Equation for modeling two-photon absorption in nonlinear waveguides

We derive a novel propagation equation for optical waveguides that properly accounts for two-photon absorption (TPA). We start from a simple quantum theory of nonlinear fibers allowing for TPA to be included in a straightforward fashion. The derived equation is shown to be in excellent agreement with numerical results of conventional pump-and-probe schemes and, to the best of our knowledge, is the first single equation capable of correctly modeling TPA in the context of broadband signals.