Spaceplates are novel flat-optic devices that implement the optical response of a free-space volume over a smaller length, effectively “compressing space” for light propagation. Together with flat lenses such as metalenses or diffractive lenses, spaceplates have the potential to enable the miniaturization of any free-space optical system. While the fundamental and practical bounds on the performance metrics of flat lenses have been well studied in recent years, a similar understanding of the ultimate limits of spaceplates is lacking, especially regarding the issue of bandwidth, which remains as a crucial roadblock for the adoption of this platform. In this work, we derive fundamental bounds on the bandwidth of spaceplates as a function of their numerical aperture and compression ratio (ratio by which the free-space pathway is compressed). The general form of these bounds is universal and can be applied and specialized for different broad classes of space-compression devices, regardless of their particular implementation. Our findings also offer relevant insights into the physical mechanism at the origin of generic space-compression effects and may guide the design of higher performance spaceplates, opening new opportunities for ultra-compact, monolithic, planar optical systems for a variety of applications.

中文翻译：

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空间可以压缩到什么程度？空间板的带宽限制

空间板是一种新型平面光学器件，可在较小长度上实现自由空间体积的光学响应，有效地“压缩空间”以进行光传播。与金属透镜或衍射透镜等平面透镜一起，空间板有可能使任何自由空间光学系统小型化。尽管近年来对平面透镜性能指标的基本和实际界限进行了很好的研究，但对空间板的最终极限缺乏类似的理解，特别是在带宽问题上，这仍然是采用这个平台。在这项工作中，我们推导出空间板带宽的基本界限，作为其数值孔径和压缩比（自由空间路径被压缩的比率）的函数。这些界限的一般形式是通用的，可以应用于不同类别的空间压缩设备并专门化，而不管它们的具体实现如何。我们的研究结果还提供了对一般空间压缩效应起源的物理机制的相关见解，并可能指导更高性能空间板的设计，为各种应用的超紧凑、单片、平面光学系统开辟新的机会。