Highly Non-Degenerate Two-Photon Absorption in Silicon Wire Waveguides

Non-degenerate two-photon absorption (TPA) is investigated in a nanophotonic silicon waveguide in a configuration such that the dispersion of the nonlinear absorption and refraction cannot be neglected. It is shown that a signal wave can strongly be absorbed by cross-TPA by interaction with a low energy pump pulse (1.2\,pJ), close to the half-bandgap and experiencing low nonlinear absorption. The experiments are very well reproduced by numerical simulations of two-coupled generalized nonlinear Schr\"{o}dinger equations (GNLSE), validating the usual approximation made to compute the cross nonlinear coefficients in indirect-gap semiconductors. We show that the nonlinear dynamics can be well described by a single GNLSE despite the wavelength separation between the pump and the signal waves. We also demonstrate that in silicon wire waveguides and contrary to optical fibers, the dispersion of the nonlinear absorption is much larger than the dispersion of the Kerr effect. This could have an impact in the design of all-optical functions based on cross-TPA, as well as on the study of supercontinuum and frequency comb generation in integrated semiconductor-on-insulator platforms.