In this article, author considers the process of generation of fiber modes carrying orbital angular momentum (vortex modes) using chiral fiber Bragg gratings; in this context, the formation of vortex modes is carried out by converting thefundamental mode into higher order modes. Within the framework of the article, a generalized mathematical model of chiral fiber Bragg gratings is presented, which includes an arbitrary function of apodization and chirping, which makes it possible to calculate

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... atings that form vortex modes of a given order for the required frequency range with the required reflection coefficient. In addition, a matrix method for describing chiral fiber Bragg gratings is proposed, based on the mathematical apparatus of the coupled modes theory and scattering matrices. This matrix approach is convenient for describing complex and / or cascaded gratings. In addition, in this work, simulation of the considered fiber structures is carried out.