Schematic overview of 2D-FSRS. (a) Three pulses are impingent on the sample: the short duration impulsive pump (blue), the long duration Raman pump (green), and the short duration probe (red). (b) The impulsive pump drives low-frequency modes into coherence. The Raman pump and probe together act to take a stimulated Raman spectrum of the sample, primarily of the high-frequency modes. (c) The primary fundamental stimulated Raman transition is observed by the amplification of the probe spectrum at , i.e., a Raman shift of . The coherence produced by the impulsive pump can generate sidebands at , which may be attributed to either anharmonic coupling between the low- and high-frequency modes or to a coherent Raman cascade.
WMEL diagrams describing (a) the traditional third-order fundamental transition occurring in FSRS; (b) a weak combination band Raman transition occurring via the traditional third-order mechanism; (c) the fifth-order signal that would produce signal at the upshifted sideband frequency and measure anharmonic coupling between the low and high-frequency modes; (d) the fifth-order signal that would produce signal at the downshifted sideband; [(e) and (f)] the third-order cascades that would produce sideband signals via two parallel third-order processes and produce cascade signal at the down- and upshifted sideband frequencies, respectively. In each diagram, time evolves from left to right and dipole couplings on the bra side of the density matrix are described by dashed arrows, while those on the ket side are solid arrows. Blue arrows indicate interactions with the impulsive pump pulse, green arrows indicate those with the Raman pump, CARS or CSRS fields, while red indicates those with the probe and the terminal signal emission (last wavy arrows).
Unperturbed FSRS of acetonitrile and FSRS spectra taken at increasing time delays, , after the impulsive pump. Sidebands are visible along the dashed lines and exhibit time-dependent line shapes that oscillate with the period of the impulsive pump driven vibrational mode.
Signal observed at the and sidebands as a function of delay time, . Each trace has been offset vertically and the signal at , showing the signal due to the perturbed FID of the Raman transitions, has been divided by 4 for clarity.
FTs of the time-dependent data shown in Fig. 4. The time-dependent oscillations in the sideband line shapes are translated into peaks in the frequency domain. Thin lines are the direct FT of the data, initiated at 0.1 ps. Thick lines are the FT of the data multiplied by a decaying exponential with a 0.8 ps time constant. The sinc function from transforming the truncated FID of the signal at 3865 and is visible in the thin lines. The smoother Lorentzian line shape is clearly visible in the thick lines. Each time-domain signal is zero padded to 1024 points to improve the spectral resolution.
(a) The 1D- and (b) 2D-FSRS spectrum of acetonitrile. Part (a) highlights the frequencies and relative intensities of the various fundamental Raman transitions in acetonitrile. In (b), sideband peaks are shifted left or right from the fundamentals on the horizontal Raman axis by an amount equal to the frequency of the driven mode. Thus, the peak at (, ) corresponds to the CN bend frequency subtracted from the CN stretch frequency. Peaks along the horizontal dashed lines all are due to sidebands from the same impulsively driven mode. Diagonal dotted lines connect all sidebands to an individual high-frequency mode.
Horizontal slices from the 2D-FSRS spectrum of acetonitrile. (a) shows the Raman shift of all acetonitrile sideband peaks that oscillate at the frequency of the driven normal mode. Peaks in (b) correspond to sidebands from the .
(a) 1D- and (b) 2D-FSRS spectrum of 50:50 mixture of acetonitrile and -acetonitrile. (a) The 1D-FSRS spectrum with the fundamental transitions labeled. The inset shows the FSRS spectrum of the low-frequency region in which the four driven modes at 348, 379, 835, and are visible. (b) 2D-FSRS spectrum produced from time-dependent data, as in Fig. 6. The presence of and sidebands off of both the C–D stretch and the C–H stretch indicates that the sidebands cannot be generated by anharmonic coupling. Frequency discrepancies between the observed Raman shift along the horizontal and the occurrences of peaks along the vertical are due to slight errors in the Raman shift calibration.
Horizontal slices from the 2D-FSRS spectrum of 1:1 mixture of acetonitrile and -acetonitrile. (a) shows the Raman shift of all acetonitrile sideband peaks that are coupled to the IRP driven normal mode. Peaks in (b) correspond to sidebands due to coupling with the . (c) contains all sideband peaks coupled to the . (d) shows all sideband peaks coupled to the . Dotted lines highlight pairs of sidebands that result from interactions between deuterated and ordinary acetonitrile molecules. Shaded peaks are due to the noisy vertical stripes visible in the 2D spectrum at the fundamental frequencies. The sideband peaks that are attributed to both deuterated and hydrogenated modes showing up as sidebands off of the CH stretch are labeled in the highlighted regions on the right.
Spectrum of the Raman pump and its associated CARS and CSRS fields at various impulsive pump/Raman pump delay times. The broad nonresonant four-wave mixing background acts as a local oscillator to enhance detection of the CARS and CSRS fields that lie at from the Raman pump frequency. A very weak CC stretch CSRS signal is detected and no CC stretch CARS signal is detected.
Dependence of sideband signals on concentration, varied by dilution of acetonitrile in water. (a) The 2D-FSRS sideband peak magnitudes at (2562,379), (3323,379), and (3865,920), corresponding to the , the , and the combinations, respectively. (b) The sideband magnitudes divided by N, the number density of acetonitrile in the sample, normalized to the average. (c) The sideband magnitudes divided by , normalized to the average. The relatively flat slope of (c) indicates that the sideband signal is most likely proportional to .
Observed frequencies and intensities of FSRS fundamental and sideband peaks.
Raman scattering parameters and impulsively driven coherent amplitude for acetonitrile.
Experimental and computational vibrational coupling parameters, .
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