Chinese Journal of Chemical Physics  2018, Vol. 31 Issue (4): 492-502

The article information

Cheng Chen, Liang-dong Zhu, Chong Fang

Femtosecond Stimulated Raman Line Shapes: Dependence on Resonance Conditions of Pump and Probe Pulses

Chinese Journal of Chemical Physics, 2018, 31(4): 492-502

http://dx.doi.org/10.1063/1674-0068/31/cjcp1805125

Article history

Accepted on: July 2, 2018
Femtosecond Stimulated Raman Line Shapes: Dependence on Resonance Conditions of Pump and Probe Pulses
Cheng Chena, Liang-dong Zhua,b, Chong Fanga,b
Dated: Received on May 29, 2018; Accepted on July 2, 2018
a. Department of Chemistry, Oregon State University, 153 Gilbert Hall, Corvallis, Oregon, 97331-4003, USA;
b. Department of Physics, Oregon State University, 301 Weniger Hall, Corvallis, Oregon, 97331-6507, USA
*Author to whom correspondence should be addressed. Chong Fang, E-mail: Chong.Fang@oregonstate.edu, Tel.: +001-541-737-6704
Abstract: Resonance enhancement has been increasingly employed in the emergent femtosecond stimulated Raman spectroscopy (FSRS) to selectively monitor molecular structure and dynamics with improved spectral and temporal resolutions and signal-to-noise ratios. Such joint efforts by the technique-and application-oriented scientists and engineers have laid the foundation for exploiting the tunable FSRS methodology to investigate a great variety of photosensitive systems and elucidate the underlying functional mechanisms on molecular time scales. During spectral analysis, peak line shapes remain a major concern with an intricate dependence on resonance conditions. Here, we present a comprehensive study of line shapes by tuning the Raman pump wavelength from red to blue side of the ground-state absorption band of the fluorescent dye rhodamine 6G in solution. Distinct line shape patterns in Stokes and anti-Stokes FSRS as well as from the low to high-frequency modes highlight the competition between multiple third-order and higher-order nonlinear pathways, governed by different resonance conditions achieved by Raman pump and probe pulses. In particular, the resonance condition of probe wavelength is revealed to play an important role in generating circular line shape changes through oppositely phased dispersion via hot luminescence (HL) pathways. Meanwhile, on-resonance conditions of the Raman pump could promote excited-state vibrational modes which are broadened and red-shifted from the coincident ground-state vibrational modes, posing challenges for spectral analysis. Certain strategies in tuning the Raman pump and probe to characteristic regions across an electronic transition band are discussed to improve the FSRS usability and versatility as a powerful structural dynamics toolset to advance chemical, physical, materials, and biological sciences.
Key words: Femtosecond stimulated Raman spectroscopy    Resonance enhancement    Raman pump and probe pulses    Wavelength tunability    Dispersive line shapes    Stokes and anti-Stokes FSRS
Ⅰ. INTRODUCTION

In the past decade, femtosecond stimulated Raman spectroscopy (FSRS) has become a powerful spectroscopic methodology that can provide the equilibrium and non-equilibrium vibrational signatures and track excited-state molecular dynamics with simultaneously high spectral and temporal resolutions [1-7]. Over recent years, a great variety of chemically and biologically relevant systems have been studied by FSRS spanning from organic photoacids and chromophores [8-15], molecular rotors [16], fluorescent proteins [3, 17], photoreceptor proteins [18-26], calcium biosensors [4, 27-29], metal complexes [30, 31], materials [32-34], and engineered molecular systems [35, 36]. The underlying photophysical and photochemical processes including excited-state proton transfer, charge transfer, vibrational cooling, internal conversion, isomerization, and bond dissociation have been successfully revealed and discussed in the larger context of effectively delineating the structure-energy-function relationships [6, 7].

Theoretically speaking, conventional FSRS signal is generated by a four-wave mixing process under off-resonance conditions where the vibronic transitions are mediated by a virtual state. It typically cannot achieve high signal intensity due to low transition probability between the real and virtual electronic states [37]. The low signal-to-noise ratio (SNR) may complicate data analysis to reliably retrieve accurate information. Therefore, pre- or on-resonance FSRS becomes favored by the community to achieve desirable SNR. In particular, the Raman pump wavelength in the optical regime can be tuned into an electronic band to effectively increase the transition probability (oscillator strength) in the four-wave mixing process, i.e., transition between two real vibronic states. However, dispersive features are often generated near or on resonance conditions, which could obscure the spectral analysis after data collection. This effect is more dramatic on the anti-Stokes side of the FSRS spectrum when compared to the Stokes side [35, 38, 39]. Therefore, it becomes important to gain a deeper understanding of the molecular origin of dispersive line shapes so they can be interpreted and made use of when necessary to streamline the FSRS data analysis.

Previous work has provided certain experimental and theoretical information on FSRS line shapes. Frontiera et al. studied the ground-state (GS) FSRS for rhodamine 6G (R6G) on both anti-Stokes and Stokes sides [38]. On the anti-Stokes side, all the Raman peaks undergo line shape progression from negative, through the oppositely phased dispersion, to positive-like as the Raman pump is tuned into the absorption band. On the Stokes side, low-frequency modes evolve from positive to dispersive while high-frequency modes remain mostly positive for all the Raman pump wavelengths. Umapathy et al. experimentally explored the line shapes for crystal violet in ultrafast Raman loss spectroscopy, shown to be equivalent to anti-Stokes FSRS [40], and they observed the mode-dependent dispersion [41] and suggested that the wavelength-dependent Franck-Condon (FC) activity plays a crucial role in generating dispersion due to the creation of different FC states when on resonance. Lee and co-workers performed a series of simulations and represented the stimulated Raman scattering (SRS) signal by eight distinct dual time-line Feynman diagrams within the coupled wave theory framework [40, 42-47]. When off-resonant in GS-FSRS [48], the narrow Stokes gain arises from the resonance Raman scattering (RRS) term while the narrow anti-Stokes loss is caused by inverse Raman scattering (IRS). In both cases, the vibrational coherence is created in the same electronic ground state (S$_0$) and major contribution comes from the ground vibrational state (i.e., quantum number $v$=0). In contrast to conventional spontaneous Raman wherein the typically weaker anti-Stokes peak intensity is subject to Boltzmann distribution, the anti-Stokes FSRS peak intensity could be larger than the Stokes side when the Raman probe wavelength is closer to an electronic transition peak [39, 41]. When Raman pulses overlap with a resonant band, the stimulated Raman line shapes become nontrivial due to additional contributions from the other SRS and IRS terms [47]. Pump-probe pulse delay experiments have also been exploited to reveal the roles of Raman pump and probe in generating FSRS signals [38, 45, 49].

