Optical cavities are an enabling technology of modern quantum science: From their essential role in the operation of lasers to applications as flywheels in atomic clocks and interaction-enhancing components in quantum optics experiments, developing a quantitative understanding of the mode shapes and energies of optical cavities has been crucial for the growth of the field. Nonetheless, the standard treatment using paraxial quadratic optics fails to capture the influence of optical aberrations present in modern cavities with high finesse, small waist, and/or many degenerate modes. In this work, we compute the mode spectrum of optical resonators, allowing for both nonparaxial beam propagation and beyond-quadratic mirrors and lenses. Generalizing prior works, we develop a complete theory of resonator aberrations, including intracavity lenses, nonplanar geometries, and arbitrary mirror forms. Harnessing these tools, we reconcile the near absence of aberration in the work of Schine et al. [N. Schine et al., Nature (London) 534, 671 (2016)] with the strongly evident aberrations in the seemingly similar cavity of Clark et al. [L. W. Clark et al., Nature (London) 582, 41 (2020)]. We further validate our approach by comparison to a family of nonplanar lens cavities realized in the laboratory, finding good quantitative agreement. This work opens prospects for cavities with smaller waists and more degenerate modes.

中文翻译：

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像差光腔

光腔是现代量子科学的一项使能技术：从它们在激光操作中的重要作用到原子钟中的飞轮和量子光学实验中的相互作用增强组件的应用，发展对光腔的模式形状和能量的定量理解对该领域的发展起到了至关重要的作用。尽管如此，使用近轴二次光学的标准处理未能捕捉到现代腔体中存在的光学像差的影响，这些腔体具有高精细度、小腰围和/或许多退化模式。在这项工作中，我们计算了光学谐振器的模式谱，允许非近轴光束传播以及超二次反射镜和透镜。概括先前的工作，我们开发了一个完整的谐振器像差理论，包括腔内透镜，非平面几何形状和任意镜像形式。利用这些工具，我们调和了 Schine 工作中几乎没有畸变的情况等。[N. Schine等人。, Nature (London) 534 , 671 (2016)] 与克拉克等人看似相似的腔中的强烈明显像差。[LW 克拉克等人。, Nature (London) 582 , 41 (2020)]。我们通过与实验室中实现的一系列非平面透镜腔进行比较，进一步验证了我们的方法，找到了良好的定量一致性。这项工作为具有更小腰围和更多退化模式的空腔开辟了前景。