A model of the random phase screen in the problem of the thermal self-defocusing of light

The two-dimensional problem of the thermal self-defocusing of light in a fixed medium is examined using the approximation of geometrical optics. An exact solution of the Cauchy problem for this approximation is obtained. Based on the solution of the Cauchy problem, an exact solution is obtained for the mean intensity and phase gradient of the beam behind a random phase screen (the average over the random initial phase). This model also describes the thermal self-defocusing of a spatially incoherent beam. It is shwon that, in order to obtain finite expressions for the mean square intensity, it is necessary to exceed the boundaries of the approximation of geometrical optics.