In addition, hot luminescence (HL) pathways have been suggested to contribute to the dispersive line shapes in FSRS [38, 45]. Different from the aforementioned RRS and IRS terms, the first interacting Raman pump and probe pulses in HL processes are both excitatory and generate the vibrational coherence in a higher lying excited state (see Scheme 1, the excited-state vibrational coherence depicted by a semi-transparent red shade). The de-excitation by the picosecond Raman pump in its second interaction after the vibrational coherence dephasing time $T_2$ cancels in phase with the first Raman pump and ensures the phase-matching condition is satisfied (i.e., the FSRS signal is emitted collinearly with the Raman probe beam). It is notable that the occurrence of HL terms to contribute narrow line shapes in FSRS requires the on-resonance condition of both pulses as the vibrational coherence has to be generated between real vibrational states in an electronic excited state population instead of a virtual state (see below for details).

 Scheme 1 Double-sided Feynman diagrams of the hot lumi- nescence (HL) terms contributing to vibrationalline shapes in anti-Stokes and Stokes FSRS.

In an electronic excited state, transient vibrational population complicates the Raman line shapes to a greater extent. The resonance with excited-state absorption (ESA) and stimulated emission (SE) bands provides more channels for "dynamic" resonance Raman during the study of a broad range of photoactive systems [20, 35, 39, 50-54]. Some theoretical work has been performed for the ES Raman line shapes [18, 20, 46, 50]. By employing different Feynman diagrams, the ES line shape can be explained based on the third-order polarization in Raman scattering after electronic excitation. Our recent work systematically explored the Stokes and anti-Stokes FSRS line shapes on resonance with the ESA band of a photoacid pyranine, 8-hydroxyperene-1, 3, 6-trisulfonic acid (HPTS) [39]. The Raman pump wavelength was tuned from the red side to the blue side of the ESA band. The anti-Stokes features exhibit a line shape change from positive to dispersive to negative and this change is much more notable for the low-frequency modes than high-frequency modes. A similar observation is made at one time delay point by tuning the Raman pump wavelength as well as fixing the Raman pump at one wavelength and comparing spectral line shapes at different time delay points after photoexcitation. We attribute the peak dispersion to the generation of vibrational coherence in a higher lying electronic state (S$_n$) mixed and interfered with the coherence created in S$_1$ due to favorable S$_1$$\rightarrowS_n transitions (i.e., ESA) for both the Raman pump and probe pulses when on resonance. In this work, we investigate the relationship between the GS-FSRS line shapes and Raman pump and probe wavelengths. Different from previous reports [38, 53], the line shapes are also examined at shorter wavelengths resonant with the blue side of the electronic absorption band which fills a current knowledge gap. R6G in methanol is used as the model system because its absorption band (maximum at \sim530 nm) lies within the wavelength tunable range (ca. 480-720 nm) of our home-built multi-stage noncollinear optical parametric amplifier (NOPA) system [5], which enables us to study all the resonance conditions from the red to blue side of the absorption band. Moreover, R6G has multiple Raman peaks across the broad spectrum up to 1800 cm^{-1}, which provides rich information and internal control for line shapes. We observed that anti-Stokes FSRS is more susceptible to resonance change with respect to the Stokes side and shows line shape variation in a cyclic manner from negative through positive back to negative, mediated by the oppositely phased dispersion. The low-frequency modes (<1000 cm^{-1}) on the Stokes side exhibit a similar cyclic trend while the high-frequency modes remain largely unchanged throughout the Raman pump wavelength tuning. Based on these systematic experimental results in conjunction with previous FSRS studies, we provide new insights into the line shapes and develop guidelines in selecting the Raman pulse wavelengths to avoid dispersion while achieving satisfactory SNR. Ⅱ. EXPERIMENTAL METHODS The R6G dye in powder form was purchased from TCI America and used without further purification. The solution sample for spectroscopic measurement was made by dissolving R6G powder in anhydrous methanol at room temperature. The UV-visible spectra were collected by a Thermo Scientific Evolution 201 spectrophotometer before and after each FSRS measurement to check sample integrity with negligible photodegradation. The sample was contained in a 1 mm thick quartz cuvette (1-Q-1, Starna Cells). Three R6G concentrations of 5, 20, and 100 μmol/L were prepared to examine the effect of solute concentration on the FSRS peak intensity and line shape, also serving as an internal peak reproducibility check (see FIG. S1 in the supplementary materials). The GS Raman measurements were performed using our home-built table-top FSRS setup with broad wavelength tunability and the details can be found elsewhere [5, 12, 13, 27]. In brief, the Raman pump and probe pulses are generated from the \sim2 W (half of the 4 W output), 800 nm fundamental pulse with 35 femtosecond (fs) duration of a mode-locked Ti:sapphire oscillator and regenerative laser amplifier (Legend Elite-USP-1K-HE, Coherent, Inc.) at 1 kHz repetition rate. The wavelength tunability of Raman pump is achieved through a series of fs and picosecond (ps) NOPAs. The fs supercontinuum white light (SCWL) for Raman probe is generated in either a 3-mm thick sapphire crystal or a 2-mm path length cuvette with deionized water depending on the target probe wavelength range for anti-Stokes FSRS and the laser pulse stability. The Raman pump and probe beams are parallel polarized. The FSRS signal collinear with the Raman probe beam is heterodyned and dispersed inside a spectrograph with a reflective grating (1200 grooves per mm, 500 nm blaze) and then imaged onto a front-illuminated 1340\times100 CCD array camera (PIXIS:100F, Princeton Instruments). In addition, the Raman pump powers of \sim2 and 0.4 mW were used to find better conditions to obtain peaks with clearer line shapes. Ⅲ. RESULTS AND DISCUSSION A. Steady-state absorption spectrum and Raman pulse wavelengths The GS-FSRS line shapes essentially correlate to the resonance conditions of Raman pump (R_{\rm{pu}}) and probe (R_{\rm{pr}}) pulses with the steady-state electronic absorption band. FIG. 1 presents the ground-state absorption (GSA) spectrum of R6G in methanol with our R_{\rm{pu}} wavelengths indicated. The band maximum is at 530 nm and the shoulder peak on the blue side could be a result of vibronic progression (involving a \sim1180 cm^{-1} mode). The FSRS line shapes on both Stokes and anti-Stokes sides are examined by tuning R_{\rm{pu}} from off-resonance toward on-resonance, and across the GSA band to pre-resonance on the blue side. The broadband probe wavelength ranges for the spectral window (covering up to the high-frequency mode of 1652 and 1656 cm^{-1} for anti-Stokes and Stokes, respectively) are displayed by the blue and red shaded bars in FIG. 1 (a) and (b). The associated R_{\rm{pr}} experiences a similar change in resonance as the R_{\rm{pu}} moves into and away from the band in the red to blue tuning direction. As mentioned above, the information about the effect of more energetic Raman pulses on the FSRS line shape is still lacking. Through this work, the R_{\rm{pu}} and R_{\rm{pr}} in pre-resonance conditions with an electronic band have shown promise in tracking the ground and excited state species with sufficient SNR and nondispersive line shapes.  