In this paper the chiral fiber Bragg gratings (ChFBG) for generation of fiber modes carrying orbital angular momentum (OAM, vortex modes) are considered. Within the framework of the article, a generalized mathematical model of ChFBG is presented including an arbitrary function of apodization and chirping, which makes it possible to calculate gratings that form vortex modes of a given order for the required frequency range with the required reflection coefficient. In addition, a matrix method based on the mathematical apparatus of the coupled modes theory for describing ChFBG is proposed, simulation of the considered fiber structures is carried out.
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