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Large Phase Shifts due to the χ (2) Cascading Nonlinearity in Large Walk-off and Loss Regimes in Semiconductors and Other Dispersive Materials

The nonlinear phase shift associated with χ(2) cascading was studied for ultrashort pulses in regimes with large temporal walk-offs between the fundamental and the χ(2)-generated second-harmonic (SH) pulses, a situation typical of semiconductors. Despite the small overlap between the fundamental and SH pulses after they walk-off each other, a nonlinear phase shift was numerically observed to occur at a rate comparable to that before they walk-off. A π/2 phase shift was demonstrated even in a waveguide 15 times longer than the walk-off length.