Modal Dispersion in Optical Fibers With Arbitrary Numerical Aperture and Profile Dispersion

Circular-symmetric, multimode, optical fibers intended for large communication capacity must have low modal dispersion and this is achievable by the quasi-complete equalization of the group velocities of all modes 1 (or rays). This equalization depends critically both on the refractive-index profile and on the profile dispersion of the fiber. The profile dispersion is defined in Section II, but here it is enough to know that it is related to the derivative of the index with respect to the wavelength. To understand better the objectives of this paper, let us first review some recent evolution of thoughts linking the index profile and the profile dispersion of a fiber to the pulse broadening caused by modal dispersion. 49 Gloge and Marcatili 2 showed that if the numerical aperture (NA) of the fiber is arbitrary but the profile dispersion is negligible, there is a family of fibers--for which the dielectric constant profiles decrease radially according to power laws--that is important for two reasons. The first reason is that the family encompasses a wide variety of easy-to-make fibers (step-index, quasi-parabolic, etc.) possessing the unique property that the group velocity of each mode is a function only of its propagation constant; this drastically simplifies the analysis. The second and more important point is that for an almost parabolic power law of the dielectric profile, a fiber with small NA has the very narrow impulse response needed for high-speed communication. Olshansky and Keck:J extended these results in a very important way by showing that if the profile dispersion is constant across the core, narrow impulse response is achievable in small NA fibers by a simple modification of the exponent of the dielectric-constant profile's power law.