Formulas for TE_01 cutoff in optical fibers with arbitrary index profile

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Abstract
The cutoff problem of TE modes of a radially inhomogeneous optical fiber is transformed into an integral equation by using a Sturm-Liouville-type boundary problem. Three types of approximate formulas for calculating the cutoff frequency of the TE0 1 mode are derived by calculating the eigen-value of this integral equation. The comparison of the cutoff frequencies calculated by means of these formulas with some exact values indicates that the third approximate formula gives the best accuracy (within 10 -3%) and requires only a few seconds of computation time. The effect of the center dip on the cutoff frequency is investigated. The single-mode condition of single-mode fibers with any arbitrary refractive index profile can be obtained with high accuracy.

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