ion; this occurs for q at slightly less than 2. The total number of modes that can propagate in a MM fiber is given by (6.1.13) R ( = r/a) Fig. 6.1-6 Radial intensity distributions (normalized to the same power) of some low-order modes in a step index fiber for V = 8. Notice that the higher order modes have a greater fraction of Fig. 6.1-7 The refractive index variation for a power law profile for power in the cladding. Reprinted from Ref. [5], p. 382, courtesy of different values of q. Reprinted from Ref. [5], p. 396, courtesy of Cambridge University Press. Cambridge University Press. Optical fiber, cable and connectors CHAPTER 6.1 For a step-index fiber q = 8 and N = V2/2. Equation It is more common to give a coupling efficiency; thus, giving the total power accepted by the fiber, the effi- (6.1.13) is only valid for large V numbers. ciency is defined as [10] One can calculate the different ray paths that are possible in a MM fiber using a geometrical optics ap- proach [8]. A more accurate view of the different modes (6.1.18) can be obtained by solving Eq. (6.1.3) using the so-called WKB approximation [3]. Using this analysis the phase where Pin is the power launched into the fiber and Plm constants for the different modes can be shown to obey the power accepted by the LP mode. For link budget the following relationship: analyses it is more convenient to deal with coupling losses in units of decibels a: a = 10.logn. (6.1.19) (6.1.14) A more general definition of the coupling efficiency n for an optical fiber that obeys the weekly guiding approxi- 6.1.1.4 Optical coupling mation can be given as [10] A first approach to estimate how much light can be coupled into an optical fiber is to use the ray picture. In (6.1.20) this picture the light is confined within the core if it undergoes total internal reflection at the core-cladding boundary. This will occur only for light entering the fiber where n2 is the refractive index of the cladding, Z o is the within an acceptance cone defined by the angle 0 free space wave 