Theory of time-dependent propagation in multimode lightguides

Abstract

A coupled system of equations governing the propagation of a signal in a statistical ensemble of multimode optical fibers is presented. It describes, besides the usual average modal powers, the evolution of the interference terms between the mode amplitudes and of the modal power fluctuations. Our procedure allows us to treat the general nonstationary nonmonochromatic case of an arbitrary signal fed into the lightguide by a source possessing a finite spectral bandwidth. The introduction of modal power fluctuations permits us to establish a theorem connecting the value of the modal power, averaged over the fiber ensemble, with the actual one concerning a single fiber. These two values coincide, in the polychromatic case, for large values of the fiber length, thus providing the main result of the paper, that is the justification of the statistical approach to the problem of propagation. Furthermore, the analysis of the interference terms presents evidence for the difference between the propagation of an amplitude-modulated and a frequency-modulated signal.