Fundamental Thickness Bounds for Wide-Field-of-View Metalenses

Metalenses—flat lenses made with optical metasurfaces—promise to enable thinner, cheaper, and better imaging systems. Achieving a sufficient field of view (FOV) is crucial toward that goal and the subject of much recent work. Here, we show that any wide-FOV lens system must have a minimal thickness, regardless of structural design and material composition. Such thickness bounds originate from the Fourier transform relation between space and angle. By analyzing the transmission matrices of ideal (aberration-free) lenses, we map out the minimal thickness as a function of the FOV, lens diamater, and numerical aperture. This bound is tight, as some inverse-designed multi-layer metasurfaces can approach such minimal thickness. Our transmission-matrix approach can also determine the thickness bounds of other systems beyond lenses. This work provides guidance for the design of future wide-FOV metasurfaces while establishing an intrinsic relation between angular diversity and spatial footprint in multi-mode systems.