Inhomogeneous "longitudinal" circularly-polarized plane waves in anisotropic elastic crystals

TL;DR

This paper derives conditions on the elastic properties of anisotropic crystals that allow certain circularly polarized longitudinal inhomogeneous waves to propagate in any given direction, linking wave behavior to material stiffness and geometry.

Contribution

It provides new criteria for wave propagation in anisotropic elastic crystals, detailing how wave speed and direction depend on elastic stiffnesses and crystal geometry.

Findings

Conditions on elastic stiffnesses for wave propagation are established.

Wave speed and attenuation directions are explicitly expressed.

Propagation is impossible when the optic axes are aligned with the sagittal plane normal.

Abstract

Conditions on the elastic stiffnesses of anisotropic crystals are derived such that circularly polarized longitudinal inhomogeneous plane waves with an isotropic slowness bivector may propagate for any given direction of the normal to the sagittal plane. Once this direction is chosen, then the wave speed, the direction of propagation, and the direction of attenuation are expressed in terms of the mass density, the elastic stiffnesses, and the angle between the normal to the sagittal plane and the normals (also called "optic axes") to the planes of central circular section of a certain ellipsoid. In the special case where this angle is zero, and in this special case only, such waves cannot propagate.