Modal analysis of a step index fiber with a parabolically decreasing refractive index grading in the core along the direction of propagation

Abstract

We make an analytical study of the modal characteristic equation of a step index fiber with a parabolically decreasing refractive index grading in the direction of propagation. We choose the cylindrical polar coordinates (ρ, φ, z) and, assuming that the propagation is along the z-direction, we use the boundary conditions under the weak guidance approximation to obtain the modal characteristic equation. The propagation constant β depends on the z-coordinate, and a typical numerical computation for the azimuthal modal index v = 1 shows local modes with an oscillatory dependence of β with z. The oscillatory behavior of β is expected to be due to a superposition of the forward wave with partially reflected backward waves. © 1998 John Wiley & Sons, Inc.