Optimum Refractive-Index Difference for Graded-Index Fibers Resulting From Concentration-Fluctuation Scattering

As is well known, multimode optical-fiber waveguides with graded refractive-index profiles can have appreciably lower mode dispersion than fibers with a step index profile for the same modal content.1-3 One consequence of this fact is that, for a given bit rate and fiber diameter, a graded-index fiber can be used that propagates many more modes. This is important when the source is incoherent, such as a light-emitting diode, since the amount of power that can be coupled into the fiber from such a source is proportional to the number of modes it can propagate. 1395 At what distance a signal of a given bit rate must be regenerated depends on how much dispersion has taken place and on the strength of the signal. At first, it seems that the distance would be maximized by increasing the number of modes until the maximum distance resulting from dispersion is equal to that resulting from signal strength. In this paper, we show that this may not be the case, and that a maximum distance can arise from signal strength considerations alone. Briefly, the argument is as follows. The refractive index of the fiber is graded by a graded concentration of a dopant in a base glass. To increase the number of modes propagating in a fiber of a given diameter, the magnitude of the index variation must be increased and, therefore, so must the dopant concentration. Associated with the dopant is an additional loss resulting from scattering by fluctuations in the composition of the glass.4 Therefore, we have a situation in which, as the number of modes is increased, the loss coefficient is also unavoidably increased.