Abstract: A mjuniversal photonic apparatus that performs an arbitrary discrete linear unitary operation on a source of light comprises a plurality of waveguides, including: a plurality of input ports that receive a plurality of first optical signals from a light source; a plurality of channels positioned in parallel for transmitting the first optical signals along a length of the waveguides; and a plurality of output ports for outputting second optical signals generated from the first optical signals according to a matrix operation; and a plurality of phase shifters constructed and arranged in a cascade structure at the plurality of channels of the waveguides. The matrix operation includes a unitary transformation matrix factorized into a plurality of interlaced discrete fractional Fourier transforms (DFrFT) layers and parameter diagonal phase shift layers.

Abstract: A universal photonic apparatus that performs an arbitrary discrete linear unitary operation on a source of light comprises a plurality of waveguides, including: a plurality of input ports that receive a plurality of first optical signals from a light source; a plurality of channels positioned in parallel for transmitting the first optical signals along a length of the waveguides; and a plurality of output ports for outputting second optical signals generated from the first optical signals according to a matrix operation; and a plurality of phase shifters constructed and arranged in a cascade structure at the plurality of channels of the waveguides. The matrix operation includes a unitary transformation matrix factorized into a plurality of interlaced discrete fractional Fourier transforms (DFrFT) layers and parameter diagonal phase shift layers.