Higher-order Laguerre-Gaussian (LG) modes form a versatile family of structured optical fields with broader and more uniform transverse intensity distributions than the commonly used fundamental Gaussian mode. These properties make them attractive for precision optical applications, including gravitational-wave detectors, where enhanced spatial averaging of thermally driven test-mass fluctuations can reduce thermal noise. Their practical implementation in precision optical applications, however, requires efficient coupling of the injected beam to the target spatial mode, such as an optical-cavity eigenmode. Residual misalignment and mode mismatch couple power out of the desired spatial mode, thereby reducing the intracavity power buildup and degrading the detector sensitivity. In this work, we analytically and numerically evaluate the power coupling loss induced by misalignment and mode mismatch for a generic ${\mathrm{LG}}_{p,\ell }$ beam. We show that the leading-order loss due to angular or lateral misalignment scales as $2p+|\ell |+1$, while the loss due to waist size or waist position mismatch scales as $2p^2+2p+(2p+1)|\ell |+1$. These results provide a quantitative reference for assessing the coupling robustness of higher-order LG modes in realistic optical cavities. While the sensitivity to imperfect mode coupling generally increases with mode order, the donut-shaped ${\mathrm{LG}}_{0,\ell }$ family exhibits a particularly favorable mode-mismatch scaling, with the loss factor reducing to $|\ell |+1$ and therefore increasing only linearly with the azimuthal index. This enhanced robustness to mode mismatch, together with their broader intensity profiles and large central dark regions that enable selective mirror masking, as suggested in recent work, provides an additional practical motivation for using ${\mathrm{LG}}_{0,\ell }$ modes in precision interferometers such as gravitational-wave detectors.

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• Gravitational waves
• Lasers
• Cavity resonators
• Gravitational wave detectors
• Laser techniques