7.3 PULSE STRETCHING AND BANDWIDTH LIMITATIONS IN MULTIMODE FIBERS
The results of the previous section can now be directly applied to model the pulse response that occurs in a multimode fiber. Let the fiber have length Z and assume a time impulse of power (short burst of light) is launched into the fiber uniformly over all angles within. The power distribution at the fiber output can be obtained, as a function of time, by using the earlier equations with z = Z. In particular, the pulse width will be obtained from Eq. (7.2.5) as
with βf given in Eq. (7.2.6). Thus the amount of pulse spreading that occurs will depend on the fiber length, its equilibrium distance, and the coefficient βf.
Since βf determines the spreading, let us examine it in more detail. If we substitute for the numerical aperture, we have
If we relate this to our earlier result in Eq. (7.1.6), we see that the spreading coefficient βf obtained from diffusion theory, is identical to the differential time delay per length, td/Z, obtained from ray line analysis. Indeed, the maximum angular ray line contribution to the pulse dispersion is significant, and dispersion reduction techniques via fiber grading are theoretically justified. However ray line analysis always predicts a linear increase in spreading with fiber length, ...