e that propagates along the geometric axis of the fiber. The time taken by this mode to reach the end of the fiber is the minimum possible and the output is delayed by that time, which is given by Senior (1992) and Buck (2004): Tmin 1111 (5.21) Multimode Fibers nm dB/km a 850 b 1300 C 1380 d 1550 Fig. 5.11 Typical spectral loss for multimode fiber. Notice the low loss at the OH wavelength. Source: Corning Inc. Wavelength (nm) Pcrit Cladding n2 Core n1 Air no=1 Axial Mode Cladding n2 Extreme Meridional Mode Fig. 5.12 Optical paths of meridional and axial modes. where the symbols have their usual meaning. Now the extreme meridional mode will reach the output of the fiber after a delay that in this particular geometric arrangement will be the maximum and given by (5.22) From Snell's law (equations 5.3 and 5.6), we have for the critical angle at the core- cladding interface the following equation: (5.23) Then, substituting into equation 5.22 for cos0, Tmax = n2 n2 .L C (5.24) Chapter 5 Optical Fibers Extreme Meridional Mode Axial Mode Input Pulse Multimode Fiber Output Pulse 5.13 Impact of the multimode fiber delay on the pulse output for a delay equal to the pulse width. The difference in the delay between the two modes is given by (5.25) where NA stands for the numerical aperture of the fiber and A is given by equation 5.10. The r.m.s. broadening of the pulse is given by (5.26) To appreciate the impact of this differential delay, let us assume that a pulse of nominal width T is launched into the fiber. If the differential delay is equal to the pulse width, the output consists of two pulses occupying a total width of 2T. This is illustrated in Figure 5.13. The receiver will therefore detect two pulses when only one was sent. This effect is called the intermodal dispersion of the fiber, and it is an additional dispersion imparted the pulse. There are a number of reasons why one has to be cautious in using equation 5.25 for long-haul communications. The first is that equation 5.25 is a worst-case scenario. In an actua