In this chapter, we use simple models for acoustical waves (Section 3.1) [59], [61], [63], [64], [59], for
water surface waves (Section 3.2) [62], [59], [61], [50], and for electromagnetic waves (Section 3.3) [65]. On the
basis of these models, we consider the new concept of parametric "black body" with conceptual possibility of
designing an active absorbing (nonreflecting) coatings in the form of a thin layer with small-scale stratification
and fast temporal modulation of parameters. Algorithms for spatial-temporal modulation of the controlled-layer
structure are studied in detail for a one-dimensional boundary-value problem. These algorithms do not require
wave-field measurements, which eliminate self-excitation problem, that is the characteristic of traditional active
systems. The majority of the considered algorithms of parametric control transforms the low-frequency incident
wave to high-frequency waves of the technological band for which the waveguiding medium inside the layer is
assumed to be opaque (absorbing). The efficient conditions of use are found for all the algorithms. It is shown
that the absorbing layer can be as thin as desired with respect to the minimum spatial scale of the incident wave
ensuring efficient absorption in a wide frequency interval (starting from zero frequency) that is bounded from
above only by a finite space-time resolution of the parameter-control operations. The structure of a threedimensional
parametric "black" coating, whose efficiency is independent of the angle of incidence of an incoming
wave is developed on the basis of the studied one-dimensional problems. The general solutions of the problem of
diffraction of incident waves from such coatings are obtained. These solutions are analyzed in detail for the case
of a disk-shaped element.
