Power coupling losses for misaligned and mode-mismatched higher-order Hermite–Gauss modes

This paper analytically and numerically investigates misalignment mode-mismatch induced power coupling coefficients losses as a function of Hermite Gauss (HG) mode order. We show that higher-order HG modes are more susceptible to beam perturbations when, for example, into optical cavities: the mode-mismatch-induced scale linearly quadratically with respect indices respectively. As result, tolerance $\mathrm{HG}_{3,3}$ is reduced factor 0.28 relative currently-used $\mathrm{HG}_{0,0}$ mode. potential hurdle using reduce thermal noise in future gravitational-wave detectors.