AI 中文总结
研究引力波探测器中拉盖尔 - 高斯模式对失准和模式失配的灵敏度，通过解析和数值评估耦合损耗，发现LG\(_{0,\ell}\)家族模式失配缩放特性有利，为精密干涉仪应用提供动机。
AI 中文摘要
高阶拉盖尔 - 高斯（LG）模式比基模高斯模式具有更宽且更均匀的横向强度分布，在引力波探测器中能减少热噪声。但其实现需将注入光束高效耦合到目标腔本征模。残余失准和模式失配会使功率耦合出所需模式，降低腔内功率积累和探测器灵敏度。本文通过解析和数值方法评估了一般LG\(_{p,\ell}\)光束因失准和模式失配引起的耦合损耗。结果表明，角向或横向失准导致的主导阶损耗与\(2p + |\ell| + 1\)成正比，腰尺寸或腰位置失配导致的损耗与\(2p^2 + 2p + (2p + 1)|\ell| + 1\)成正比。虽然对不完全耦合的灵敏度通常随模式阶数增加，但LG\(_{0,\ell}\)家族具有有利的模式失配缩放特性，其损耗因子降至\(|\ell| + 1\)，仅随方位角指数线性增加。这种稳健性及其宽强度分布和中心暗区允许选择性镜面掩蔽，为在精密干涉仪（包括引力波探测器）中使用LG\(_{0,\ell}\)模式提供了额外的实际动机。
英文摘要
Higher-order Laguerre-Gaussian (LG) modes have broader and more uniform transverse intensity distributions than the fundamental Gaussian mode, making them attractive for precision optical applications. In gravitational-wave detectors, their enhanced spatial averaging of thermally driven test-mass fluctuations can reduce thermal noise. Their implementation, however, requires efficient coupling of the injected beam to the target cavity eigenmode. Residual misalignment and mode mismatch couple power out of the desired mode, reducing intracavity power buildup and degrading detector sensitivity. Here, we analytically and numerically evaluate the 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 $2p+|\ell|+1$, whereas that due to waist size or waist position mismatch scales as $2p^2+2p+(2p+1)|\ell|+1$. Although sensitivity to imperfect coupling generally increases with mode order, the donut-shaped $\mathrm{LG}_{0,\ell}$ family exhibits favorable mode mismatch scaling: its loss factor reduces to $|\ell|+1$ and therefore increases only linearly with the azimuthal index. This robustness, together with their broad intensity profiles and central dark regions that permit selective mirror masking, provides additional practical motivation for using $\mathrm{LG}_{0,\ell}$ modes in precision interferometers, including gravitational-wave detectors.
Comments17 pages, 5 figures
