Thermal Deformation Reduction in High-Power Interferometry with Higher-Order Laser Modes

Test-mass thermal noise is a limiting noise source for current and next-generation ground-based gravitational-wave observatories. Uniform-intensity higher-order laser beams, including Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) modes, have been proposed as alternatives to the fundamental Gaussian beam due to their thermal-noise advantages. As interferometer power increases toward the megawatt regime, thermal aberrations from absorption in the test-mass coatings become increasingly significant. In this work, we quantify the robustness of higher-order modes against absorption-induced thermal deformation. We show that, under identical operating conditions, higher-order modes produce substantially more uniform thermal distortions than the fundamental mode, requiring significantly less thermal compensation power. The optimal curvature correction is reduced to 33% for the LG$_{2,2}$ mode and 24% for the HG$_{3,3}$ mode relative to the fundamental mode. We further show that the residual thermal deformation of higher-order modes results in lower optical loss, larger cavity power buildup, and improved modal purity in an aLIGO-like cavity. In addition, astigmatism compensation further enhances the intracavity purity of HG modes under self-heating-induced deformation. These results demonstrate that higher-order modes not only mitigate thermal noise but also intrinsically reduce beam self-heating effects, making them promising candidates for future high-power gravitational-wave interferometers.