Algorithm improvements for optical eigenfunction computers

Abstract

Prior iterative approaches to optical eigenfunction solution have at least three major problems: slow convergence (sometimes); decreasing accuracy after the first solution; and imperfect parallel renormalization (leading to poor use of system dynamic range and hence poor accuracy). We introduce new approaches and algorithms to solve these problems. The new algorithms lead to a tight error bound on eigenvalues and an automatic handling of degenerate or near degenerate eigenvalues. Applications are discussed.