# Modulated Noncollinear Optical Parametric Amplifier Output Induced by Stimulated Raman Scattering
## 2 Experimental Setup
Equations (1) and (3) differ from Equation (2) in terms of the number of coupling terms on the right side. However, both Equations (1) and (3) can have a secondary term in the same way as Equation (2). In the time range \(t<<T_{1}\),\(T_{2}\), Equations (4) and (5) become:  
\[Q^{*}=\int_{-\infty}^{t}(\kappa_{2S}E_{S}E_{P}^{*}+\kappa_{2A}E_{P}E_{AS}^{*} )dt^{\prime}. \tag{6}\]  
\[n=\frac{1}{8\hbar}\int\ (a_{A}(E_{AS}E_{P}^{*}Q^{*}+E_{AS}^{*}E_{P}Q)+a_{s}(E_{P}E_{ S}^{*}Q^{*}+E_{P}^{*}E_{S}Q))dt^{\prime}. \tag{7}\]  
In the time scale of the experiment, \(T_{1}\) is sufficiently long [34; 35] that the population dynamics can be disregarded. Thus, \(n\) is constant in the present discussion. The interaction of the fields with the spectral components of the idler and Stokes frequencies (\(\omega_{i}\) and \(\omega_{s}\), respectively) for the pump pulse and coherent vibrations can be described by Equations (1)-(3). In the same way, the interaction of the fields with the spectral components of the idler and anti-Stokes frequencies (\(\omega_{i}\) and \(\omega_{ss}\), respectively) for the pump pulse and coherent vibrations are described by Equations (4) and (5). The vibrational population decay is neglected. Because there is no coherent molecular vibration prior to laser irradiation in the thermal incoherent state, the initial condition for \(Q\) (\(t\)) is \(Q\) (\(0\)) = 0. After the pump pulse has been transmitted through the sample, the molecular vibration is sustained in the material during the vibrational coherence time. Subsequently, the ultrashort probe pulse arrives with the same spectrum as the pump pulse. The delay time between these two pulses is varied using an optical stage. Even though the pump pulse and probe pulse have the same spectrum, their spectroscopic functions are different. In case the spectrum of the pump is not fully covering the sample absorption spectrum, the spectral components which do not covering the absorption do not contribute the electronic excitation of the material being studied. While in the case of the probe, the even spectral component not covering the absorption can probe the sample with the interaction by stimulated emission and/or excited absorption induced by the excited state(s) generated by the pump pulse in the spectral range of no absorption by the ground state of the sample. In the case of resonant condition of pump pulse spectrum with the sample electronic spectrum then not only excited electronic state generation but also vibronic excitation can take place in the sample. In such a case complicated processes take place as discussed in the following. Interactions among the coherent molecular vibrational amplitude \(Q\) and the pulsed fields \(E_{A}\), \(E_{P}\), and \(E_{S}\) are determined by Equations (1)-(3). Depending on the vibrational phase of the coherent molecular vibrations, the field intensities of \(E_{S}\), \(E_{P}\), and \(E_{AS}\) are increased or reduced by amplification or deamplification, respectively. As mentioned above, Equations (1) and (3) can have a secondary term in the same way as Equation (2). The two terms can compete or constructively contribute to increase or reduce the intensity. Furthermore, the coherent molecular vibration amplitude couples to all pairs of the relevant fields in the available bandwidth. It is thus expected to have a very complex temporal behavior. However, the frequencies of the signal components introduced by the molecular vibrations are given by those of the vibrational modes, as observed. The complexity appears as the probe wavelength dependence of the amplification (deamplification), as discussed in this paper. For the experiment discussed in the present paper, the intensity of the incident seed pulse is fixed within an inevitable fluctuation. This differs from the case when a single pump pulse that is not accompanied with a probe pulse incident on the nonlinear crystal. In this case, the initial condition is given by \(Q(0)=0\) and the creation of the signal originates from vacuum fluctuations.