A direct analysis of the dispersion equation in birefringent optical fibres

Weakly-guiding, anisotropic step-index fibres are considered in the case where the permittivity tensor is everywhere diagonalized in the axes of the fibre. A method is shown which allows one to derive a mode and its dispersion equation with arbitrary accuracy in terms of the powers of the weak-guiding parameter. The method is applied to the derivation of the leakage loss of they-polarized LP₀₁ mode when_x>_y.