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Abstract
Vibrational spectroscopy is significant for identifying chemical specification. Here, the spectral band frequencies corresponding to the same molecular vibration in sum frequency generation (SFG) and difference frequency generation (DFG) spectra present delay-dependent deviation. Through numerical analysis of time resolved SFG and DFG spectra with a frequency marker in the incident IR pulse, the frequency ambiguity was not caused by any structure and dynamic variation on the surface, but from the dispersion in the incident visible pulse. Our results provide a helpful method to correct the vibrational frequency deviation and improve the assignment accuracy for SFG and DFG spectroscopies.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The importance of interface stems from their indispensable and unique effects in many chemical, biological and physical processes. Vibrational spectroscopy can provide abundant structural information of target surfaces/interfaces, but often interfered by dominated bulk signals. Vibrational sum frequency generation (SFG) and difference frequency generation (DFG) spectroscopies are second order nonlinear methods with intrinsic surface selectivity, and their signal will vanish or be very small for the bulk with centrosymmetry or random orientation under the electric dipole approximation. Thus, SFG and DFG are widely used to access buried interfaces in electrochemistry [1,2] and catalysis [2,3]. In SFG and DFG, an infrared pulse (IR) at frequency ωIR excites surface vibrations, and a following visible pulse (VIS) at ωVIS reads out the vibrational response and create SFG and DFG signals at ωVIS ± ωIR [1]. Theoretically, SFG and DFG bands are at the high and low frequency sides of the VIS with exactly the same Raman shift |ωSig – ωVIS| for each vibration, just like the anti-Stokes and Stokes peaks in a Raman spectrum.
The SFG and DFG signals consist of resonant contribution from interfacial molecular vibrations and IR wavelength insensitive non-resonant (NR) contribution from electronic responses [4]. Because of surface plasmon [5–7] or electronic resonance [8,9], metal surfaces can produce strong SFG/DFG signals independent to IR wavelength, which is still termed as NR herein. The NR signal dephases much faster than the resonant, and usually appears as a broadband spectral feature which represents the incident IR spectrum [4,10]. The resonant signal from interfacial species is generally with narrow bandwidth determined by the corresponding vibrational dephasing dynamics [9]. The overall SFG or DFG spectrum will be the coherent addition of the resonant and NR signals. The lineshape of SFG and DFG bands are remarkably different with strong NR signals because of their different perturbation processes [1]. If electronic transition is involved in the readout step (double resonant condition), intensity of the NR SFG and DFG signals may vary measurably [8,9,11]. Additionally, the SFG and DFG may couple differently with other processes, such as surface plasmon resonance [7,12]. Combination of SFG and DFG is helpful to determine surface molecular location [12] or the intensity of resonant signal [1] with higher accuracy.
In SFG and DFG, the resonant band position (usually refers to the center frequency of a spectral peak) is one of the most important parameters to identify molecular structure, such as adsorption sites, orientation, and molecular interactions. For example, CO on Pt surface terrace or step sites [13] and different local environment of the two $- \textrm{C}{\textrm{H}_3}$ groups of dimethyl sulfoxide [14] will appear with different resonant band positions in the SFG and DFG spectra. The Tafel slope of the potential-dependent band position, such as $\textrm{SC}{\textrm{N}^ - }$ on Au electrode, is associated with the surface molecular orientation of the adsorbed species [15]. The surface coverage-dependent band position shift indicates the intermolecular interactions [16]. The delay-dependent band position implies the surface dynamics like hydrogen-bond network rearrangement after the laser excitation [17].
However, many effects may cause difficulties in SFG and DFG spectral analysis. For example, lineshape will be strongly influenced by experimental geometry [18], incident light profile [19,20], time delay [10], and NR contribution [21]. When there are bulk layer contributions [18], interference from multi-interfaces [22,23], pulse distortions [24], and non-linear scattering [25], the SFG or DFG spectrum can be much more complicated, sometimes even problematic to analyze. Conventional single and multi-curve fitting can help spectral analysis with preset physical models of the targeted systems [26,27]. To reduce ambiguity and error from preset models and improve reliability and accuracy, mathematical algorithms with numerical deconvolution, such as frequency domain nonlinear regression (FDNLR) [28], principle component generalize projection (PCGP) [24], and time-domain ptychography [29], are proposed to retrieve the SFG and DFG responses without preset conditions.
