Sparsity-based super-resolution and phase-retrieval in waveguide arrays

We present a scheme for recovering the complex input field launched into a waveguide array, from partial measurements of its output intensity, given advance knowledge that the input is sparse. In spite of the fact that in general the inversion problem is ill-conditioned, we demonstrate experimentally and in simulations that the prior knowledge of sparsity helps overcome the loss of information. Our method is based on GESPAR, a recently proposed efficient phase retrieval algorithm. Possible applications include optical interconnects and quantum state tomography, and the ideas are extendable to other multiple input and multiple output (MIMO) communication schemes.