The analytical models for the propagation of wave beams in the presence of strong refraction in liquid media have been developed, applicable to both narrow and wide, including structured laser beams used for probing inhomogeneities with significant refractive index gradients. Laser diagnostics of water stratifications with significant refractive index gradients, as a rule, is based on solving the inverse problem of refraction of optical radiation, which requires the development of models for the propagation of probing beams in and out of the medium. The propagation of laser radiation in highly inhomogeneous liquid media is accompanied by a change in its characteristics: curvature of the ray trajectories, distortion of the beam shape, and the formation of caustics. In this case, it is advisable to carry out measurements based on probing the medium with structured laser radiation, which makes it possible to record not the change in intensity, but the relative displacement of the structural elements of the beam.

Image discretization at the physical level can be carried out based on the use of structured laser beams for probing, formed using diffractive optical elements (DOE). DOEs that focus laser radiation into thin lines or small regions of space are the most promising for use in diagnosing gradient inhomogeneities. The use of beams with such a structure significantly expands the possibilities of traditional laser gradient methods.

The wave field of a structured laser beam with a known wavelength which has passed through an optical inhomogeneity with a given change in the refractive index can be described based on the Kirchhoff integral or using the spectral approach. Beam propagation in an inhomogeneous medium is described by the Helmholtz equation, which under a number of assumptions can be reduced to a parabolic one and solved by numerical methods. An alternative is to use an approach that simultaneously uses the principles of geometric optics and the spectral method. The advantage of this approach is the possibility of obtaining an approximate solution in an analytical form that is the same for wide and narrow beams, which makes it possible to solve the inverse problem without using laborious computational methods.

Using the stationary phase method, an asymptotic representation is obtained for the wave field of structured laser beams passing through an optically inhomogeneous medium, which is valid in the region of caustics and in the region of multirays. On the basis of experimental refractive images and the developed wave models, the reconstruction of the spatial and temporal characteristics of thermophysical and wave processes in liquid, including those accompanied by an abrupt perturbation of its parameters, can be carried out. The use of wave models in this case is fundamental for describing the position of the caustics and the significant spreading of the structural elements of the beam.

Обоснована актуальность исследования и сформулированы проблемы, возникающие при разработке математических моделей распространения волновых пучков в условиях сильной рефракции. Предложены модели пучков, формируемых на основе дифракционных оптических элементов. Представлены результаты моделирования прямотеневых рефракционных изображений для лазерных пучков различных типов при распространении их в стратифицированной жидкой среде в отсутствие и при наличии каустик.