Comprehensive analytical model to characterize randomness in optical waveguides
Résumé
: In this paper, the coupled mode theory (CMT) is used to derive
the corresponding stochastic differential equations (SDEs) for the modal
amplitude evolution inside optical waveguides with random refractive index
variations. Based on the SDEs, the ordinary differential equations (ODEs)
are derived to analyze the statistics of the modal amplitudes, such as the
optical power and power variations as well as the power correlation
coefficients between the different modal powers. These ODEs can be solved
analytically and therefore, it greatly simplifies the analysis. It is
demonstrated that the ODEs for the power evolution of the modes are in
excellent agreement with the Marcuse' coupled power model. The higher
order statistics, such as the power variations and power correlation
coefficients, which are not exactly analyzed in the Marcuse' model, are
discussed afterwards. Monte-Carlo simulations are performed to
demonstrate the validity of the analytical model.