Circularly-polarized plane waves in a deformed Hadamard material

TL;DR

This paper investigates the conditions under which circularly-polarized plane waves can propagate in a deformed Hadamard material, revealing that such waves are limited to specific directions and types, with explicit solutions provided.

Contribution

It establishes the conditions for circular polarization of small amplitude waves in deformed Hadamard materials using complex bivectors, and explores the diverse possibilities of wave propagation.

Findings

Homogeneous circularly-polarized waves propagate only along acoustic axes.

Inhomogeneous circularly-polarized waves include infinite transverse and longitudinal possibilities.

Explicit solutions are provided for all cases of circular polarization.

Abstract

Small amplitude inhomogeneous plane waves propagating in any direction in a homogeneously deformed Hadamard material are considered. Conditions for circular polarization are established. The analysis relies on the use of complex vectors (or bivectors) to describe the slowness and the polarization of the waves. Generally, homogeneous circularly-polarized plane waves may propagate in only two directions, the directions of the acoustic axes, in a homogeneously deformed Hadamard material. For inhomogeneous circularly-polarized plane waves, the number of possibilities is far greater. They include an infinity of "transverse waves", as well as "longitudinal waves", and the superposition of "transverse waves" and "longitudinal waves", where "transverse" and "longitudinal" are used in the bivector sense. Each and every possibility of circular polarization is examined in turn, and explicit examples of solutions are given in every case.