First-order correction to 'weak-guidance' approximation in fibre optics theory

The paper considers mode propagation in a straight optical fibre of arbitrary cross-section index profile, in the limit of small index contrast. A perturbation analysis is applied to the vector wave equation which governs the problem, with the zero-order limit corresponding to the generally assumed scalar approximation. Simple expressions are obtained for the first-order term in an asymptotic power series expansion of the mode propagation constants, in terms of the index contrast parameter. The effect is discussed of the various possible symmetries of the index profile.