MODAL-ANALYSIS OF A STEP-INDEX FIBER WITH A PARABOLICALLY DECREASING REFRACTIVE-INDEX GRADING IN THE CORE ALONG THE DIRECTION OF PROPAGATION

We make an analytical study of the modal characteristic equation of a step index fiber with a parabolically decreasing refractive index grad ing in the direction of propagation. We choose the cylindrical polar c oordinates (rho, phi, z) and assuming that the propagation is along th e z direction, we use the boundary conditions under the weak guidance approximation to obtain the modal characteristic equation. The propaga tion constant beta depends on the z-coordinate, and a typical numerica l computation for the azimuthal modal index nu = 1 shows local modes w ith an oscillatory dependence of beta with z. The oscillatory behavior of beta is expected to be due to a superposition of the forward wave with partially reflected backward waves. (C) 1998 John Wiley & Sons, I nc.