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We develop a method for mapping the anharmonic lattice potential using thetime-dependent electric field of the transmitted pulse through thin samplesupported by a substrate of non-negligible thickness. Assuming linearpropagation in the substrate we fully take into account internal reflection init while the sample can show arbitrary nonlinear response. We examine theeffect of frequency averaging appropriate for broad-band pulse and compare theresults taking into account the full frequency dependence. We illustrate theprocedure applying it to a model based on recently observed ferroelectricsoft-mode nonlinearity in SrTiO$_3$.

Mapping the lattice-vibration potential using terahertz pulses