FIG. 1 Normalized ground-state absorption spectrum of R6G in methanol with the R_{\rm{pr}} wavelength range indicated for each R_{\rm{pu}} wavelength by the color-coded rectangle shaded bars in the (a) anti-Stokes and (b) Stokes region. The chemical structure of R6G is shown in the inset of (a) wherein the middle phenyl group is perpendicular to the xanthene ring to minimize steric hindrance. The probe ranges for the 596 and 648 nm R_{\rm{pu}} in (b) are truncated at the red end of the wavelength axis. B. Anti-Stokes FSRS line shapes In the ground state, both spontaneous Raman and stimulated Raman on the anti-Stokes side exhibit absorptive features under off-resonance condition. The anti-Stokes stimulated Raman can be attributed to an IRS term where probe acts as the excitatory pulse. Unlike spontaneous Raman, the anti-Stokes stimulated Raman signal is not necessarily weaker than its Stokes counterpart in spite of the inversely mirrored vibrational modes [39, 40, 48, 55, 56]. This is because: (ⅰ) R_{\rm{pr}} initiates the Raman process from the most populated vibrational ground state (v=0) in IRS, (ⅱ) the resonance of both Raman pump and probe pulses are important for the signal strength. The latter factor may explain the mode-dependent enhancement in the observed peak intensity. In this work, the 648 nm R_{\rm{pu}} generates the off-resonance spectrum below 1700 cm^{-1} because all the probe photons corresponding to the Raman modes are off-resonant with the chromophore GSA band (see FIG. 1(a)). As R_{\rm{pu}} is tuned into resonance with the GSA band from the red side, the anti-Stokes FSRS line shapes exhibit complicated changes with a clear mode dependence (FIG. 2(a)). Notably, we used three sample concentrations (5, 20, and 100 μmol/L) and two R_{\rm{pu}} powers (\sim0.4 and 2 mW) at each R_{\rm{pu}} wavelength to study their effect on the FSRS peak intensity and line shape. Only the spectrum with the clearest and reproducible line shape at each R_{\rm{pu}} wavelength is scaled (see Table S1 in the supplementary materials for the selected combination of R6G concentration and Raman pump power leading to the spectral data presentation in FIG. 2) and displayed without any baseline subtraction [39, 52] for reliable comparison and retrieval of molecular information.  FIG. 2 Ground-state (a) anti-Stokes and (b) Stokes FSRS spectra from 500-1750 cm^{-1} of R6G in methanol as R_{\rm{pu}} is tuned across the visible region. Major peak positions are labeled by the vertical dotted lines. The solvent peak at 1033 cm^{-1} is indicated by the green vertical dashed line. The spectra are scaled for comparison and the scaling factor is shown in blue by the corresponding spectrum. The different R_{\rm{pu}} wavelengths are listed in red to the right side of the stacked spectra. Semi-transparent orange and green shades highlight some positive and negative peaks in (a). Magenta arrows denote some characteristic mode frequency redshift as R_{\rm{pu}} is tuned to be bluer. In the anti-Stokes FSRS (FIG. 2(a)), both high- and low-frequency peaks are negative at 648 nm R_{\rm{pu}} due to the off-resonant pump and probe. As R_{\rm{pu}} is tuned into resonance with the GSA band, the line shape undergoes a cyclic change, i.e., negative\rightarrowdispersive\rightarrowpositive\rightarrowoppositely phased dispersive\rightarrownegative. The line shape alteration pattern for high-frequency modes is more conspicuous than low-frequency modes. For example, the 1652 and 1575 cm^{-1} modes convert back to negative features at R_{\rm{pu}}=557 nm. The middle 1511, 1364, 1311, and 1183 cm^{-1} modes become negative again at a bluer R_{\rm{pu}} of 546 nm. The low-frequency modes at 773 and 611 cm^{-1} do not seem to regain a negative line shape even with the bluest R_{\rm{pu}} used (479 nm). The line shapes of the high-frequency modes at 479 and 491 nm R_{\rm{pu}} are challenging to determine due to the extremely low SNR on a broad sloping baseline. This can be explained by the weakening of resonance conditions of R_{\rm{pu}} and R_{\rm{pr}}, and the deficiency of probe photons in blue wavelength region of the SCWL [13, 15]. This effect occurs for the 500 and 512 nm R_{\rm{pu}} as well but to a lesser extent. What is the underlying cause for the dispersive line shapes in FSRS? The appearance of dispersion at resonance has been discussed on the basis of hot luminescence (HL) terms where a vibrational coherence is created in an electronic excited state (different from the original ground state S_0, see Scheme 1) by the resonant R_{\rm{pu}} and R_{\rm{pr}} in a third-order \chi^{(3)} nonlinear process [38, 46]. In this case, both R_{\rm{pu}} and R_{\rm{pr}} are excitatory. McCamant et al. explained the dispersive line shapes observed in the ES-FSRS of bacteriorhodopsin by "Raman initiated by nonlinear emission" (RINE), which is equivalent to the HL terms for GS-FSRS in nature. The imaginary part of susceptibility \chi^{(3)} can be used to account for the dispersive line shapes from RINE or HL, which are essentially a function of R_{\rm{pu}}, R_{\rm{pr}}, vibrational frequency, and line widths of the pertinent electronic and vibrational transitions [39, 46, 50]. However, the role of R_{\rm{pu}} and R_{\rm{pr}} has not been discussed in detail when dispersive peaks are generated under various resonance conditions. Since the community has long considered the resonance condition of Raman pump to be crucial in determining the FSRS line shape and signal intensity, we aim to demonstrate that the Raman probe is equally if not more important in determining the FSRS line shape in the \chi^{(3)} process based on our systematic experimental observations. Using the framework from a previous report [50], the imaginary part of \chi^{(3)} in HL processes can be expressed by Eq.(1):  \begin{eqnarray} {\rm Im} [{\chi ^{(3)}}({\omega _2})] = A \cdot \{ b{\gamma _{\textrm{e}, n}} - {\Gamma _{\textrm{ge}}}[{\omega _2} - ({\omega _1} \pm {\omega _{n, n + 1}})]\} \end{eqnarray} (1) where \omega_1, \omega_2, and \omega_{n, n+1} are the Raman pump, probe, and the vibrational mode frequency, respectively. \gamma_{\textrm{e}, n} is the homogeneous line width of the vibrational transition in the excited state (e.g., S_1). \Gamma_{\rm{ge}} is the homogeneous line width of the e\leftarrowg electronic transition, which is the same for all the vibrational coherences generated in S_1. "\pm" marks the difference for Stokes (-) and anti-Stokes (+) frequencies. The first term A includes the Lorentzian peak at center vibrational frequency in S_1 and the Raman excitation profile [11, 57]. The second term introduces the line shape change deviating from a Lorentzian. Specifically, b=\omega_{\rm{ge}}$$-$$\omega_2 defines the resonance of the probe frequency corresponding to each vibrational peak. To the first approximation, the vibrational damping time (\gamma_{\textrm{e}, n})^{-1} and electronic lifetime (\Gamma_{\rm{ge}})^{-1} lead to minor difference in the vibrational line widths for all the peaks when HL terms create coherences in the excited state. This highlights the importance of the remaining b factor, i.e., resonance of the mode-corresponding-probe wavelength, in determining the FSRS line shape which is corroborated by the nonsynchronous line shape change for high- and low-frequency modes in the anti-Stokes FSRS spectra (FIG. 2(a)). In other words, within one FSRS spectrum, different vibrational modes cannot be considered to have the same value of b factor [50] especially when the Raman probe wavelength is approaching an electronic transition gap (i.e., b$$\rightarrow$0) and the dispersion term becomes dominant.

