# Modulated Noncollinear Optical Parametric Amplifier Output Induced by Stimulated Raman Scattering
## 2 Experimental Setup  
The laser source was a regenerative amplifier that produces 2.5-mJ, 40-fs, 1-kHz pulses at 800 nm (Micra and Legend-USP, Coherent). In the present experiment, a 500-\(\upmu\)J pulse was split into 80% and 20% components using an 80% transmission beam splitter. This fraction was further split into two beams. As shown in Figure 1, a small fraction of the fundamental was tightly focused onto a 2-mm-thick sapphire plate to generate a white-light continuum through a single stable filament. The other portion of the beam was frequency doubled in a 0.17-mm-thick BBO (type I at \(\theta\) = 29.2\({}^{\circ}\)) and was then separated from the fundamental and utilized as the pump in the noncollinear optical parametric process. The external noncollinear angle between the pump beam and the seed beam was 6.4\({}^{\circ}\) on the BBO crystal, corresponding to an internal angle of 3.7\({}^{\circ}\) and providing broadband phase matching. The pulse duration of the white-light seed after the sapphire plate was evaluated as \(\sim\)200 fs using the dispersion relation of the BBO crystal (available from a crystal providing company). The duration of the second-harmonic pump pulse after the BBO was evaluated as \(\sim\)50 fs by the risetime of bleaching of strongly absorbing phthalocyanine dye doped in a polymer film (Yamada Chemical). There are two ways to match the pulse width between  
Figure 1: Experimental setup: BS, beam splitter (R = 20% at 800 nm); BBO1, 170-\(\upmu\)m BBO crystal (cut at an angle of 29.2\({}^{\circ}\)); BBO2, 1-mm BBO crystal (cut at an angle of 31.5\({}^{\circ}\)); UVFS, ultraviolet-grade fused silica; S, 2-mm-thick sapphire plate; M1 and M2, harmonic separators (HR at 400 nm and AR at 800 nm); M3, silver-coated mirror; CM, chirped mirror pair (Layertec GmbH, model 103189). the seed and the pump: compressing the seed using chirped mirror pairs or stretching the pump pulse in fused silica. We used the second method. Two-dimensional spectra of the amplified signal against the pump-seed delay time were obtained using a multichannel lock-in amplifier (MCLA) with 128 channels to cover the whole spectral range of the signal pulses after amplification for various delay times between the pump and probe pulses. Theoretical Background of Interactions between Coherent Molecular Vibrations and Electric Fields of Ultrashort Pulses via a Stimulated Raman Process  
Utilizing a moving coordinate frame (\(x^{\prime}\), \(t^{\prime}\)) that is related to a stationary frame (\(x\), \(t\)) by \(x^{\prime}=x\) and \(t^{\prime}=t-x/v\), the stimulated Raman process is described in terms of the following coupled differential equations for a two-vibrational-level system with a very distant electronic excited state [34; 35]:  
\[\frac{\partial}{\partial x^{\prime}}E_{s}=\kappa_{1S}E_{P}Q. \tag{1}\]  
\[\frac{\partial}{\partial x^{\prime}}E_{P}=\kappa_{1S}E_{S}Q+\kappa_{1A}E_{AS} Q^{*}. \tag{2}\]  
\[\frac{\partial}{\partial x^{\prime}}E_{AS}=\kappa_{1A}E_{P}Q. \tag{3}\]  
\[\left(\frac{\partial}{\partial t^{\prime}}+\frac{1}{T_{2}}\right)Q^{*}=\kappa _{2S}E_{S}E_{P}^{*}+\kappa_{2A}E_{P}E_{AS}^{*}. \tag{4}\]  
\[\left(\frac{\partial}{\partial t^{\prime}}+\frac{1}{T_{2}}\right)n=\frac{a_{ S}}{8\hbar}(E_{P}E_{S}^{*}Q^{*}+E_{P}^{*}E_{S}Q)+\frac{a_{A}}{8\hbar}(E_{AS}E_{P}^{*}Q ^{*}+E_{AS}^{*}E_{P}Q). \tag{5}\]  
Here, \(T_{2}\) is the vibrational phase (transverse) relaxation time and \(T_{1}\) is the population (longitudinal) relaxation time, \(\hbar\) is the reduced Planck constant, \(\kappa_{1S}\), \(\kappa_{2S}\), \(\kappa_{1A}\), and \(\kappa_{2A}\) are the corresponding coupling constants to the relevant coupling processes in the equations, \(Q\) is the vibrational amplitude of the corresponding normal mode and \(E\) is the electric field amplitude, and \(n\) is the population difference between the lowest and second lowest vibrational levels with quantum numbers of 0 and 1, respectively. The subscripts \(S\), \(P\), and \(AS\) denote the Stokes, pump, and anti-Stokes fields, respectively.