Absorption of Long Waves by Nonresonant Parametric Microstructures

Using simple acoustical and mechanical models, we consider the conceptual possibility of designing an active absorbing (nonreflecting) coating in the form of a thin layer with small-scale stratification and fast time modulation of parameters. Algorithms for space-time 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 eliminates the self-excitation problem that is characteristic of active systems. The majority of the considered algorithms of parametric control transform 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 use conditions are found for all the algorithms. It is shown that the absorbing layer can be as thin as desired with respect to minimum spatial scale of the incident wave and ensures 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 three-dimensional 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 solution of the problem of diffraction of incident waves from such a coating is obtained. This solution is analyzed in detail for the case of a disk-shaped element.