Impact of beamsplitter thermal distortions for next-generation gravitational-wave detector design

Gravitational-wave detectors are revolutionizing astrophysics by providing a fundamentally new means to observe the universe. This study focuses on the upgrades of current detectors and the design of next-generation detectors aimed at enhancing their quantum-limited sensitivity and astrophysical reach. Increasing the circulating optical power to megawatt levels is central to achieving these goals, but is limited by thermal distortions due to laser power absorption in the core interferometer optics. Current gravitational-wave detectors have Thermal Compensation Systems (TCS) to mitigate these distortions on the test masses. We show that in the era of LIGO A# and beyond, similar TCS measures will also need to be implemented on the beamsplitter to enable the planned increase in circulating power. We present an analysis of the effects of thermally induced distortions on the beamsplitter for the case of the A# LIGO detector upgrade, exploring the parameter space to identify an optimal configuration of optic parameters and TCS correction. We show that this issue is also fundamental to future gravitational-wave detectors, including Cosmic Explorer. We show how this issue, in fact, may drive the Cosmic Explorer design to an optical layout very different from LIGO.