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The optical properties of solid-core micro-structured optical fibers (SC MOFs) have been studied for a long time. The process of the energy outflow of the core modes has always been associated with the process of constructive interference of the core modes fields under reflection from the photonic crystal cladding. In this paper, we want to offer a new look at the light localization in the core of SC MOFs related to the behavior of spin and orbital parts of the Poynting vector of these core modes and singularities arising in it. Such an approach can help in forming a better understanding of the process of the core modes energy leakage and also in the creation of SC MOFs with a simplified design and low losses.

We study coaxial superpositions of Gaussian optical vortices described by a geometric progression. The topological charge (TC) is obtained for all variants of such superpositions. The TC can be either integer or half-integer in the initial plane. However, it always remains integer when the light field propagates in free space. In the general case, the geometric progression of optical vortices (GPOV) has three integer parameters and one real parameter, values which define its TC. The GPOV does not conserve its intensity structure during propagation in free space. However, the beam can have the intensity lobes whose number is equal to one of the family parameters. If the real GPOV parameter is equal to one, then all angular harmonics in the superposition are of the same energy. In this case, the TC of the superposition is equal to the order of the average angular harmonic in the progression. Thus, if the first angular harmonic in the progression has the TC of k and the last harmonic has the TC of n, then the TC of the entire superposition in the initial plane is equal to (n + k)/2, but the TC is equal to n during propagation. The experimental results on generating of the GPOVs by a spatial light modulator are in a good agreement with the simulation results.