Programmable Holographic Technique For Implementing Unitary And Nonunitary Transformations

Beyond the possibilities of linear transformations in polarization space, whose dimensionality is constrained by limited orthogonal states, we propose a technique for implementing both unitary and nonunitary transformations with higher dimensionality. Any high-dimensional matrix can be decomposed into a product of two processes realizable by utilizing spatial phase modulation and free-space propagation, in a simple, fixed, and scalable setup. Given that perfect power transmission for an arbitrary matrix may not be possible, the method is optimized to reach the theoretical best. Projected applications of the method described here include a means of restricting the infinite-dimensionalHilbert space to a finite-dimensional basis for information processing purposes, simultaneous multichannel optical routing, and a method of optical orbital angular momentum sorting and generation.