces a universal integral expression that characterizes coating thermal noise dependence on beam shape, applicable to all low-frequency thermal noise forms.

Findings

Integral formula for thermal noise dependence on beam shape

Enables comparison of Gaussian and non-Gaussian beams

Applicable to all low-frequency thermal noise types

Abstract

Advanced LIGO's sensitivity will be limited by coating noise. Though this noise depends on beam shape, and though nongaussian beams are being seriously considered for advanced LIGO, no published analysis exists to compare the quantitative thermal noise improvement alternate beams offer. In this paper, we derive and discuss a simple integral which completely characterizes the dependence of coating thermal noise on shape. The derivation used applies equally well, with minor modifications, to all other forms of thermal noise in the low-frequency limit.