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.
Journal of the optical society of America 70 (4), 388-394, 1980-04
Optical Society of America