Fast Exact Inversion of the Generalized Zakharov–Shabat Problem for Rational Scattering Data: Application to the Synthesis of Optical Couplers

Abstract

An exact method is presented for the inversion of the generalized Zakharov–Shabat problem, for the case where the scattering data are (or are approximated by) rational functions. The presence of bound states is also accounted for. The problem is examined with the aim of obtaining an exact synthesis procedure for a class of two-mode optical couplers, including lossy and active structures. The present method yields a closed-form solution, thereby leading to very fast numerical implementation. The implications of the synthesis technique on the physical problem at hand are briefly discussed, and some numerical examples are presented.