Mode analysis of graded-index optical fibers using a scalar wave equation including gradient-index terms and direct numerical integration

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Abstract
A new mode analysis is proposed for optical fibers with arbitrary refractive-index profile. Scalar wave equations including gradient-index terms and characteristic equations including an abrupt change of the refractive index at the core-cladding boundary are derived for HE, EH, TE, and TM modes. The propagation constant, cutoff frequency, group velocity, and field distribution of each mode are calculated with high accuracy by direct numerical integration of a differential equation and the numerical solution of a transcendental equation.

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