Analysis of optical fibers with graded-index profile by a combination of modified Airy functions and WKB solutions

An almost exact eigenvalue equation for optical fibers with graded-index profile is derived mathematically based on a combination of the modified Airy functions and the Wentzel, Kramers, Brillouin (WKB) trial solution. By applying proper boundary conditions, a phase shift correction term /spl delta/ is found out which improves the inherent error problems of the conventional WKB method. It is shown through computer simulations that results of the derived eigenvalue equation are in excellent agreement with those of the finite-element method.