On the ability of bounded inhomogeneous waves to experimentally verify the behavior of infinite inhomogeneous plane waves

Abstract

Infinite inhomogeneous plane waves have been controversial because of the appearance of a reflection coefficient exceeding unity in some cases. Even though it had already been shown that this is consistent with the principle of energy conservation, and results in a shift in position, full acceptance of the notion of infinite inhomogeneous plane waves appeared only after some experiments have been performed that produce results that are in agreement with theory. However, experiments can only be performed by means of bounded inhomogeneous waves. The current paper answers the ultimate question why bounded inhomogeneous waves are able to behave as if they were infinite inhomogeneous waves and what exactly is the physical and mathematical connection between bounded inhomogeneous waves and infinite inhomogeneous waves. [Work supported by The Flemish Institute for the Encouragement of the Scientific and Technological Research in Industry (I.W.T.).]