Pulse propagation in optical fibres with index profiles slowly varying along their length

This paper describes the formalism for calculating the effect of profile variations along the fibre on transit times and path parameters for rays in multimode fibres. The ideal case of power-law profiles is considered in detail and it is shown that when the exponentq is given byq=q₀+f (z), the fibre may be described by an equivalent exponentq_e. Simple formulae forq_e in terms of the average properties off(z) are given. The ray parameter varies and this is shown to have only a minor effect on transit time, but does imply that some rays suffer an attenuation when0. If the amount of dopant in any crosssection is assumed constant, the fibre radius must vary whenq varies and profiles with this attribute are examined and shown to have ray behaviour similar to that described above.