V. A. Buts

It is shown that at interaction of waves in the distributed systems exist more general conditions of synchronism than the well known conditions. The well known conditions of synchronism are just the particular case of these more general conditions. It has been shown that these new conditions lead to new opportunities for effective scattering of waves in a periodically-heterogeneous medium (for example, in a crystal), new conditions for waves decay in nonlinear media and to new interaction processes in quantum systems. Let-s give some explanation for appearing of new conditions of effective interaction of the waves in distributed systems. For this purpose shortly we shall remind well-known conditions of synchronism. For simplicity we shall consider physical systems, in which only three waves participate in interaction. Thus the conditions of effective interaction of waves (condition of synchronism) can be presented as: ; . Here are frequencies of interacting waves; is wave vectors of interacting waves. These four conditions can be interpreted as a conditions of synchronism along each of axes of four-dimension space (along three spatial coordinates and along an axis of time). If any of the formulated above four conditions is carried out not strictly, the efficiency of interaction of waves is reduced.. So, for example, if instead of exact synchronism in time ( ) there is condition , then the effective interaction between waves will occur only on intervals of time . The interaction of waves in the distributed systems, generally, occurs along some directions, which often has name as characteristic directions. Therefore it is enough for effective interaction that the synchronism between waves was saved not strictly along each of axes, but only along characteristic directions. Thus the detuning (even large detuning) along one of axes can be compensated by detuning along other axes. These qualitative considerations are confirmed by the quantitative consideration which has been carried out in this work. At this, first of all, the process of waves interaction was considered in media, which dielectric permeability contain periodically varying in time and in space component: , . It is known, that in such media two waves can effectively interact, the frequencies and wave vectors of which are satisfy to usual conditions of synchronism: , . In work is shown, that in such media can effectively interact and waves, the frequencies and wave vectors of which are satisfy to more general conditions: , . These conditions are new conditions. These conditions contain, as a special case, well-known conditions of synchronism. As the elementary but not trivial example of the opportunity of complete back reflection of an electromagnetic wave at scattering on stationary ( ), non-uniform periodic dielectric is considered in the work. This reflection is similar to Bragg reflection. However conditions of such reflection essentially differ from Bragg reflection. It is known, that at back Bragg reflection the following well-known conditions should be carried out: . In the work is shown, that the similar complete back reflection will be realized and at performance of conditions: , , where is the angle between vectors and . As it is visible, these conditions are essentially differing from Bregg conditions. In the work the process of three-wave interaction of waves in nonlinear media also is considered. In such media also for effective interaction of waves standard are the conditions: , . In the work is shown, that and in this case the interaction between waves occurs along the characteristics and conditions of effective interaction of waves will be the conditions which were formulated above - new conditions of synchronism. As a simple but not trivial example of weak nonlinear three-wave interaction the process of decay of a transverse electromagnetic wave on a transverse electromagnetic wave and on one of own waves of magnetized plasma waveguide is considered. (process ). Is shown, that for a case, when the frequencies and wave vector of interacting waves are on one straight line, all conceivable triplets of waves can participate in effective process of interaction. Let's note that the usual conditions of synchronism permit to exist only limited number of possible triplets of interacting waves. It is shown, that the similar generalization of synchronism conditions can be carried out and for quantum systems. In the work such generalization is carried out for the Schrödinger equation, containing periodically varying in time and in space potential