Behavior of high-order stimulated Raman scattering in a highly transient regime

We have investigated the behavior of high-order stimulated Raman scattering in a highly-transient regime. We demonstrate efficient collinear generation of vibrational sidebands in molecular hydrogen and methane using two-color pumping with pulses of duration $\tau \sim 100\mathrm{fs}$ tuned to a vibrational Raman transition. A Raman spectrum with a large bandwidth was observed, ranging from the IR to the UV. Under some conditions strong pump depletion was observed and up to five anti-Stokes sidebands were observed to have energies exceeding 10% of the transmitted pump pulse energies. A numerical simulation reproduces qualitatively and quantitatively the experimental results and allows us to explain key experimental features. The simulation also confirms that the molecular coherence in the medium is substantially increased by the two-color pumping and allows us to deduce values for the degree of material excitation. The use of this technique looks promising for efficient subfemtosecond pulse generation.

Figure 1

Stimulated Raman scattering in the impulsive regime. The laser pulse bandwidth is larger than the frequency spacing of the Raman transition, therefore the pulse contains pairs of Raman-resonant frequency components (${\omega }_L$ and ${\omega }_s$).

Figure 2

Stimulated Raman scattering in a highly-transient regime with one pump pulse. The laser pulse bandwidth is smaller than the frequency spacing of the Raman transition, therefore the Stokes frequency ${\omega }_s$ must grow from noise through spontaneous Raman scattering pumped by ${\omega }_L$. This is not required if two Raman-resonant pump pulses are used instead.

Figure 3

Layout of the two-color stimulated Raman scattering experiment.

Figure 4

In every experiment the wavelength ${\lambda }_2$ of the OPA pulse is tuned in such a way to obtain a condition of Raman resonance. (a) In the case of hydrogen the width of the fundamental vibrational transition is $4155{\mathrm{cm}}^{-1}$, hence the OPA wavelength is set to ${\lambda }_2=600\mathrm{nm}$. (b) In the case of methane the width of the fundamental vibrational transition is $2917{\mathrm{cm}}^{-1}$, hence the OPA wavelength is set to ${\lambda }_2=649\mathrm{nm}$.

Figure 5

HSRS spectra generated in hydrogen at different pressures: (a) $100\mathrm{mbar}$; (b) $500\mathrm{mbar}$; (c) $800\mathrm{mbar}$; (d) $900\mathrm{mbar}$; (e) $1.7\text{bar}$; (f) $3\text{bar}$. In each graph the grey curve represents the output spectrum using two input pulses (i.e., the first two lines from the left are the input wavelengths and the other components are Raman sidebands). The black curves represent the output spectra obtained for each gas pressure using only the infrared ${\lambda }_1$ pump pulse.

Figure 6

HSRS spectra generated in methane at different pressures: (a) $300\mathrm{mbar}$; (b) $500\mathrm{mbar}$; (c) $700\mathrm{mbar}$; (d) $900\mathrm{mbar}$; (e) $1.6\text{bar}$; (f) $3\text{bar}$. In each graph the grey curve represents the output spectrum using two input pulses (i.e., the first two lines from the left are the input wavelengths and the other components are Raman sidebands). The black curves represent the output spectra obtained for each gas pressure using only the infrared ${\lambda }_1$ pump pulse.

Figure 7

HSRS spectra generated using two Raman-resonant input pulses in methane at different pressures: (a) $100\mathrm{mbar}$; (b) $300\mathrm{mbar}$; (c) $600\mathrm{mbar}$; (d) $900\mathrm{mbar}$. Differently from Fig. 6, the ${\lambda }_1$ pump pulse was stretched from $\tau \simeq 100\mathrm{fs}\text{to}\tau \simeq 400\mathrm{fs}$ by propagating it through a $20\text{‐}\mathrm{cm}$-long fused silica block.

Figure 8

HSRS spectra generated in methane at a pressure of $3\text{bar}$. In each graph the the grey curve represents the output spectrum using two input pulses, i.e., the first two lines from the left are the input wavelengths and the other components are Raman sidebands, whereas the black curves represent the output spectra obtained for each gas pressure using only the infrared ${\lambda }_1$ pump pulse only. (a) Output spectra using a short ${\lambda }_1$ pulse $({\tau }_1\simeq 100\mathrm{fs})$, same as in Fig. 6f. (b) Output spectra using a longer ${\lambda }_1$ pulse $({\tau }_1\simeq 400\mathrm{fs})$.

Figure 9

HSRS spectra generated using two linearly polarized input pulses, either parallel (grey curve) or perpendicular (black curve) to each other.

Figure 10

HSRS spectra generated after changing to circular the polarization of the ${\lambda }_1$ input pulse, while keeping the polarization of the ${\lambda }_2$ pulse linear (black curve), compared to the case of both polarizations linear and parallel to each other (grey curve).

Figure 11

Calculated Raman spectrum after a propagation length $z=40\mathrm{cm}$ and with pulse intensities as in Fig. 12. The input frequencies are the lines at $0.375\mathrm{PHz}$ $({\lambda }_1=800\mathrm{nm})$ and $0.5\mathrm{PHz}$ $({\lambda }_2=600\mathrm{nm})$.

Figure 12

3D plot of the calculated Raman sidebands intensity as a function of the frequency and the propagation distance for pump pulse intensities of $I_1=1.5\times {10}^{13}\mathrm{W}{\mathrm{cm}}^{-2}$ and $I_2=1.5\times {10}^{12}\mathrm{W}{\mathrm{cm}}^{-2}$.

Figure 13

3D plot of the polarization $\mathit{v}$ of the medium calculated as a function of time and propagation distance (note that the orientation of the distance axis is reversed with respect to Fig. 12).

Figure 14

HSRS spectra obtained with both pump pulses (grey curves) in both cases of (a) shorter $({\tau }_1\simeq 100\mathrm{fs})$ and (b) longer $({\tau }_1\simeq 400\mathrm{fs})$ ${\lambda }_1$ pump pulses. The insets show the corresponding Fourier transforms (pulse intensity as a function of time). Case (a): an isolated pulse with a full width at half maximum (FWHM) duration of $\tau \simeq 1.0\mathrm{fs}$ would be supported, with satellite pulses having an intensity smaller than 1% of the main peak. Case (b): as a consequence of the modulation of the spectrum one gets a temporal structure which is more similar to a pulse train, with a strong main pulse and satellite pulses separated from the main one by a time equivalent to the vibrational period $\tau =12\mathrm{fs}$; the satellite pulses have intensities of the order of 10% of the main pulse. The FWHM duration of the main pulse is $\tau \simeq 0.82\mathrm{fs}$.

Figure 15

Scheme of Raman scattering of a delayed pulse over the molecular coherence generated by two Raman-resonant resonant pump pulses.