# Evolution of time-harmonic electromagnetic and acoustic waves along waveguides

## TL;DR

This paper develops a mathematical framework for analyzing time-harmonic electromagnetic and acoustic waves in waveguides with non-smooth cross sections, establishing a spectral correspondence using a new functional calculus for non-self adjoint operators.

## Contribution

It introduces an infinitesimal generator and a novel functional calculus for non-self adjoint operators in waveguides with irregular cross sections, enabling spectral analysis of wave propagation.

## Key findings

- Established estimates for the functional calculus of the operators.
- Proved a spectral correspondence between bounded waves and spectral subspaces.
- Provided a mathematical foundation for wave analysis in complex waveguide geometries.

## Abstract

We study time-harmonic electromagnetic and acoustic waveguides, modeled by an infinite cylinder with a non-smooth cross section. We introduce an infinitesimal generator for the wave evolution along the cylinder, and prove estimates of the functional calculi of these first order non-self adjoint differential operators with non-smooth coefficients. Applying our new functional calculus, we obtain a one-to-one correspondence between polynomially bounded time-harmonic waves and functions in appropriate spectral subspaces.