Ray method for solving the coherence function equation in the case of inhomogeneously absorbing (amplifying) media

An investigation was made of the propagation of partially coherent radiation in refractive media with strong absorption when account must be taken of the ray trajectory curvature owing to the inhomogeneity of the imaginary component of the relative permittivity of the medium. This investigation was carried out on the basis of the equation for the coherence function. It is shown that the equation can be reduced to a system of ray equations permitting construction of effective numerical algorithms for its solution. A self-similar solution was obtained for the coherence function in the case of a parabolic distribution of the relative permittivity of the medium and an initially Gaussian distribution of the average radiation intensity. In the geometrical-optics approximation, an equation was derived for the ray trajectorys of partially coherent radiation. The distinctive features of the propagation of coherent and partly coherent Gaussian beams, with the same Fresnel numbers, in an inhomogeneous medium were discovered.