Inverse scattering in multimode structures

TL;DR

This paper develops a method to solve inverse scattering problems in one-dimensional multimode structures, enabling the extraction of mode coupling information from reflection data, with applications to optical waveguides.

Contribution

It introduces a novel layer-stripping and matrix factorization approach to identify both contradirectional and codirectional mode couplings in multimode structures.

Findings

Successfully applied to multimode optical waveguides with perturbations

Able to distinguish between contradirectional and codirectional coupling

Addresses ambiguities with potential resolution strategies

Abstract

We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional, and may be distributed continuously or in discrete points. The local coupling as a function of position is obtained from reflection data using a layer-stripping type method, and the separate identification of the contradirectional and codirectional coupling is obtained using matrix factorization. Ambiguities are discussed in detail, and different {\it a priori} information that can resolve the ambiguities is suggested. The method is exemplified by applications to multimode optical waveguides with quasi-periodical perturbations.