Abstract: A photonic circuit comprises a first waveguide lattice having a first length for providing a discrete fractional Fourier transform operation on the input optical signal; a programmable modular array of tunable phase shifters for providing the fractional Fourier transform of the kernel and performing a point-wise product on the previously transformed input optical signal; a second wavelength lattice having a second length for providing an inverse discrete fractional Fourier transform operation on the previous processed optical signal; and a processor that determines a convolved output of the input signal and the convolution kernel.

Abstract: A device for performing unitary matrix computations comprises a light source configured to generate first optical signals; an array of waveguides, including: inputs that receive the first optical signals from the light source; a plurality of channels positioned in parallel for transmitting the first optical signals along a length of the waveguides; and outputs for outputting second optical signals generated according to a matrix multiplication operation from the first optical signals. The device further comprises phase shifters constructed and arranged in a cascade structure at the channels of the waveguides, the waveguides include sections or directional couplers between adjacent phase shifter. The matrix multiplication operation includes coupling coefficient values between adjacent waveguides and length values of the sections of the waveguides. General non-unitary matrix computations are implemented by interlacing two embodiments of the device together with an array of amplitude modulators.