A simple method for prediction of first-order modal field and cladding decay parameter in graded index fiber

Based on a series expansion method involving the Chebyshev technique, we present analytical expressions for first higher order modal field as well as cladding decay parameter in case of graded index fiber. This method utilizes the formulation of a linear relation of the ratio of first- and zero-order modified Bessel functions, with reciprocal of Cladding decay parameter. This leads to the evaluation of the Cladding decay parameter from a simple equation involving a third-order determinant and the first higher order modal field is thereafter found from two simple equations. Thus the paper presents the technique of avoiding complicated calculations of Chebyshev coefficients and therefore, the present formalism will be extremely important for practical engineering problems. Taking step and parabolic index fibers as examples, we show that our estimations of the said propagation characteristics agree excellently with the available exact results. The concerned calculations involve very little computations.