About group velocity of electromagnetic wave in linear isotropic non-homogeneous medium

Researches of spatial distribution of group velocity of different laser beams are of high actuality for the last years. These researches are important for developing of information technologies, especially for laser communication systems. The most of these works are applicable for particular cases of laser beams in homogeneous medium [1,2]. In the new work the theoretical model is presented, which allows not only to find spatial distribution of group velocity of beams (direct problem), but also to find spatial structure of beams with necessary group velocity (inverse problem). This model is applicable to any type of laser beams and for any linear isotropic inhomogeneous medium. No additional approximations, like paraxial one, are used. Solutions of the final system of equations are always satisfy energy conservation law, because the system includes it in explicit form. It is also shown condition, where evanescent wave appears and beam with necessary group velocity is spatially limited. This model is of high generality and prospective for applications for information technologies, like laser communications in atmosphere, free space and developing of photonic integrated circuits. [1] D. Giovannini et al., Science. 347, 857 (2015). [2] F. Bouchard et al., Optica. 3, 351 (2016)