Li Shiyu, Hsu Chia Wei
Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, 90089, USA.
Light Sci Appl. 2022 Dec 1;11(1):338. doi: 10.1038/s41377-022-01038-6.
Metalenses-flat lenses made with optical metasurfaces-promise to enable thinner, cheaper, and better imaging systems. Achieving a sufficient angular field of view (FOV) is crucial toward that goal and requires a tailored incident-angle-dependent response. Here, we show that there is an intrinsic trade-off between achieving a desired broad-angle response and reducing the thickness of the device. Like the memory effect in disordered media, this thickness bound originates from the Fourier transform duality between space and angle. One can write down the transmission matrix describing the desired angle-dependent response, convert it to the spatial basis where its degree of nonlocality can be quantified through a lateral spreading, and determine the minimal device thickness based on such a required lateral spreading. This approach is general. When applied to wide-FOV lenses, it predicts the minimal thickness as a function of the FOV, lens diameter, and numerical aperture. The bound is tight, as some inverse-designed multi-layer metasurfaces can approach the minimal thickness we found. This work offers guidance for the design of nonlocal metasurfaces, proposes a new framework for establishing bounds, and reveals the relation between angular diversity and spatial footprint in multi-channel systems.
金属透镜——由光学超表面制成的平面透镜——有望实现更薄、更便宜且性能更好的成像系统。实现足够的角视野（FOV）对于实现该目标至关重要，并且需要定制与入射角相关的响应。在此，我们表明，在实现所需的广角响应与减小器件厚度之间存在内在的权衡。与无序介质中的记忆效应类似，这种厚度限制源于空间和角度之间的傅里叶变换对偶性。可以写下描述所需角度相关响应的传输矩阵，将其转换到空间基，在该基中其非局域程度可通过横向扩展来量化，并基于这种所需的横向扩展确定最小器件厚度。这种方法具有通用性。当应用于宽视野透镜时，它可预测最小厚度作为视野、透镜直径和数值孔径的函数。该限制是严格的，因为一些反向设计的多层超表面可以接近我们发现的最小厚度。这项工作为非局域超表面的设计提供了指导，提出了一个建立限制的新框架，并揭示了多通道系统中角度多样性与空间占用之间的关系。
