Bell-shaped refractive index profiles of multimode optical fibers and methods for calculating their optical properties

The paper investigates the optical properties of multimode fibres whose profiles are represented by a broad class of bell-shaped analytical functions. We consider the profiles with different curvature and described by (i) the Fermi–Dirac distribution function, (ii) the Gaussian, (iii) the cycloid function, and (iv) a family of hyperbolic functions. Main approaches are presented to obtain the solution of the eigenvalue problem. A comparative analysis is performed of the optical properties of the mode composition of optical fibres, and their advantages and limitations for fibre-optic information transmission systems are discussed.