Approximating ideal diffractive optical systems

In numerical wave optics involving diffractive optical elements one is required, at some point, to form a multiplicative matrix factorization. This paper is concerned with such representations and related approximations of ideal diffractive optical systems. Various simple diffractive optical elements are used. The basic factoring problem being highly nonlinear, a minor parallelism in terms of beam splitters and beam combiners makes the task computationally much more tractable and versatile. This gives rise to several matrix nearness problems of geometric nature.