L is the length of the fiber. BL This only gives us a rough estimate of a fundamental limitation of step-index fibers. Such fibers can communicate data at a bit rate of 10Mbps over distances up to 10km and may be suitable for some local area networks. If we compare this inequality to the previous one, we can easily verify that the BL of such fibers is improved by nearly three orders of magnitude compared with the step-index fibers. And as matter fact, the first generation of lightwave systems used graded-index fibers.
Further improvement is possible only by using single-mode fibers.
From this set of equations, many useful results have been obtained. However, we are interested in using fibers for communications and not the very detailed background, we are not going to cover them here. One can find many electricalmagntic books have detailed deriation for all kinds of equations used to describled all kinds of charactistics of the fibers.