Diffraction by a Dirichlet right angle on a discrete planar lattice

TL;DR

This paper investigates wave scattering by a Dirichlet right angle on a discrete lattice using the discrete Helmholtz equation and Sommerfeld integral transform, providing an algebraic form of the solution.

Contribution

It introduces a novel algebraic formulation of the Sommerfeld transformant for the discrete Helmholtz equation in this scattering problem.

Findings

Solution expressed as an algebraic function of the Sommerfeld transformant

Extension of previous work on scattering problems on discrete lattices

Provides analytical tools for discrete diffraction analysis

Abstract

A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld transformant of the field is built as an algebraic function. The paper is a continuation of [1].