An analytic model is developed to describe the influence of coherent vibrational motion on optical third harmonic generation. The vibrational coherence is prepared and probed by a pair of collinear optical pulses, focused at the interface of a crystal that has vibrational modes that are accessible to impulsive Raman scattering. Under these conditions, the probe pulse generates a third harmonic signal that is perturbed by the vibrational coherence through three mechanisms uncovered by this model: (1) coherent second hyper-Raman scattering, (2) cascaded amplitude modulation, and (3) perturbation of Fresnel transmission and reflection at the interface. Upon scanning the optical pulse delay and translating the crystal through the focal plane, these three contributions exhibit key differences, which may be observed experimentally.
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