Some general characteristics of coupled-mode equations

Light waves diffraction on acoustic waves is described by the pair of coupled-mode equations as well as many other physical effects. The exact decision of the equations can only be found for some definite spatial distributions of acoustic waves. In general case, the steady wave approximation of the incident wave is used to solve them, while the realistic solution can only be obtained numerically. Here, we present a solution of said equations, which is the convergent series of terms in the form of multiple integrals. This exact solution leads to following important results. First, it allows to construct in explicit form an approximate analytical solutions, which give qualitative and quite precise quantitative description of both spatial and spectral dependence of diffracted wave. Second, the exact solution serves for the basis of the general theorem concerning the smoothing features of instrument function of acousto-optical (AOTF) spectrometers and their spectral resolution. The theorem was used for optimization of measuring procedure of AOTF spectrometers and development new spectrum reconstruction techniques. All the results follow from the solution of the pair of truncated coupled-mode equations and therefore can be extended to those physical phenomena, which are described with such a set of equations, in particular, to the processes of light parametric generation or conversion