Non-perturbative results for the spectrum of surface-disordered waveguides

TL;DR

This paper presents a non-perturbative analysis of the spectrum of scalar waves in waveguides with randomly rough boundaries, revealing a non-analytic dependence on roughness dispersion and extending beyond traditional perturbation methods.

Contribution

It introduces an exact boundary scattering potential approach to analyze waveguide spectra beyond perturbation theory, highlighting non-analytic behavior related to boundary roughness.

Findings

Spectrum is nearly real and non-analytic in roughness dispersion.

Non-perturbative method extends understanding beyond small roughness approximations.

Large boundary defects summarized but not detailed.

Abstract

We calculated the spectrum of normal scalar waves in a planar waveguide with absolutely soft randomly rough boundaries beyond the perturbation theories in the roughness heights and slopes, basing on the exact boundary scattering potential. The spectrum is proved to be a nearly real non-analytic function of the dispersion $\zeta^2$ of the roughness heights (with square-root singularity) as $\zeta^2 \to 0$. The opposite case of large boundary defects is summarized.