Material dispersion of graded-index fibers from numerical aperture measurements

The material dispersion of a parabolic graded-index fiber can be completely characterized through numerical aperture measurements. The relation between the dispersion slope and wavelength of zero dispersion is discussed for single-mode fibers, and the corresponding relation for material dispersion in multimode fibers is presented. Then the effective wavelength of zero material dispersion in a multimode fiber is expressed in terms of a quantity that resembles a numerical aperture. Formulas relating that quantity to measured numerical apertures are derived in the Appendix. Starting with just numerical aperture measurements, therefore, one may determine the effective wavelength of zero material dispersion and effective material dispersion slope for a multimode fiber.