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

From Maxwell's equations, using a Fourier expansion, spatial harmonic balance and Green's functions, closed-form expressions are found for the longitudinal electric and magnetic fields, for two orthogonally polarised modes of a birefringent fibre with or without a central index dip. Propagation constants can then be calculated to the desired degree of accuracy. Corrections up to third order are found to be significant. The linear polarisation ratio in the core and in the cladding is almost insensitive to birefringence but exhibits large variations in the central dip, where it deteriorates as the birefringence increases.