Homogeneous and inhomogeneous time-harmonic plane waves propagating in unbounded viscoelastic anisotropic media are generally elliptically polarized. Exceptions are P and S waves propagating along some specific directions, along which they are linearly polarized. A typical case are SH waves propagating in a plane of symmetry of a viscoelastic anisotropic medium. Two most important characteristics of the polarization are the orientation of the axes of the polarization ellipse and its eccentricity. They both usually vary considerably with the direction of wavefront propagation, and with varying strength of inhomogeneity of the considered plane wave. The orientation of the polarization ellipse generally differs from the direction of wavefront propagation, being usually closer to the direction of the energy flux. The eccentricity of the polarization ellipse depends particularly strongly on the inhomogeneity of the plane wave. For homogeneous plane waves, the polarization is usually nearly linear, with large eccentricity. The eccentricity decreases with increasing inhomogeneity of the wave. For strongly inhomogeneous plane waves, the polarization ellipse becomes nearly circular, eccentricity being very small. The eccentricity of the polarization ellipse usually also decreases in a vicinity of singular directions.
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