Pulse Broadening in Multimode Optical Fibers

Light-emitting diodes supply their optical power in a time and space incoherent form. The line width is typically of the order of 200 A, and the radiation is approximately lambertian with an emissive area of the order of 50 X 50 /xm. Time and space incoherent optical pulses can be transmitted by oversized optical fibers. However, optical pulses propagating in such fibers tend to broaden as they travel. This is in part due to the nonzero line width of the source and the dispersion (d2k/du2) of the fiber material. The other cause of pulse broadening is associated with the fact that the time of flight of a pulse along a ray depends on the ray trajectory. Pulses traveling along axial rays usually go faster than pulses traveling along rays of large amplitude. Because both types of rays are excited by spatially incoherent sources, the difference in axial group velocity causes a broadening of the input pulse. In the main text of this paper, we assume that the carrier is 1179 monochromatic and that the spatial distribution of the rays is timeinvariant. This is the case, for instance, when the source is an injection laser that oscillates simultaneously on many transverse modes. The difference in frequency between these various transverse modes can usually be neglected. It was first pointed out by Kompfner 1 that pulse broadening in step-index fibers could be drastically reduced by introducing ray equalizers at various locations along the fiber. The role of ray equalizers is to exchange fast and slow rays.