In FIG. 2(a), the high-frequency modes experience an "earlier" line shape change than low-frequency modes when $R_{\rm{pu}}$ is tuned from red to blue. Therefore, the resonance condition of $R_{\rm{pu}}$ alone cannot explain the different behavior of each mode at the same $R_{\rm{pu}}$ wavelength under pre- and on-resonance conditions. By inspecting the associated probe wavelengths, we note that the modes with similar line shapes correspond to similar $R_{\rm{pr}}$ wavelengths. For instance, the positive peak appears at: (ⅰ) 1575 cm$^{-1}$ for 581 nm $R_{\rm{pu}}$, (ⅱ) 1183 cm$^{-1}$ for 566 nm $R_{\rm{pu}}$, (ⅲ) 773 cm$^{-1}$ for 557 nm $R_{\rm{pu}}$. The pertinent $R_{\rm{pr}}$ wavelengths for these modes are $\sim$532, 530, 534 nm, respectively, which are all close to the GSB peak maximum (FIG. 1). Notably, the 1652 cm$^{-1}$ mode at 581 nm $R_{\rm{pu}}$ shows positive line shape with a slight dispersive character, which leads us to predict that a positive-definite line shape would be generated for this mode at a $R_{\rm{pu}}$ wavelength between 581 and 596 nm (e.g., 583 nm while $R_{\rm{pr}}$=532 nm). This can be further validated by reducing the wavelength increment of $R_{\rm{pu}}$. Likewise, the positive-definite peak for the 1364 cm$^{-1}$ mode will appear at a redder $R_{\rm{pu}}$ wavelength between 566 and 581 nm (e.g., 574 nm while $R_{\rm{pr}}$=532 nm). The 1511 and 611 cm$^{-1}$ positive-definite peaks, on the other hand, will appear at slightly bluer $R_{\rm{pu}}$ wavelengths than 581 and 557 nm, respectively, based on the phase of dispersion. The $R_{\rm{pr}}$ wavelengths corresponding to each mode at all the $R_{\rm{pu}}$ wavelengths used are summarized in Table S2 in the supplementary materials. It can be concluded that the same line shape will be generated at the same probe wavelength region as Raman pump is tuned into a resonant band when HL becomes a prominent contributor. This is in accord with Eq.(1) where the $R_{\rm{pr}}$ resonance condition, measured by $b$, plays a critical role in determining line shapes. It is interesting that a fully on-resonance $R_{\rm{pr}}$ alone does not lead to dispersive line shapes, likely because the $R_{\rm{pu}}$ is pre- or off-resonant with the electronic band (see FIG. 1(a)). The only exception concerns very low frequency modes where the $R_{\rm{pu}}$ and $R_{\rm{pr}}$ wavelengths are close. Moreover, the clearly broadened bandwidths of dispersive peaks also evince the generation of ES vibrational coherences due to the excitatory $R_{\rm{pu}}$ and $R_{\rm{pr}}$ pulses in HL terms. The generation of ES and GS vibrational coherences in parallel could in principle introduce further interference terms and dispersive line shapes in FSRS [39].

