Coupled evolution equations for axially inhomogeneous optical fibres

Publisher Website
Google Scholar
Abstract
At ‘monomode’ frequencies, a uniform axisymmetric optical fibre can support left- and right-handed circularly polarized modes having the same dispersion relation. Nonlinearity introduces cubic terms into the evolution equations, which are coupled nonlinear Schrödinger equations (Newboult, Parker, and Faulkner, 1989). This paper analyses signal propagation in axisymmetric fibres for which the distribution of dielectric properties varies gradually, but significantly, along the fibre. At each cross-section, left- and right-handed modal fields are defined, but their axial variations introduce changes into the coupled evolution equations. Two regimes are identified. When axial variations occur on length scales comparable with nonlinear evolution effects, the governing equations are determined as coupled nonlinear Schrödinger equations with variable coefficients. On the other hand, for more rapid axial variations it is found that the evolution equations have constant coefficients, defined as appropriate averages of those associated with each cross-section. Situations in which the variable coefficient equations may be transformed into constant coefficient equations are investigated. It is found that the only possibilities are natural generalizations of thosefound by Grimshaw (1979) for a single nonlinear Schrödinger equation. In such cases, suitable sech-envelope pulses will propagate without radiation. Numerical evidence is presented that, in some other cases with periodically varying coefficients, a sech-envelope pulse loses little amplitude even after propagating through 40 periods of axial inhomogeneity of significant amplitude.

This publication has 0 references indexed in Scilit: