Modal Analysis and Propagation Properties of the Multilayered Circular Optical Fiber

We propose an alternative approach for solving modes of optical fibers with azimuthal symmetry. We approximate arbitrary smooth profile functions by that of a multi step-index fiber with up to thousands of steps. We analytically establish a transcendental eigenvalue equation and solve it numerically using a fast algorithm of linear complexity with respect to the number of steps. We show accordance between our multi step-index mode solver and other techniques. Compared to the finite-difference method, our method yields results of higher calculation accuracy within mere seconds. To highlight high optimization potential of the algorithm, we consider a GRIN fiber and optimize differential mode group delay of 10 LP modes.