As the $R_{\rm{pu}}$ wavelength is tuned further into the GSA band maximum and blue side, the peaks maintain negative line shape except for low-frequency modes. The 1364, 1311, and 1183 cm$^{-1}$ modes appear as broadened negative peaks at close-to-GSA-maximum 534 nm and bluer $R_{\rm{pu}}$ wavelengths. These features cannot solely arise from the GS vibrational coherence via the IRS(Ⅰ) pathway (see FIG. 3(a)) due to their broad bandwidths. The aforementioned HL terms could contribute but to a small extent. For the off-resonant $R_{\rm{pu}}$ and $R_{\rm{pr}}$ on the red side of GSA, the HL terms make marginal contributions owing to longer wavelengths (i.e., lower energy) than the transition gap. When on the blue side of GSA, the shorter wavelength $R_{\rm{pr}}$ is less resonant with $\omega_{\rm{ge}}$ than $R_{\rm{pu}}$, which can still stimulate transitions between S$_0$ and S$_1$ but with a lower probability caused by the reduced FC factors further away from the GSA maximum (FIG. 1(a), for the high-frequency modes above 1000 cm$^{-1}$). In fact, the HL signal magnitude is manifested in Eq.(1) by the factor $A$ which is approximately proportional to FC factors at each vibronic transition wavelength.

 FIG. 3 Energy-level diagrams illustrating the ground-state FSRS signal generation of R6G on the (a, b) anti-Stokes and (c, d) Stokes sides at different resonance conditions. The phase-matching condition $k_{\rm{sig}}$=$k_{\rm{pu}}$+$k_{\rm{pr}}$$-$$k_{\rm{pu}}$ of Raman pump (blue) and probe (red) pulses is satisfied. Solid and dash arrows represent the light-matter interactions/dipole couplings on the ket and bra sides of the molecular density matrix in the double-sided Feynman diagrams, respectively. The interaction proceeds from left to right in time. The green ellipse highlights the vibrational coherence generated in the electronic ground state (S$_0$) or excited state (e.g., S$_1$). For proof of principle, one representative HL and $\chi^{(5)}$ term is shown for the pre- and on-resonance condition.

This rationale could be supported by the dispersive modes at 773 and 611 cm$^{-1}$. At variance with the modes above 1000 cm$^{-1}$, these two modes remain dispersive as $R_{\rm{pu}}$ is tuned to blue from the GSA maximum. The 773 cm$^{-1}$ mode line shape is obscured by weak peak intensity for $R_{\rm{pu}}$ below 512 nm, likely due to the weak FC activity of this non-symmetric mode (see Table S3 in the supplementary materials for the vibrational normal mode assignment of R6G in methanol). The distinct line shape behavior lies in different resonance conditions of the mode-dependent $R_{\rm{pr}}$ wavelength (i.e., $\omega_2$ in Eq.(1)). The $R_{\rm{pr}}$ photons experience better resonance for the low-frequency modes than high-frequency modes with the blue-sided $R_{\rm{pu}}$ (see FIG. 1(a)), indicating that the HL contribution remains appreciable in the low-frequency region. In contrast, broad negative peaks observed in the high-frequency region have minor contributions from HL terms, and much less dispersive line shapes because the $R_{\rm{pu}}$ and $R_{\rm{pr}}$ wavelengths differ by a greater extent for those modes.

Notably, peak broadening appears from 546 nm $R_{\rm{pu}}$ in the red$\rightarrow$blue tuning direction when $R_{\rm{pu}}$ becomes strongly resonant with the GSA band. Considering the ps duration of the $R_{\rm{pu}}$ pulse, direct absorption of $R_{\rm{pu}}$ photons could allow more channels for higher-order nonlinear signaling at resonance [20, 58]. The large spectral baselines in FIG. 2 (a) and (b) are indicative of the depleted GS and transient ES populations caused by $R_{\rm{pu}}$ on or near the electronic resonance [13, 39, 52]. A previous report by Ernsting and co-workers proposed that after a preceding photoexcitation pulse, a resonant $R_{\rm{pu}}$ could induce ES population depletion at early time before $R_{\rm{pr}}$ arrives for $\chi^{(3)}$ processes and lead to line broadening [20]. Later, the resonance FSRS without actinic excitation was demonstrated for all-trans $\beta$-carotene [58]. The broadened peaks at resonant $R_{\rm{pu}}$ wavelengths indicate the $\chi^{(5)}$ generation of ES vibrational coherence with a shorter electronic lifetime, which can be considered as six-wave mixing in generating the FSRS signal [59]. In this scenario, $R_{\rm{pu}}$ first functions as an excitation pulse and promotes the S$_1$ population likely in the first half of its pulse duration (e.g., $\sim$1 ps in our case) [5, 20]. The later arrival of $R_{\rm{pr}}$ initiates the Raman $\chi^{(3)}$ process in the excited state (see FIG. 3(b)) and gives rise to the negative signal in the anti-Stokes FSRS. Remarkably in FIG. 2(a), the 1652, 1575, 1511, and 1311 cm$^{-1}$ modes all exhibit a frequency red shift as $R_{\rm{pu}}$ is tuned to the blue side. One possible reason is the photoinduced mode frequency redshift within the FC region due to electronic redistribution [3, 13]. It could also imply that $R_{\rm{pu}}$ accesses high-lying vibrational levels in S$_1$ and consequently generates vibrational coherences with high quanta in an anharmonic potential energy surface, leading to a frequency red shift [39, 52]. Furthermore, because the emission typically occurs at longer wavelengths with respect to absorption so the $\chi^{(3)}$ process on resonance with an SE band in S$_1$ is less likely when a more energetic $R_{\rm{pu}}$ is used. The IRS(Ⅰ) process with an excitatory probe could be responsible for the observed negative features in FSRS with bluer $R_{\rm{pu}}$ wavelengths (e.g., $\leq$534 nm). The energy-level diagram representing one possible $\chi^{(5)}$ pathway is depicted in FIG. 3(b). We emphasize that the observed mode intensity and line shape consist of the contributions from all possible $\chi^{(3)}$ and higher-order nonlinear pathways, which could involve different interacting pulse sequences, overlap with an SE transition, vibrationally hot or relaxed states, and possible interference between the GS and ES vibrational coherences generated via the concurrent pathways [39, 47]. We discuss the most likely pathway(s) in this work to illustrate the relevant principles for anti-Stokes FSRS line shapes which are supported by our experimental data and theoretical rationale.

