发表机构
Université Paris Cité, CNRS, Astroparticule et Cosmologie（巴黎西岱大学，法国国家科学研究中心，粒子与宇宙学实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过优化镜面曲率破除模式简并，减少引力波干涉仪中高阶拉盖尔-高斯模式的耦合损耗，并设计校正表面轮廓以提升模式纯度与鲁棒性，显著优于现有损耗工程方法。
AI 中文摘要
高阶拉盖尔-高斯模式可以降低引力波干涉仪中测试质量的热噪声，但其实际应用受到现实高精细度腔体中由简并引起的耦合损耗的限制。我们通过优化镜面曲率以破除模式简并来减轻这些损耗。我们开发了一个通用框架，用于设计轴对称的校正测试质量表面轮廓，该轮廓可解除六阶拉盖尔-高斯子空间的简并，同时保持注入的环形$\nmathrm{LG}_{0,6}$模式。该轮廓在傅里叶-贝塞尔基中展开，其优化目标是最大化与最近非期望模式的频率分裂，同时最小化目标模式的损耗。对于类室女座（Virgo）的法布里-珀罗臂腔，优化后的轮廓将$\nmathrm{LG}_{0,6}$共振与最近的同阶共振$\nmathrm{LG}_{1,4}$分离了自由光谱范围的2.04%，在目标模式共振处将非期望模式的增益降至1以下，并抑制了它们的共振增强。该轮廓引入了可忽略的目标模式损耗，并提高了对像散和现实镜面表面畸变的鲁棒性。使用现实镜面缺陷的蒙特卡洛模拟产生了平均对比度缺陷为368 ppm，平均反射光学损耗为979 ppm，相当于所建模腔体的往返损耗约为3.5 ppm。这些结果显著优于基于选择性损耗工程的中心抗反射镜掩模方法，使反射光学损耗在相同模拟条件下达到基本高斯模式所得损耗的两倍以内。该方法为未来具有现实缺陷的精密干涉仪中实现鲁棒的环形拉盖尔-高斯模式提供了一条途径。
英文摘要
Higher-order Laguerre-Gaussian modes can reduce test-mass thermal noise in gravitational-wave interferometers, but their implementation is limited by degeneracy-induced coupling losses in realistic high-finesse cavities. We mitigate these losses by optimizing the mirror curvature to break modal degeneracy. We develop a general framework for designing an axisymmetric corrective test-mass surface profile that lifts the degeneracy of the sixth-order Laguerre-Gaussian subspace while preserving an injected donut-shaped $\mathrm{LG}_{0,6}$ mode. Expanded in a Fourier-Bessel basis, the profile is optimized to maximize the frequency splitting from the nearest unwanted mode while minimizing target-mode loss. For a Virgo-like Fabry-Perot arm cavity, the optimized profile separates the $\mathrm{LG}_{0,6}$ resonance from the nearest same-order resonance, $\mathrm{LG}_{1,4}$, by 2.04% of the free spectral range, reducing unwanted-mode gains below unity at the target-mode resonance and suppressing their resonant enhancement. The profile introduces negligible target-mode loss and improves robustness against astigmatism and realistic mirror surface distortions. Monte Carlo simulations with realistic mirror imperfections yield an average contrast defect of 368 ppm and an average reflected optical loss of 979 ppm, equivalent to a round-trip loss of approximately 3.5 ppm for the modeled cavity. These results substantially improve upon the central anti-reflective mirror mask approach based on selective loss engineering, bringing reflected optical loss within a factor of two of that obtained with the fundamental Gaussian mode under the same simulation conditions. This approach offers a route toward robust donut-shaped Laguerre-Gaussian modes in future precision interferometers with realistic imperfections.
Comments14 pages, 11 figures
