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Proposed near-future upgrades of the current advanced interferometricgravitational wave detectors include the usage of frequency dependent squeezedlight to reduce the current sensitivity-limiting quantum noise. We quantify anddescribe the degradation effects that spatial mode-mismatches between opticalresonators have on the squeezed field. These mode-mismatches can to first orderbe described by scattering of light into second-order Gaussian modes. As ademonstration of principle, we also show that squeezing the second-orderHermite-Gaussian modes $\mathrm{HG}_{02}$ and $\mathrm{HG}_{20}$, in additionto the fundamental mode, has the potential to increase the robustness tospatial mode-mismatches. This scheme, however, requires independently optimizedsqueeze angles for each squeezed spatial mode, which would be challenging torealise in practise.

Multi-spatial-mode effects in squeezed-light-enhanced interferometric gravitational wave detectors