C. Stokes FSRS line shapes

The FSRS spectra on the Stokes side show different and less complicated line shape changes, implying a variation in nonlinear contributions. In FIG. 2(b), dispersive peaks are identified in the low-frequency region while positive peaks persist for high-frequency modes above 1000 cm$^{-1}$ across the $R_{\rm{pu}}$ tuning range. At off- and pre-resonant $R_{\rm{pu}}$ wavelengths of 648, 596, and 581 nm, Stokes FSRS exhibits clear positive peaks generated by the RRS(Ⅰ) term (see FIG. 3(c)). As $R_{\rm{pu}}$ is tuned into resonance, low and high-frequency modes start to differ. The dispersion of 614 and 773 cm$^{-1}$ modes could be ascribed to the HL contribution because the corresponding $R_{\rm{pr}}$ wavelengths are more resonant than the high-frequency modes with the same $R_{\rm{pu}}$. The 614 cm$^{-1}$ mode exhibits an "earlier" line shape change (i.e., from absorptive to dispersive) relative to the 773 cm$^{-1}$ mode as $R_{\rm{pu}}$ is tuned toward the blue side (FIG. 2(b)), which is consistent with the anti-Stokes side (FIG. 2(a)) and further highlights the important role of $R_{\rm{pr}}$ in determining line shapes in HL processes [35, 39]. As $R_{\rm{pu}}$ is tuned from the GSA maximum to blue side ($\leq$512 nm), these two modes regain positive line shape but show a broadened peak width. We attribute it to the $\chi^{(5)}$ contribution where $R_{\rm{pu}}$ excites some GS populations, followed by a $\chi^{(3)}$ process in the ES (see FIG. 3(d)).

For high-frequency modes above 1000 cm$^{-1}$, in sharp contrast to the anti-Stokes side, no dispersive line shapes are observed before $R_{\rm{pu}}$ is tuned into resonance. This result arises from different resonance conditions of $R_{\rm{pr}}$ on the Stokes and anti-Stokes sides. With red-sided $R_{\rm{pu}}$, the anti-Stokes $R_{\rm{pr}}$ photons can be on-resonance with the GSA band while the Stokes photons remain off-resonant, leading to small contribution from HL terms on the Stokes side. It is conceivable that dispersive line shapes could appear when $R_{\rm{pu}}$ is tuned to shorter wavelength until the mode-associated $R_{\rm{pr}}$ photons go into resonance, which cannot be easily observed in the Stokes spectra unless the $R_{\rm{pu}}$ and $R_{\rm{pr}}$ achieve comparable resonance conditions. Consequently, all the high-frequency modes show peak broadening but not significantly dispersive line shapes. Moreover, the 1656, 1578, 1513, and 1311 cm$^{-1}$ modes red shift in center frequency, reminiscent of the anti-Stokes side. This key observation implies that the $\chi^{(5)}$ contribution becomes significant with these $R_{\rm{pu}}$ wavelengths and a transient ES population is involved (FIG. 3(d)). Therefore, the absence of dispersion for high-frequency modes in the Stokes FSRS lies in the fact that $\chi^{(5)}$ contributions become dominant over HL terms when the less energetic $R_{\rm{pr}}$ approaches resonance, while $R_{\rm{pu}}$ "overshoots" to the blue side (see FIG. 1(b)) and has excessive energy for electronic excitation. In contrast, the more energetic $R_{\rm{pr}}$ on the anti-Stokes side gets into resonance before $R_{\rm{pu}}$ goes from pre- to on-resonance with the GSA band (FIG. 1(a)). This intrinsic difference in pulse resonance conditions between the Stokes and anti-Stokes FSRS governs the peculiar line shape behaviors.

Moreover, the 1656, 1578, and 1513 cm$^{-1}$ modes exhibit some intriguing changes from the 534 nm to 479 nm $R_{\rm{pu}}$ (FIG. 2(b)). The 1656 cm$^{-1}$ mode red shifts to $\sim$1600 cm$^{-1}$ with 534 nm to 522 nm $R_{\rm{pu}}$ and reappears with 512 nm to 479 nm $R_{\rm{pu}}$, essentially showing the competition between different contributions under certain resonance conditions. The red-shifted feature could be assigned to a $\chi^{(5)}$ signal with minor HL contribution involving ES vibrational coherences while the unshifted, narrower peak mainly arises from the RRS(Ⅰ) term involving GS vibrational coherences. The red shift and frequency gap of the two peaks also indicate large anharmonicity of the 1656 cm$^{-1}$ mode which could involve vibrationally hot states after electronic excitation by a bluer $R_{\rm{pu}}$ (see above). For comparison, the 1578 and 1513 cm$^{-1}$ modes only exhibit red-shifted peaks in FSRS with bluer $R_{\rm{pu}}$ wavelengths, and the latter mode shows very weak peak intensity as it red shifts. The same phenomenon is also observed in the anti-Stokes spectra (FIG. 2(a)), indicating the weak FC activity of this particular mode (see Table S3 in the supplementary materials for assignment) at blue wavelengths during the course of multidimensional vibronic transitions [39, 57, 60] of a photoexcited molecule in solution.

