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

Higher-order Laguerre-Gauss (LG) modes have previously been investigated as acandidate for reducing test-mass thermal noise in ground-basedgravitational-wave detectors like Advanced LIGO. It has been shown however thatLG modes' fragility against mirror surface figure imperfections limits theircompatibility with the current state-of-the-art test masses. In this paper weexplore the alternative of using higher-order Hermite-Gauss (HG) modes forthermal noise reduction, and show that with the deliberate addition ofastigmatism they are orders of magnitude more robust against mirror surfacedistortions than LG modes of equivalent order. We present simulations ofAdvanced LIGO-like arm cavities with realistic mirror figures which can supportHG$_{33}$ modes with average arm losses and contrast defects in a Fabry-PerotMichelson interferometer configuration which are well below the typicalmeasured values in Advanced LIGO. This demonstrates that the mirror surfaceflatness errors will not be a limiting factor for the use of these modes infuture gravitational-wave detectors.