Radiation from a periodically bent dielectric cylinder with a graded-index profile

The scattering of guided modes on a dielectric cylinder is investigated for periodically bent cylinders. The graded-index cylinders, in which the relative permittivity changes along the cylinder radius, are treated. Analytical expressions for the amplitude and phase variations of the radiation cylindrical waves are found in a uniform and self-consistent way. Fibers with arbitrary values of the core and cladding index of refraction have been investigated. The general analysis of periodic and nonperiodic deformations of small amplitudes are presented and the special cases of sinusoidally and helically bent fibers, having parabolic index profiles, are considered in detail. The two types of fiber perturbations yield similar characteristics with more radiation losses resulting from a helically bent fiber. A weak inhomogeneity of relative permittivity does not effect the characteristics significantly modifying the phase, but not the amplitude variations of interacting modes. The conversion between guided and radiation modes of different polarizations is stronger in cylinders of smaller radii. The higher order modes of a uniform cylinder are scattered stronger than the lower order modes, and the radiation losses decrease with the increasing cylinder radius.