On radiation modes in the time-dependent coupled power theory for optical waveguides

A derivation in terms of a statistical theory of power coupling is performed in order to estimate the effects of the radiation modes of an optical waveguide. Earlier, the loss term introduced in this theory was always of heuristic origin. In this paper, we derive an identical term from first principles. Accordingly, we find that coupling from radiation to guided modes along the waveguide can be neglected.