Generalized susceptibility approach to transient nonlinear optical processes

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Abstract
Recent pump-probe experiments in the femtosecond time scale exhibit features that cannot be understood in terms of conventional frequency-dependent susceptibilities either in linear or nonlinear regimes. Here duration of the pulses becomes comparable to typical vibrational periods and the linear-response theory cannot be used because the system never reaches a steady-state regime. To this end, we develop an approach to handle these problems. It requires the introduction of a time- and frequency-dependent susceptibility based on the mode-mode frequency conversion. Then, we focus on second-order processes with a particular application to second-harmonic generation.