A Novel Parametrization of Arbitrary Complex Matrices for Photonic Realization of General Discrete Linear Transformations

With the surge of photonic-enabled computing technologies, there is growing interest in designing and deploying architectures that perform specific mathematical operations by exploring light propagation solely. Notably, it has been recently shown that discrete linear unitary operations can be parametrized through diagonal phase parameters interlaced with a fixed operator that enables efficient photonic realization of unitary operations by cascading phase shifter arrays interlaced with a multiport component.



This talk presents a broader class of factorizations that allows for parametrizing arbitrary complex-valued square matrices in terms of diagonal matrices alternating with a fixed unitary matrix. This novel architecture can implement general discrete linear operations, where unitary operations are recovered as a particular case. The proposed architecture is built on factorizing an NxN matrix operator in terms of N+1 amplitude and N+1 phase modulation layers, interlaced with fixed unitary layers implemented via a coupled waveguide array. The proposed architecture enables the development of novel families of programmable lossy and lossless photonic circuits for on-chip analog information processing.