Effects of mirror birefringence and its fluctuations to laser interferometric gravitational wave detectors

TL;DR

This paper analyzes how mirror birefringence and its fluctuations impact the sensitivity of laser interferometric gravitational wave detectors, providing estimates for acceptable fluctuation levels in materials like silicon and AlGaAs.

Contribution

It offers an analytical estimation of birefringence effects and fluctuations in mirror substrates and coatings, crucial for future detector sensitivity optimization.

Findings

Birefringence fluctuations must be below 10^{-8} rad/√Hz in silicon substrates.

Fluctuations should be below 10^{-10} rad/√Hz in AlGaAs coatings.

Optical cavity response significantly affects depolarization-related optical losses.

Abstract

Crystalline materials are promising candidates as substrates or high-reflective coatings of mirrors to reduce thermal noises in future laser interferometric gravitational wave detectors. However, birefringence of such materials could degrade the sensitivity of gravitational wave detectors, not only because it can introduce optical losses, but also because its fluctuations create extra phase noise in the arm cavity reflected beam. In this paper, we analytically estimate the effects of birefringence and its fluctuations in the mirror substrate and coating for gravitational wave detectors. Our calculations show that the requirements for the birefringence fluctuations in silicon substrate and AlGaAs coating will be on the order of $10^{-8}$ and $10^{-10}$ rad/$\sqrt{\rm Hz}$ at 100~Hz, respectively, for future gravitational wave detectors. We also point out that optical cavity response needs to be carefully taken into account to estimate optical losses from depolarization.