ance, and a is the profile parameter that gives the refractive index profile. For a = 8 the representation corresponds to the step index profile. Figure 5.14 illustrates the fiber refractive index for various values of the profile parameter a. The step index profile is obtained by setting a = 8. The improvement in differential delay can be observed by considering the modes multimode fiber with the profile parameter a set to 2 (Figure 5.15). Two effects may be observed. First, the axial mode propagates through the section of the fiber core where the refractive index has its maximum value, which implies that the axial mode is slowed down. The meridional modes are bent toward the axis of the fiber, reducing their flight time. Together these two effects reduce the differential delay. If electromagnetic theory is employed to analyze the differential delay, the value obtained is (5.29) Refractive Index n(r) Fig. 5.14 Fiber refractive index for different values of the profile parameter a. Source: Adapted from Senior (1992). Used with permission. Core Axis Radial Distance r Chapter 5 Optical Fibers Refractive Index n(r) Cladding Axial Ray Fig. 5.15 Graded index multimode fiber: (a) refractive index profile; (b) meridional modes within the fiber. Source: Adapted from Senior (1992). Used with permission. The implication of this equation is to highlight the fact that the reduction of the differ- ential delay for step index fiber is A/8. The r.m.s. pulse broadening is now given by (5.30) and there is a A/10 reduction in the r.m.s. pulse broadening. It is now straightforward to compare the r.m.s. pulse broadening for step and graded index fibers. From the example studied before, we have a 10-km graded index fiber with a core refractive index of 1.5 and A = 2%. Then, from equation 5.30, the r.m.s. pulse broadening is and the maximum bitrate that can be used with this graded index fiber is now 434 Mbit/s! Comparing the r.m.s. pulse broadening of the two fibers for a length of 1 km, one obtains and Oslgraded - 0.057ns/km Because