Radiative transfer can be used to simplify the problem of propagating low-coherence optical fields through scattering and absorbing media when a full electromagnetic analysis would be intractable. One reason why radiative transfer greatly simplifies such a problem is that it does not explicitly account for interference. To determine the conditions under which the intensity- or power-dependent scattering of radiative transfer could be applied to waveguide systems, we performed a time-domain derivation of the time-dependent equation of transfer. For systems in which there is little time-averaged mode coupling over the distance that it takes the pairwise differences in the modal group delays to exceed the source temporal coherence time, the time-averaged modal powers exhibit no interference. The net amount of power transferred between modes is a function only of the time-averaged modal powers themselves. The rate at which power is transferred between modes is described by the power coupling coefficients. This derivation shows how the effective power coupling coefficients representative of a particular waveguide depend not only on the perturbations driving the power transfer but also on the propagation coefficients of the modes, the group velocities of the modes, and the autocorrelation function of the source.
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