Ultrasonic inhomogeneous waves: Three decades of fascination

Abstract

Inhomogeneous waves are mathematically described as pure homogeneous plane waves except for the important fact that all wave parameters, i.e., wave vector, polarization vector and frequency, can be complex valued. Even though the existence of a complex wave vector was known for a long time, Henry Cooper was the first to study such waves and their interaction with interfaces. It was not until 1980 that researchers became aware of the fact that inhomogeneous waves are mandatory phenomena in the description of reflection/transmission phenomena between lossy media. Later, it was shown that inhomogeneous waves also formed natural building blocks of bounded beams and formed a physical explanation for the Schoch effect. This paper describes this development from a historical point of view and describes scientific properties (e.g., their polarization, dispersion) whenever needed in order to understand the evolution from 1980 until the present. All topics of inhomogeneous wave research are taken into account, such as waves in viscoelastic solids and liquids, thermo-viscous liquids and solids, anisotropic viscoelastic materials, periodically rough materials, the features of complex frequency and the experimental generation of inhomogeneous waves. [Work supported by The Flemish Institute for the Encouragement of the Scientific and Technological Research in Industry (I.W.T.).]