Propagation in rough waveguides: Forward and inverse problems

TL;DR

This paper investigates wave propagation in rough waveguides, addressing both forward scattering calculations using operator splitting and inverse surface recovery from field measurements, with broad applicability to various geometries.

Contribution

It introduces a novel algorithm for surface recovery in waveguides that generalizes previous methods and applies operator splitting for efficient scattering computation.

Findings

Effective calculation of scattered fields in 2D and 3D waveguides.

A new integral equation-based method for surface profile recovery.

Applicability of the formulas to diverse geometries.

Abstract

We discuss here the direct and inverse problems for wave propagation in a waveguide with rough internal surface and arbitrary mean shape. The high degree of multiple scattering inside the waveguide poses significant challenges both for the forward computation and for the recovery of the surface profile, and raises important questions about scattering cross-sections. This paper falls into two parts corresponding to these issues. We first apply Left-Right (L-R) operator splitting to calculate the scattered fields in 2- and 3-dimensional waveguides. Using this we illustrate the scattered fields and the effect of surface roughness. In the second part we formulate an algorithm for surface recovery from field measurements along the waveguide axis, which generalises recent work on surfaces in 2 dimensions. This method utilizes forward scattering assumptions in effect by formulating an integral equation in the unknown surface field, treated as a function of the surface. Although discussed in the context of waveguides, the formulae are given in a form applicable to a variety of geometries, with coefficients which will depend on and be determined by each specific application.