Abstract
An efficient 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 psi and its derivative d psi /dV. Two variational problems are then formed and solved as matrix equations by using the finite-element method. The first one is a conventional eigenvalue problem with eigen-solution (w, psi ) and dominates the computing time. The second one is a direct problem for d psi /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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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