Computational inverse design for cascaded systems of metasurface optics

Metasurfaces are an emerging technology that may supplant many of the conventional optics found in imaging devices, displays, and precision scientific instruments. Here, we develop a method for designing optical systems composed of multiple unique metasurfaces aligned in sequence and separated by distances much larger than the design wavelengths. Our approach is based on computational inverse design, also known as the adjoint-gradient method. This technique enables thousands or millions of independent design variables (e.g., the shapes of individual meta-atoms) to be optimized in parallel, with little or no intervention required by the user. The assumptions underlying our method are as follows: we use the local periodic approximation to determine the phase-response of a given meta-atom, we use the scalar wave approximation to propagate light fields between metasurface layers, and we do not consider multiple reflections between metasurface layers (analogous to a sequential-optics ray-tracer). To demonstrate the broad applicability of our method, we use it to design an achromatic doublet metasurface lens, a spectrally-multiplexed holographic element, and an ultra-compact optical neural network for classifying handwritten digits.