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An exact and fast analytic method based on power series is established to predict the modal field distributions, Petermann-2 spot size, the normalized propagation constant corresponding to fundamental and first higher order mode in graded index fibers with any arbitrary power law profile. The variation of normalized cut-off frequencies of some LPlm modes in graded index fibers with different profile exponents are also shown here and an empirical relation between them is determined. </p

An Exact Analysis of the Fundamental and First Higher Order Mode in Graded Index Fibers with Direct Power Series Method