An eficient algorithm is proposed for calculating the dispersion characteristics of optical fibers with radially arbitrary refractive-index profiles. It is based on a variational finite-element formulation. Formulas for the derivatives of the normalized propagation constant w with respect to the normalized frequency V up to the second order are derived by using a reaction formula. These formulas contain the modal field $ and its derivative d $ / d V . Two variational problems are then formed

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... solved as matrix equations by using the finite-element method. The first one is a conventional eigenvalue problem with eigen-solution { w . $} and dominates the computing time. The second one is a direct problem for d$/dV and can be solved by a few simple matrix manipulations. The proposed algorithm turns out to be a rapidly convergent one and careful arrangement results in saving for both storing memory and computing time.