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arXiv:physics/9904056 · The European Physical Journal B

Pump and probe nonlinear processes: new modified sum rules from a simple oscillator model

F. Bassani, Valerio Lucarini

Published Nov 1, 1999• 11 citations
arXivHTMLPDF
DOI
10.1007/s100510051011

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The nonlinear oscillator model is useful to basically understand the most important properties of nonlinear optical processes. It has been shown to give the correct asymptotic behaviour and to provide the general feature of harmonic generation to all orders, in particular dispersion relations and sum rules. We investigate the properties of Pump and Probe processes using this model, and study those cases where general theorems based on the holomorphic character of the Kubo response function cannot be applied. We show that it is possible to derive new sum rules and new Kramers-Kronig relations for the two lowest moments of the real and imaginary part of the third order susceptibility and that new specific contributions become relevant as the intensity of the probe increases. Since the analitic properties of the susceptibility functions depend only upon the time causality of the system we are confident that these results are not model depemdent and therefore have a general validity, provided one substitutes to the equilibrium values of the potential derivatives the density matrix expectation values of the corresponding operators.
Recently derived sum rules for nonlinear optics are shown to be relevant to a number of experiments in atomic and solid-state physics. To interpret the experiments on atomic transitions and exciton transitions in solids, we analyze the three-level model and examine the modification of the optical spectrum induced on a probe light by the presence of an additional intense light beam. We show that the nonlinear sum rules explain the known experimental data and predict anomalous asymmetry in the nonlinear line shape. We also consider the cases of vibrational states of diatomic molecules and of optical modes of polar crystals and treat them with the model of the anharmonic oscillator. The nonlinear sum rules are shown to be obeyed, thus clarifying the processes of nonlinear absorption.