Theory of the profile-moments description of single-mode fibres

Single-mode optical fibres are characterised by the moments ¿m of their refractive-index profiles. An accurate description of light propagation along such fibres is obtained when the complete profile details are replaced by the reduced profile data in the form of ¿0, ¿2 and ¿4. The average or effective waveguide parameter V¿, which incorporates ¿0, emerges naturally and universal formulas are given in terms of V¿, ¿¿2 = ¿2/¿0 and ¿¿4 = ¿4/¿0. These formulas cover the fundamental-mode eigenvalue, group velocity and dispersion parameters, field spot size and fraction of power propagating within the core, and the cutoff parameter for the second waveguide mode. They are simple to apply and their good accuracy, which is demonstrated for a wide variety of examples, indicates that they are suitable for use in fibre design studies. The formulas also naturally lead to a qualitative description ofwaveguide behaviour: different fibres have similar properties when these are considered as functions of V¿, and a residual magnitude scaling can be attributed to profile shape which enters principally through ¿¿2.