发表机构
Institute for Quantum Studies, Chapman University; Nexus for Quantum Technologies, University of Ottawa; German Aerospace Center (DLR), Institute of Quantum Technologies（查普曼大学量子研究所; 渥太华大学量子技术联盟; 德国航空航天中心（DLR）量子技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将携带轨道角动量的近轴光束衍射环形聚焦构建为变分优化问题，推导了最优光瞳的解析解，实验验证了其性能，确立了仅振幅聚焦的涡旋光束类似物并明确了结构化波衍射聚焦的基本极限。
AI 中文摘要
我们将携带轨道角动量（OAM）的近轴光束通过有限圆形孔径的衍射环形聚焦问题，构建为变分优化问题。对于固定的拓扑荷，我们确定实值径向光瞳，该光瞳在输入场的归一化约束下，使指定环半径和传播距离处的强度最大化。所得问题存在精确解析解：最优光瞳结合了熟知的菲涅耳相位结构与依赖OAM的贝塞尔径向调制，其特征值为可实现的环形强度提供了严格上界。我们进一步分析了透镜辅助构型，推导了一个简单界，可直接比较衍射型与折射型涡旋聚焦。该理论还为评估实用掩模设计的性能提供了定量框架，包括二元菲涅耳-贝塞尔波带片和振幅加权光瞳。我们已在光学领域通过实现对应涡旋光束光瞳，将其传播与聚焦性能同最优解对比，实验验证了我们的预测。我们的结果确立了仅振幅聚焦的涡旋光束类似物，并确定了结构化波衍射聚焦的基本极限。
英文摘要
We formulate diffractive ring focusing of paraxial beams carrying orbital angular momentum (OAM) through a finite circular aperture as a variational optimization problem. For a fixed topological charge, we determine the real-valued radial pupil that maximizes the intensity at a prescribed ring radius and propagation distance under a normalization constraint on the input field. The resulting problem admits an exact analytical solution: the optimal pupil combines the familiar Fresnel phase structure with an OAM-dependent Bessel radial modulation, and the associated eigenvalue yields a rigorous upper bound on the achievable ring intensity. We further analyze the lens-assisted configuration and derive a simple bound that allows direct comparison between diffractive and refractive vortex focusing. The theory also provides a quantitative framework for evaluating the performance of practical mask designs, including binary Fresnel-Bessel zone plates and amplitude-weighted pupils. We have experimentally tested our predictions in the optical domain by implementing the corresponding vortex beam pupils and comparing their propagation and focusing performance with the optimal solution. Our results establish the vortex-beam analogue of optimal amplitude-only focusing and identify the fundamental limits governing diffractive concentration of structured waves
