Optical complex media as universal reconfigurable linear operators

Abstract

Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunications to optical analog computation and machine learning. For many of these applications, key requirements are robustness to fabrication inaccuracies, reconfigurability, and scalability. We propose a way to perform linear operations using complex optical media such as multimode fibers or scattering media as a computational platform driven by wavefront shaping. Given a large random transmission matrix representing light propagation in such a medium, we can extract any desired smaller linear operator by finding suitable input and output projectors. We demonstrate this concept by finding input wavefronts using a spatial light modulator that cause the complex medium to act as a desired complex-valued linear operator on the optical field. We experimentally build several 16×16 operators and discuss the fundamental limits of the scalability of our approach. It offers the prospect of reconfigurable, robust, and easy-to-fabricate linear optical analog computation units.