Analysis of graded-index optical fibers by the rigorous WKB

Among the mathematical analysis for graded-index optical fibers, the most widely used method is the WKB method. To overcome the WKB's inherent errors incurred in phase shift at turning points, a few researchers have suggested modified versions of the method. In this paper, the modified Airy functions are used in the core region and the conventional WKB trial solution in the cladding region, respectively, so as not to diverge at turning points and to ensure almost exact solution in cladding regions where fields decay. It turns out that this peculiar combination of both functions enable us to find out the phase shift correction term /spl delta/, which significantly improves the precision of solutions. It is demonstrated that results by the method agree almost exactly with those of the finite element method (FEM) not only in eigenvalues, but also in eigenfunctions.