Modal analysis of polarisation effects in weakly-guiding fibres

A complete set of modes of the scalar wave equation on a circular fibre of arbitrary refractive-index profile is presented as a basis for perturbation analyses of a range of optical waveguide problems. Using these modes, we have generalised, in a systematic way, results which were previously known only for the step-index fibre, namely (i) the degree of birefringence in a monomode fibre whose core is slightly elliptical and (ii) the vector corrections to the modal fields due to the nonzero difference between the refractive indexes of the core and cladding. The validity of the perturbation theory for birefringence has also been verified by considering higher-order perturbations.