Statistical Approximations in Studying the Interaction of Broadband Laser Radiation in a Complex Environment

Abstract

In this paper, statistical expressions describing the change in the degree of coherence of broadband laser radiation with a tilted coherence layer in a homogeneous medium have been theoretically studied. The case of changing the spatial coherence of intersecting broadband light beams with parallel layers of coherence has been considered. The region of coherent interaction has been estimated for this case and it has been determined that the degree of coherence of a dispersed beam decreases noticeably faster with distance than in the case without the use of a dispersive element. In the framework of the used models, it has been found that the violation of coherence in the propagation of a light beam increases with an increase in the tilt angle of the coherence layers. The possibility of significantly increasing the area of coherent interaction of intersecting beams as a result of tilting their coherence layers in such a way that by setting a certain value of the angle of their intersection, it was possible to obtain parallelism of the coherence layers for them has also been studied. In this case, restrictions on the transverse size of the overlapping beams are removed and it becomes possible to use the entire area of their overlap. A general scheme for constructing the asymptotics of the obtained analytical solutions has been outlined. It has been shown that the universal character of asymptotic methods for calculating wave impulses can be combined with some universal heuristic conditions and criteria for the applicability of these methods. These criteria provide internal control over the applicability of the used asymptotic methods, and in some cases, on the basis of the formulated criteria, it is possible to evaluate wave fields where these methods are not applicable. This opens up a wide range of possibilities for analyzing wave patterns in general, which is important both for the correct formulation of theoretical studies and for performing evaluation calculations for experimental or field measurements of wave packets of laser radiation.