Saddle point method for transient processes in waveguides

TL;DR

This paper introduces a modified saddle point method for analyzing transient wave processes in waveguides, involving analytical continuation of the dispersion diagram and classification based on saddle point topology.

Contribution

It presents a novel modification of the saddle point method tailored for non-stationary waveguide processes, including a new way to identify contributing saddle points.

Findings

Analytical continuation of the dispersion diagram enables better saddle point analysis.

A criterion for saddle point contribution to wavefield decomposition is proposed.

Waveguides are classified based on the topology of saddle points.

Abstract

A modification of the saddle point method is proposed for computation of non-stationary wave processes (pulses) in waveguides. The dispersion diagram of the waveguide is continued analytically. A set of possible saddle points on the dispersion diagram is introduced. A method of checking whether the particular saddle points contribute terms to the field decomposition is proposed. A classification of the waveguides based on the topology of the set of possible saddle points is outlined.