Extreme limit in linear polarisation ratio in step-index single-mode fibres with a central

From Maxwell's equations, using a Fourier expansion, spatial harmonic balan ce and Green's functions, closed-form expressions are found for the longitu dinal electric and magnetic fields, for two orthogonally polarised modes of a birefringent fibre with or without a central index dip. Propagation cons tants can then be calculated to the desired degree of accuracy. Corrections up to third order are found to be significant. The linear polarisation rat io in the core and in the cladding is almost insensitive to birefringence b ut exhibits large variations in the central dip, where it deteriorates as t he birefringence increases.