TO THE THEORY OF WAVES IN PERIODIC STRUCTURES IN INVERSE PROBLEM APPROACH

Abstract

We show that the mechanism of spectral gap formation while switching on periodic perturbation has a "hidden resonance" nature. It consists of a coherent wreck of physical solutions (making them asymptotically unrestricted increasing/decreasing). This notion also gives us paradoxically the key for understanding of wave behavior in allowed zones as alternation of these mutually destructive but compensating regimes resulting in wave beating. The inversion technique also gives rise to zone spectral control algorithms. We reveal a new degree of freedom: the possibility to manipulate the rate of divergence of the solutions in any chosen energy point of the forbidden zone. This forbiddenness makes a deep physical sense, for example, penetration property of separate sectors of heterogeneous structures at chosen energy. We demonstrate examples of application of our theory changing forbiddenness and shifting spectral bands boundaries including instructive merging of zones.