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We propose an efficient inverse design approach for multifunctional opticalelements based on adaptive deep diffractive neural networks (a-D$^2$NNs).Specifically, we introduce a-D$^2$NNs and design two-layer diffractive devicesthat can selectively focus incident radiation over two well-separated spectralbands at desired distances. We investigate focusing efficiencies at twowavelengths and achieve targeted spectral lineshapes and spatial point-spreadfunctions (PSFs) with optimal focusing efficiency. In particular, wedemonstrate control of the spectral bandwidths at separate focal positionsbeyond the theoretical limit of single-lens devices with the same aperturesize. Finally, we demonstrate devices that produce super-oscillatory focalspots at desired wavelengths. The proposed method is compatible with currentdiffractive optics and doublet metasurface technology for ultracompactmultispectral imaging and lensless microscopy applications.

Inverse design of ultracompact multi-focal optical devices by diffractive neural networks