A closed-form approximate dispersion formula for α-power graded-core fibers

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Abstract
In a previous paper, two of the authors proposed a closed-form dispersion formula for α-power graded-core fibers. However, it was found later that an important approximation implied in the analysis had been overlooked. In this paper, the same formula is newly derived in a correct manner but as an approximation. The overlooked approximation is clarified and stated explicitly. The derived approximate formula is relatively accurate for near-uniform-core fibers (such as those with α = 4 or α = 8), but the error increases appreciably for quadratic-core fibers (α = 2), which are of practical importance. A modification of the dispersion formula is proposed to improve its accuracy for the quadratic-core case. In the final part of this paper, the accuracy of the derived formulas (including the modified one) is investigated by comparing the computed characteristics with rigorous solutions.