Higher-order Hermite-Gauss modes as a robust flat beam in interferometric gravitational wave detectors

TL;DR

This paper proposes higher-order Hermite-Gauss modes as a more robust alternative to Laguerre-Gauss modes for reducing thermal noise in gravitational wave detectors, demonstrating their resilience to mirror imperfections through simulations.

Contribution

It introduces the use of astigmatism-enhanced Hermite-Gauss modes for thermal noise reduction, showing they are more tolerant to mirror surface distortions than Laguerre-Gauss modes.

Findings

HG modes can be supported with low losses in realistic mirror conditions

Astigmatism improves the robustness of HG modes against surface imperfections

Mirror surface errors are unlikely to limit future detector performance

Abstract

Higher-order Laguerre-Gauss (LG) modes have previously been investigated as a candidate for reducing test-mass thermal noise in ground-based gravitational-wave detectors like Advanced LIGO. It has been shown however that LG modes' fragility against mirror surface figure imperfections limits their compatibility with the current state-of-the-art test masses. In this paper we explore the alternative of using higher-order Hermite-Gauss (HG) modes for thermal noise reduction, and show that with the deliberate addition of astigmatism they are orders of magnitude more robust against mirror surface distortions than LG modes of equivalent order. We present simulations of Advanced LIGO-like arm cavities with realistic mirror figures which can support HG$_{33}$ modes with average arm losses and contrast defects in a Fabry-Perot Michelson interferometer configuration which are well below the typical measured values in Advanced LIGO. This demonstrates that the mirror surface flatness errors will not be a limiting factor for the use of these modes in future gravitational-wave detectors.