Generalized Soft-and-Hard/DB Boundary

TL;DR

This paper introduces a generalized class of boundary conditions called GSHDB, derived using differential-form formalism, which encompasses previous boundary types and has applications in wave reflection and material interface design.

Contribution

The paper develops the GSHDB boundary conditions using differential-form and dyadic formalism, extending previous soft-and-hard/DB boundaries with a broader, more natural framework.

Findings

GSHDB boundary conditions are governed by two one-forms.

For two eigenpolarizations, GSHDB can be replaced by PEC or PMC boundaries.

Dispersion curves for GSHDB boundaries are provided.

Abstract

A novel class of boundary conditions is introduced as a generalization of the previously defined class of soft-and-hard/DB (SHDB) boundary conditions. It is shown that the conditions for the generalized soft-and-hard/DB (GSHDB) boundary arise most naturally in a simple and straightforward manner by applying four-dimensional differential-form and dyadic formalism. At a given boundary surface, the GSHDB conditions are governed by two one-forms. In terms of Gibbsian 3D vector and dyadic algebra the GSHDB conditions are defined in terms of two vectors tangential to the boundary surface and two scalars. Considering plane-wave reflection from the GSHDB boundary, for two eigenpolarizations, the GSHDB boundary can be replaced by the PEC or PMC boundary. Special attention is paid to the problem of plane waves matched to the GSHDB boundary, defined by a 2D dispersion equation for the wave vector, making the reflection dyadic indeterminate. Examples of dispersion curves for various chosen parameters of the GSHDB boundary are given. Conditions for a possible medium whose interface acts as a GSHDB boundary are discussed.