Optical fibres are widely used in optical communication systems because they can transmit signals in the form of extremely short pulses of quasi-monochromatic light over large distances with high intensities and negligible attenuation. A fibre that is monomode and axisymmetric can support both left- and right-handed circularly polarised modes having the same dispersion relation. The evolution equations are coupled nonlinear Schröinger equations, the cubic terms being introduced by the nonlinear response of the dielectric material at the high optical intensities required. In this thesis we analyse signal propagation in axisymmetric fibres both for a fibre with dielectric properties which vary gradually, but significantly, along the fibre and for a fibre which is curved and twisted but with material properties assumed not to vary along the fibre. For fibres with axial inhomogeneities, we identify two regimes. When the axial variations occur on length scales comparable with nonlinear evolution effects, the governing equations are found to be coupled nonlinear Schröinger equations with variable coefficients. Whereas 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. The results of numerical experiments show that a sech-envelope pulse and a more general initial pulse lose little amplitude even after propagating through many periods of an axial inhomogeneity of significant amplitude. For a curved and twisted fibre, it is found that the pulse evolution is governed by a coupled pair of cubic Schröinger equations with linear cross coupling terms have coefficients related to the local curvature and torsion of the fibre. These coefficients are not, in general, constant. However for the case of constant torsion and constant radius of curvature which is comparable to the nonlinear evolution length, numerical evidence is presented which shows that a nominally non-distorting pulse is unstable but the onset of instability is delayed for larger values of torsion.
|University of Edinburgh
|Electronic Thesis or Dissertation
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