Calculation of dispersion in graded-index multimode fibers by a propagating-beam method

Methods are developed for extracting from a numerical propagating-beam solution of a scalar wave equation the information necessary to compute the impulse-response function and the pulse dispersion for a multimode graded-index fiber. It is shown that the scalar Helmholtz equation and the parabolic wave equation have the same set of eigenfunctions in common and that the eigenvalues for the two equations are simply related. Thus one can work exclusively with the simpler parabolic equation. Both the mode eigenvalues (propagation constants) and mode weights, which are necessary for determining the impulse response, can be obtained with high accuracy from a numerical Fourier transform of the complex field-correlation function by the use of digital-filtering techniques. It is shown how a solution obtained in the absence of profile dispersion can be simply corrected for the presence of profile dispersion. In an illustrative example a gradedindex fiber with a central dip in its profile is considered.