or 53.27 corre- sponds to the maximum value and if used in system design it gives the worst case. Since in practice the value obtained is smaller but Figure 53.7 Propagation of extreme rays: (a) in step depends on a number of random parameters it is acceptable to use index fibre; (b) in parabolic refractive index fibre the root mean square value of the pulse broadening. Assuming that the light is launched into the fibre uniformly over the cone of (53.22) acceptance the r.m.s. pulse broadening for step index and parabolic graded index fibre is given by Equation 53.28. Using Snell's law of refraction gives Equation 53.23. (53.23) (53.28) The delay difference Atd between the two rays is given by The total dispersion of the multimode fibre is given by the sum of Equation 53.24. the intramodal and intermodal dispersion but in the mean square sense. The reason for this lies in the independence of the physical effects that cause the pulse broadening. The total dispersion, of is At = Atmax - At given by Equation 53.29, where am and ad are the chromatic LINIAN (53.24) (intramodal) and intermodal pulse broadening respectively. (53.29) Using the numerical aperture of the fibre gives Equation 53.25. The total fibre dispersion can be used to establish an important (53.25) figure of merit for a fibre, the bandwidth-length product, Bopt L. This is given by Equation 53.30, where o refers to the dispersion per unit length usually the kilometre. Using = 1.5 and An=0.01 we obtain 50ps/km. Compar- (53.30) ing this to the material dispersion of a single mode fibre around 1.3um the difference is substantial and the question is as to whether or not the dispersion of a multimode fibre can be reduced. Before we discuss this issue it will be very important to see what happens The performance of a state of the art single mode fibre regarding in practice. losses and dispersion is summarised in Figures 53.5 and 53.6. The The maximum dispersion (see Equation 52.25) is usually reduced loss in a state of the art multimode fibre is similar to th