Group- and phase-velocity-mismatch fringes in triple sum-frequency spectroscopy

The effects of group and phase velocity mismatch are well-known in optical\nharmonic generation, but the non-degenerate cases remain unexplored. In this\nwork we develop an analytic model which predicts velocity mismatch effects in\nnon-degenerate triple sum-frequency mixing, TSF. We verify this model\nexperimentally using two tunable, ultrafast, short-wave-IR lasers to\ndemonstrate spectral fringes in the TSF output from a 500 $\\mu$m thick sapphire\nplate. We find the spectral dependence of the TSF depends strongly on both the\nphase velocity and the group velocity differences between the input and output\nfields. We define practical strategies for mitigating the impact of velocity\nmismatches.\n