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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.