  We report deep learning-based design of a massively parallel broadband
diffractive neural network for all-optically performing a large group of
arbitrarily-selected, complex-valued linear transformations between an input
and output field-of-view, each with N_i and N_o pixels, respectively. This
broadband diffractive processor is composed of N_w wavelength channels, each of
which is uniquely assigned to a distinct target transformation. A large set of
arbitrarily-selected linear transformations can be individually performed
through the same diffractive network at different illumination wavelengths,
either simultaneously or sequentially (wavelength scanning). We demonstrate
that such a broadband diffractive network, regardless of its material
dispersion, can successfully approximate N_w unique complex-valued linear
transforms with a negligible error when the number of diffractive neurons (N)
in its design matches or exceeds 2 x N_w x N_i x N_o. We further report that
the spectral multiplexing capability (N_w) can be increased by increasing N;
our numerical analyses confirm these conclusions for N_w > 180, which can be
further increased to e.g., ~2000 depending on the upper bound of the
approximation error. Massively parallel, wavelength-multiplexed diffractive
networks will be useful for designing high-throughput intelligent machine
vision systems and hyperspectral processors that can perform statistical
inference and analyze objects/scenes with unique spectral properties.
