Propagation of Gaussian and Hermite-Gaussian non-paraxial beams in a homogeneous and inhomogeneous atmosphere

The communication with Earth satellites depends on propagation of a laser beam through the atmosphere. The advantages of an optical wave system over a conventional radio frequency system were analyzed earlier [1]. When using optical transmitters there are a number of problems. We must know the structure of turbulent fluctuations in the atmosphere and beam distortions that occur due to those fluctuations. Recently we set forth the solution for electromagnetic field of a non-paraxial Gaussian beam [2]. The main computational difficulty is the fact that the solution includes highly oscillatory integrands. The data were revised and supplemented. Some of the calculations were performed again. We have considered the propagation of a laser beam in both homogeneous and inhomogeneous media. The components of the electromagnetic field at different distances from the source were calculated. In addition to the results that refer to the Gaussian beam the paper contains data that refer to the Hermite-Gaussian beam. The task of beam propagation in an inhomogeneous atmosphere is reduced to solving the equation E=F{n(r),E(r). Here n is the refractive index and F is a known function. The equation can be solved by the method of successive approximations. We used only the first approximation. We supposed that permeability is equal to unity. A function describing the dependence of the refractive index on coordinates was selected. An example of the calculation is given in the paper. The solution may be generalized to the case when the refractive index depends on time.