Minimizing the thickness of an inhomogeneous layer at a given reflection coefficient for a monochromatic wave

Abstract

The problem of wave absorption in an inhomogeneous impedance layer is a familiar one in acoustics and electrodynamics. In practice, impedance systems are designed with account for known optimum requirements, the most important of which is the requirement that the absorbing layer be of minimum thickness. The corresponding mathematical problems for sound absorbers in air were treated by various artificial approaches toward the end of the 1930's by Malyuzhinets, who attracted the attention of the authors, and by Svirskii, in a dissertation (Moscow State University, 1943). Similar (and more general) optimization problems can be studied systematically when they are treated as Mayer-Bolza variational problems. That point of view is adopted in this paper, in which the thickness of an inhomogeneous layer on which a plane monochromatic wave is incident normally is minimized.