Multimode Dispersion of Light Wave Propagation in Graded-index Cladded Fiber-optic Cable

An optical fiber essentially consists of a transparent core medium with a thin cladding of a slightly less refractive index for total internal reflection of a passing signal of light. The material is usually homogeneous, but lately graded-index fiber cables are gaining increased application for greater efficiency in the propagation characteristics. Technology has evolved to furnish grading of the refractive index of the core to have different profiles. A parabolic profile of some degree <img src=image/12637878_01.gif> is often mentioned in texts (Keiser [7], p .63), but lately profiles of various other shapes, including nonsmooth steps (Cvijetic [1], p.35) have come in to usage for better wave guide action. A theoretical study of light waves propagating through such fibers is presented in this article, based strictly on the Maxwell equations of electromagnetism solved in terms of the single Hertz vector <img src=image/12637878_04.gif>. The dispersion equation for the guided wave propagation is obtained in general terms from the theory. The method is first developed for the case of the parabolic profile and then extended to any general form of the refractive index. Numerical computation of the dispersion equation, for the first three modes in the parabolic case, with <img src=image/12637878_02.gif>, show interestingly enough that the dispersion curves are pairs of segmented curves having opposite curvatures. A study of a non-smooth index fiber, like that of NZDSF, is also carried out from the general method developed, for which the dispersion equation does not show any dispersion whatsoever for the fundamental mode <img src=image/12637878_03.gif> - the purpose for which it is designed for practical use.