Properties of the electromagnetic field of a non-paraxial Gaussian beam propagating through homogeneous and inhomogeneous air

The propagation of laser beams through the atmosphere is of interest for problems of communication with Earth satellites. Unfortunately, only paraxial beams are currently being investigated. Non-paraxial beams are considered in [1, 2]. We studied a non-paraxial Gaussian beam. The problem has been considered on the basis of our previous paper [3] which was revised and substantially supplemented. The task was reduced to a calculation of a line integral. Systematic computations were fulfilled, the distance of beam propagation varied from a few meters to one kilometer. First of all, we considered the beam propagation through homogeneous gas. The results are as follows. The distribution of the transverse component of the electric field is similar to that of the paraxial beam at small distances. But there arise additional maxima on the periphery, if the distance exceeds several tens of meters. Those maxima appear due to diffraction. They do not exist for paraxial beams. The axial component of the electric field has its maxima on two curves located on the plane which is normal to the beam axis ( at x2=const ). The value of the component is linearly dependent on x1 along the curves. A procedure was set forth which allows to solve the problem when the beam propagates through the inhomogeneous gas. If the permittivity is close to unity and the permeability is equal to unity we get the explicit solution. The obtained solution may be generalized to the case when the permittivity depends on time.