D. Competition between different nonlinear pathways

We have experimentally elucidated that the resonance conditions of both Raman pump and probe pulses are key players responsible for the FSRS line shapes. The Stokes and anti-Stokes spectra have distinct line shape behaviors particularly under pre- (quasi-) and on-resonance conditions. The stimulated Raman scattering has been addressed as a third-order nonlinear effect, thereby leading to various contributions caused by different pulse sequences of the pictosecond $R_{\rm{pu}}$ and femtosecond $R_{\rm{pr}}$. When these incident laser pulses approach resonance with the electronic band(s), the FSRS signal is complicated by more pathways involving the generation of vibrational coherences in different electronic states. In conjunction with relevant literature, our experiments provide further insights into the FSRS line shapes and intrinsic competition between possible pathways under the vibrational-mode-dependent resonance conditions. With an off-resonance $R_{\rm{pu}}$, off-resonance $\chi^{(3)}$ processes such as RRS(Ⅰ) and IRS(Ⅰ) contribute dominantly to sharp positive and negative line shapes in the Stokes and anti-Stokes FSRS, respectively (see FIG. 3 (c) and (a)), because other resonant $\chi^{(3)}$ as well as $\chi^{(5)}$ processes are not favored without notable resonance. However, when $R_{\rm{pu}}$ becomes pre- or on-resonant with an electronic band, competing pathways become significant with a strong dependence of the mode-dependent $R_{\rm{pr}}$ resonance as the following: (ⅰ) HL terms with ES vibrational coherences which lead to the apparent mode dispersion line shapes (see Scheme 1), and/or (ⅱ) the IRS(Ⅰ) or RRS(Ⅰ) with both ES population and vibrational coherences which lead to mode broadening and a discernible frequency redshift.

When $R_{\rm{pu}}$ is pre-resonant on the red side of GSA band, Stokes and anti-Stokes spectra show distinct line shapes due to different resonance conditions of $R_{\rm{pr}}$. In anti-Stokes FSRS (FIG. 2(a)), we observe circular line shape changes of the high-frequency modes when $R_{\rm{pu}}$ is tuned from 648 nm to 557 nm (see Table S2 in the supplementary materials), strongly suggesting that the resonant $R_{\rm{pr}}$ favors HL terms over the resonant IRS(Ⅰ) process. In contrast, weaker resonance of $R_{\rm{pr}}$ in Stokes FSRS leads to minor contribution from HL while the main contributor RRS(Ⅰ) is evinced by narrow, positive, high-frequency peaks with $R_{\rm{pu}}$ from 596 nm to 557 nm (FIG. 2(b)). Meanwhile, the low-frequency modes actually become more dispersive which indicates that HL contribution increases with better resonance of $R_{\rm{pr}}$. This direct comparison between multiple vibrational modes under identical experimental conditions (see FIG. 2 (a) and (b)) further confirms that $R_{\rm{pr}}$ is crucial in determining the FSRS line shapes from the HL terms.

When $R_{\rm{pu}}$ approaches full resonance, higher-order nonlinear pathways become appreciable as confirmed by the broadened and red-shifted peaks with $R_{\rm{pu}}$ at 534, 527, and 522 nm. Different line shapes in high- and low-frequency regions reveal the competition between HL and $\chi^{(5)}$ pathways in addition to the IRS(Ⅰ) and RRS(Ⅰ) terms. Since the high-frequency modes correspond to less resonant $R_{\rm{pr}}$, the HL contributions diminish, while prominent $\chi^{(5)}$ processes generate positive and negative peaks on the Stokes and anti-Stokes sides, respectively. However for the low-frequency modes, the $R_{\rm{pr}}$ achieves comparable resonance with $R_{\rm{pu}}$, so the HL pathways still make notable contributions and lead to dispersive line shapes. Furthermore, we observed that the 614 and 773 cm$^{-1}$ modes in Stokes FSRS at 522 nm $R_{\rm{pu}}$ exhibit different line shapes with different $R_{\rm{pu}}$ powers (see FIG. S1 in supplementary materials). This peculiar power dependence may suggest that the pertinent $\chi^{(3)}$ and $\chi^{(5)}$ processes, i.e., HL and RRS(Ⅰ) in FIG. 3 (c) and (d), strongly compete when both $R_{\rm{pu}}$ and $R_{\rm{pr}}$ are close to fully on-resonance conditions and there could be a phase relationship between the ground and excited state vibrational coherences. In contrast, the unchanged broad line shape of high-frequency modes above $\sim$1000 cm$^{-1}$ reveal that the $\chi^{(5)}$ process is more prominent than the HL terms (e.g., Eq.(1), leading to dispersive line shapes when $b$$\rightarrow$0). We expect that line shape changes may be observed at other resonant $R_{\rm{pu}}$ wavelengths with a larger variation of the $R_{\rm{pu}}$ power.

