Transmission characteristics of graded-index oval (GIO) core fibers are theoretically analyzed, and basic equations representing the specific properties of the fiber are obtained. Formulas for the propagation constant, the field-profile function, the cutoff condition, and the total number of guided modes are derived in explicit forms. The formula for the change of the Gaussian beam radius as a function of the propagation distance is also given, and the numerical example agrees well with experimental data and agrees completely with that obtained by the beam-propagation method. These explicit expressions are useful for finding optimum structural parameters of GIO fibers to be used in practical fields.
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