Subpicosecond pulse propagation in optical fibres with transverse and longitudinal inhomogeneities

Short optical pulse propagation is investigated in the light guide characterized with a strong dependence of the fibre material refractive index on the radial coordinate and a weak dependence on the longitudinal coordinate, with a weak spatial bending of the light guide axis being allowed as well. A three-dimensional nonlinear wave equation used in modeling the process is solved asymptotically with respect to a small parameter setting the order of magnitude of the pulse amplitude. A relationship between the propagating modes and the eigenvalues and eigenfunctions of a singular Sturm–Liouville problem is elucidated. The pulse propagation is shown to be three-scale: the high-frequency carrier is modulated with the envelope which evolves in a two-scale manner and is described with a nonlinear Schrödinger equation with coefficients depending on the longitudinal coordinate. For several types of the transverse and longitudinal inhomogeneities, expressions through elementary functions are obtained for the transverse distribution of the wave field and the envelope soliton. The possibility is stated for managing pulse parameters by means of varying the transverse and longitudinal inhomogeneities of the light guide.