Theoretical bounds are commonly used to assess the limitations of photonic design. Here we introduce a more active way to use theoretical bounds, integrating them into part of the design process and identifying optimal system parameters that maximize the efficiency limit itself. As an example, we consider wide-field-of-view high-numerical-aperture metalenses, which can be used for high-resolution imaging in microscopy and endoscopy, but no existing design has achieved a high efficiency. By choosing aperture sizes to maximize an efficiency bound, setting the thickness according to a thickness bound, and then performing inverse design, we come up with high-numerical-aperture ({\rm NA} = {0.9}${\rm NA} = {0.9}$) metalens designs with, to our knowledge, record-high 98% transmission efficiency and 92% Strehl ratio across all incident angles within a 60° field of view, reaching the maximized bound. This maximizing-efficiency-limit approach applies to any multi-channel system and can help a wide range of optical devices reach their highest possible performance.

中文翻译：

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通过最大化效率极限而设计的高效高数值孔径超透镜

理论界限通常用于评估光子设计的局限性。在这里，我们介绍一种更积极的方法来使用理论边界，将它们集成到设计过程的一部分中，并确定最大化效率极限本身的最佳系统参数。例如，我们考虑宽视场高数值孔径超镜头，它可用于显微镜和内窥镜中的高分辨率成像，但现有设计尚未实现高效率。通过选择孔径大小以最大化效率界限，根据厚度界限设置厚度，然后执行逆设计，我们提出了高数值孔径（{\rm NA} = {0.9}${\rm NA} = {0.9}$）超透镜设计，以据我们所知，60°视场内所有入射角的传输效率达到创纪录的 98%，斯特列尔比达到 92%，达到了最大极限。这种最大化效率限制的方法适用于任何多通道系统，可以帮助各种光学设备达到尽可能高的性能。