Wave scattering at a rectangular junction of four waveguides

TL;DR

This paper analyzes wave scattering at a four-way junction of waveguides using symmetry reduction and eigenfunction matching, providing a scattering matrix and visualizing time-domain responses for various incident pulses.

Contribution

It introduces a method to solve wave scattering at a four-way junction by symmetry reduction and eigenfunction matching, and constructs the time-domain solution from frequency domain analysis.

Findings

Derived the scattering matrix for the junction

Demonstrated time-domain wave propagation visualization

Validated the method with different waveguide geometries

Abstract

We consider the scattering of linear waves in two dimensions by a rectangular region at the junction of four waveguides. A solution to the frequency domain problem is obtained by exploiting reflective symmetry to reduce the full problem to sub-problems defined on one quadrant of the junction. These sub-problems are solved using the eigenfunction matching method. The solution to the problem on the full region is then recovered from the solutions to the sub-problems, and a scattering matrix for the junction is presented. Finally, the solution in the time domain is constructed as a superposition of the frequency domain solutions and visualised for a range of incident pulses and waveguide geometries.