On the analysis of optical fibers described in terms of Chebyshev polynomials

An analysis is made of an optical fiber whose arbitrary refraction function is expressed in terms of the Chebyshev polynomials. The method of separation of variables is used for solving the corresponding wave equation. As the general solution of this equation, the series with undetermined coefficients and the same kind of Chebyshev polynomials is obtained. These undetermined coefficients are calculated on the basis of the corresponding coefficients of the assumed refraction function. It is shown that the proposed analysis algorithm is accurate, fast convergent, and reliable from the standpoint of numerical calculations. The validity of the presented approach and analysis algorithm has been confirmed by a numerical experiment.>