Photonic implementation for arbitrary complex-valued matrices

This talk discusses a new photonic implementation to perform general discrete linear operations. This is achieved by properly factorizing any arbitrary NxN complex matrix in terms of a prefixed unitary discrete fractional Fourier transform (DFrFT) matrix and complex diagonal matrices. This approach is handy as it allows for an all-optical implementation using N+1 amplitude and N+1 phase modulation layers, interlaced with fixed DFrFT layers implemented via a coupled waveguide array. Numerical optimizations show that target matrices can indeed be represented through this approach by accordingly tunning the phase and amplitude layers. The proposed architecture enables the development of novel families of programmable lossy and lossless photonic circuits for on-chip analog information processing.