When $R_{\rm{pu}}$ is pre-resonant on the blue side of GSA band, $R_{\rm{pr}}$ is more resonant in Stokes FSRS while less resonant in anti-Stokes FSRS. The weaker resonance of anti-Stokes $R_{\rm{pr}}$ favors $\chi^{(5)}$ processes that lead to the broadened and red-shifted high-frequency peaks with $R_{\rm{pu}}$ from 512 nm to 479 nm (FIG. 2(a)). In contrast, the low-frequency mode at 611 cm$^{-1}$ shows dispersive character due to the comparable resonance of $R_{\rm{pr}}$ and thus the HL contribution. It also explains a slight dispersion of the 614 cm$^{-1}$ mode on the Stokes side. The high-frequency modes above 1000 cm$^{-1}$ in Stokes FSRS exhibit certain mode dependence. The 1182, 1311, 1364, and 1578 cm$^{-1}$ modes appear as broadened positive peaks with frequency red shift at 1311 and 1578 cm$^{-1}$ (highlighted by magenta arrows in FIG. 2(b)), implying that $\chi^{(5)}$ pathways are likely dominant. The 1513 cm$^{-1}$ mode red shifts and diminishes as $R_{\rm{pu}}$ becomes bluer. It is plausible that the vibronic transition along this vibrational degree of freedom only constitutes the red edge of the GSA band and as a result, the resonance enhancement of the 1513 cm$^{-1}$ mode is much weaker than other modes at blue $R_{\rm{pu}}$ wavelengths (see above). As support, the 1513 cm$^{-1}$ mode is the strongest peak at off-resonant $R_{\rm{pu}}$ wavelengths (e.g., 648 nm) due to the proximity of $R_{\rm{pu}}$ and $R_{\rm{pr}}$ to this vibronic transition beneath the broad GSA band (FIG. 1). Regarding the 1656 cm$^{-1}$ mode at GS vibrational frequency, its peak width at these blue $R_{\rm{pu}}$ wavelengths remains narrow and unchanged so the RRS(Ⅰ) pathway could be a main contributor. The new peak around 1600 cm$^{-1}$ that may evolve from the 1656 cm$^{-1}$ peak is consistent with an ES vibrational coherence generated through a $\chi^{(5)}$ process. Therefore, we speculate that this vibrational motion undergoes a notable frequency change upon photoexcitation typically as mode softening, corroborated by the experimentally observed mode frequency at 1647 cm$^{-1}$ using resonance Raman at 532 nm excitation [57] and 1600 cm$^{-1}$ in resonance Raman with 488 nm excitation [61], while the $\chi^{(5)}$ contribution is comparable to the $\chi^{(3)}$ contribution. In addition, two other red-shifted modes at 1311 and 1578 cm$^{-1}$ do not show clear GS peaks at these blue $R_{\rm{pu}}$ wavelengths (479, 491, 500, and 512 nm in FIG. 2(b)) probably because $\chi^{(5)}$ pathways contribute more to the FSRS signal than the RRS(Ⅰ) terms.

On the mechanistic level and molecular time scales, we can attribute these observed peak frequency, intensity, and line shape variations in FIG. 2 to the vibrational-mode-dependent nature on a multidimensional potential energy surface [13, 15, 20, 35, 60]. However, one intrinsic and potentially key difference between the pre-resonance HL terms in FIG. 3 (a) and (c) could explain why dispersive line shapes are generally more prevalent in anti-Stokes FSRS than Stokes FSRS. Since the nascent ES vibrational coherence relaxes (i.e., pure dephasing and vibrational population relaxation) during the FSRS signal generation typically on the ps time scale, the HL term favors a less energetic (redder) $R_{\rm{pu}}$ than a more energetic (bluer) $R_{\rm{pu}}$ during its second interaction with the relevant vibrational state. In other words, the ES vibrational relaxation leads to much less population on the higher lying vibrational state, which is required to interact with the bluer $R_{\rm{pu}}$ in the HL pathways on the Stokes side [38]. As a result, less dispersive line shapes are observed in the Stokes FSRS, which is beneficial for spectral data analysis especially at pre-resonance conditions to simultaneously avoid large sloping baselines. Alternatively, the resonance conditions can be exploited at strategic $R_{\rm{pu}}$ and $R_{\rm{pr}}$ combinations mostly on the red side of an electronic band to achieve absorptive line shapes with enhanced SNR to access the GS and/or ES species.

Ⅳ. CONCLUSION

In summary, we have systematically investigated the relationship between the Raman pump and probe resonance conditions with an electronic transition band and the stimulated Raman line shape using a highly fluorescent dye in solution. The fine tuning of Raman pump wavelengths with small increments from the red to blue side of the ground-state absorption band of R6G in methanol has enabled the exploration of comprehensive resonance conditions across a broader spectral range. The resonance condition of Raman probe is revealed to play an important role in determining the circular line shape changes (i.e., absorptive to absorptive peak) involving the oppositely phased dispersion. The broadened and red-shifted peaks at resonant Raman pump wavelengths suggest that the higher-order $\chi^{(5)}$ pathways make significant contributions and generate some excited-state population and vibrational coherences in addition to ground-state vibrational coherences generated via the $\chi^{(3)}$ pathways. With the same Raman pump, the low- and high-frequency modes exhibit distinct line shape patterns which can be essentially attributed to the competition between different pathways due to different resonance conditions achieved by the mode-corresponding Raman probe. This comprehensive line shape study lays the foundation for exploiting the FSRS methodology on both the Stokes and anti-Stokes sides, and with the incorporation of a preceding actinic pump [2, 7, 13, 52] that can be separately tuned, to study photosensitive systems with desirable SNR and obtain crucial information about reaction dynamics on molecular time scales and the structure-energy-function relationships.

Supplementary materials: FIG. S1 on the Stokes FSRS spectra of R6G in methanol with concentration and Raman pump power dependence, Table S1 on the experimental conditions for the ground state FSRS spectra with tunable Raman pump wavelengths, Table S2 on the Raman probe wavelengths corresponding to various Raman modes in the anti-Stokes FSRS, and Table S3 on the ground state Raman peak assignment for R6G in methanol, additional references and the full authorship of the Gaussian 09 software are available.

Ⅴ. ACKNOWLEDGEMENTS

The work was supported by the U.S. National Science Foundation CAREER grant (CHE-1455353) and the Oregon State University (OSU) Research Equipment Reserve Fund (Spring 2014) to C. Fang (USTC 9603). We also thank the Wei Family Private Foundation in supporting C. Chen (USTC 0903) during his graduate studies at OSU Chemistry.

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a. 美国俄勒冈州立大学化学系, 俄勒冈州, 科瓦利斯 97331-4003;
b. 美国俄勒冈州立大学物理系, 俄勒冈州, 科瓦利斯 97331-6507