  The ultrafast optical Kerr effect (OKE) is widely used to investigate the
structural dynamics and interactions of liquids, solutions and solids by
observing their intrinsic nonlinear temporal responses through nearly-collinear
four-wave mixing (FWM). Non-degenerate mixing schemes allow for background free
detection and can provide information on the interplay between a material's
internal degrees of freedom. Here we show a source of temporal dynamics in the
OKE signal that is not reflective of the intrinsic nonlinear response but
arises from group index and momentum mismatch. It is observed in two-color
experiments on condensed media with sizable spectral dispersion, a common
property near an optical resonance. In particular birefringence in crystalline
solids is able to entirely change the character of the OKE signal via the
off-diagonal tensor elements of the nonlinear susceptibility. We develop a
detailed description of the phase-mismatched ultrafast OKE and show how to
extract quantitative information on the spectrally resolved birefringence and
group index from time-resolved experiments in one and two dimensions.
