a Schematic of a diffractive optical network that connects an input field-of-view (aperture) composed of Ni points to a desired region-of-interest at the output plane/aperture covering No points, through K-diffractive surfaces with N neurons per surface, sampled at a period of λ/2n, where λ and n represent the illumination wavelength and the refractive index of the medium between the surfaces, respectively. Without loss of generality, n = 1 was assumed in this paper. b The communication between two successive diffractive surfaces occurs through propagating waves when the axial separation (d) between these layers is larger than λ. Even if the diffractive surface has deeply subwavelength structures, as in the case of, e.g., metasurfaces, with a much smaller sampling period compared to λ/2 and many more degrees of freedom (M) compared to N, the information-processing capability of a diffractive surface within a network is limited to propagating modes since d ≥ λ; this limits the effective number of neurons per layer to N, even for a surface with M N. H and H* refer to the forward- and backward-wave propagation, respectively
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