Abstract:
Tailored physical systems were recently exploited to rapidly solve hard computational challenges, such as spin
simulators, combinatorial optimization, and focusing through scattering media. Here, we address the phase
retrieval problem where an object is reconstructed from its scattered intensity distribution. This is a key problem
in many applications, ranging from x-ray imaging to astrophysics, and currently, it lacks efficient direct reconstruction
methods: The widely used indirect iterative algorithms are inherently slow. We present an optical approach based
on a digital degenerate cavity laser, whose most probable lasing mode rapidly and efficiently reconstructs the
object. Our experimental results suggest that the gain competition between the many lasing modes acts as a
highly parallel computer that could rapidly solve the phase retrieval problem. Our approach applies to most
two-dimensional objects with known compact support, including complex-valued objects, and can be generalized
to imaging through scattering media and other hard computational tasks.