The distortion of ultrashort pulse propagating in a medium has been intensively investigated [30]. The distortion of the incidents would also impact the SFG and DFG profile. However, for SFG and DFG studies of buried interfaces, the pulse distortion caused by the bulk layer is still difficult to compensate because the bulk responses are sensitive to frequency, incident power and nature of the medium [24,30]. The bulk distortion on the IR pulse adds extra narrowband features on the SFG spectra assembled together with the resonant bands which will cause problem in spectral assignment [24]. Although the bulk layer can cause VIS pulse distortion through nonlinear refraction [30], it is still not clear that how this distortion affects the measured SFG or DFG spectrum.
In this paper, time-resolved SFG and DFG spectra of octadecanethiol (ODT) self-assembled monolayer (SAM) on a gold surface were thoroughly analyzed. A thin polyethylene (PE) film was inserted in the IR light path and its absorption lines were used as frequency markers. The band positions of resonant SFG and DFG bands (Raman shifts with respect to the VIS) corresponding to each C$- $H stretching molecular vibration were carefully measured, and their evolution with the delay time in the time-resolved SFG and DFG spectra were investigated.
2. Principle
The energy diagram of SFG and DFG processes are shown in Figs. 1(a) and (b), where |g>, |v > and |e > are the ground state, vibrational excited state and the virtual state, respectively. In SFG (DFG), IR at frequency ωIR creates the vibrational polarization at |v>, ${P^{(1 )}}$ (${P^{(1 )\mathrm{\ast }}}$), and the following VIS at frequency ωVIS probes or ‘reads’ out the response and generates the SFG signal at ωVIS + ωIR or DFG signal at ωVIS – ωIR. The relative durations of the incident and created fields are presented in Fig. 1(c). The broadband IR (∼100 fs pulse duration) is much shorter than the dephasing time of the induced polarization at |v > (∼1.5 ps for $- \textrm{C}{\textrm{H}_3}$ stretching), and the VIS duration (∼2.5 ps in our experiment). In the time domain, the SFG/DFG field ESFG/DFG(t) proportional to P(1)(t)EVIS(t) can be expressed as,
where t and τ are the evolution time and delay time, respectively. Notice that, ${P^{(1 )}}$ rises sharply around t = 0 and decays much slower. SFG and DFG signals are mainly from the active part of EVIS at t > 0, EVIS, act.
Fig. 1. Diagram of (a) broadband SFG, (b) DFG and (c) the temporal evolution of related fields (EIR red, ${P^{(1 )}}$ black, EVIS blue, EVIS, act green, and ESFG/DFG purple).
The electric fields of SFG and DFG in the frequency domain, ESFG/DFG(ω), can be approximated as,
The $\chi _{SFG/DFG}^{(2 )}$ can be expressed as,
3. Experiment
Details of the SFG setup were described previously [7,9]. Briefly, a femtosecond laser (Legend Elite Duo Femto, Coherent Inc.) was used to pump OPAs (Light Conversion) to create the broadband fs IR and narrowband ps VIS. The IR and VIS temporally and spatially overlapped on the sample at ∼60 degree incident angle (with a ∼2 degree vertical cross angle) to generate SFG and DFG signal. The SFG and DFG signals were recorded by a spectrometer with a CCD camera. The VIS peak frequency, ωVIS was the center frequency from the fitting of the measured VIS spectrum. And the SFG and DFG vibrational band frequency was denoted in Raman shift |ωVIS – ωSFG/DFG|.
The Au film (100 nm) was e-beam evaporated on borosilicate glass. The ODT/Au SAM was prepared by immersing Au film plat in 0.1 mM ODT ethanol solution for 24 hours. All surfaces were cleaned and dried before measurement.
4. Results and discussion
Figure 2 displays the SFG and DFG spectra of ODT/Au SAM at delay τ = 0 and 3.7 ps. The x-axis in Fig. 2 is the Raman shift respect to the VIS center wavelength (λVIS), calculated from ωSFG,Raman = (1/λSFG – 1/λVIS) × 107 and ωDFG,Raman = (1/λVIS – 1/λDFG) × 107 for better comparison. For Au surface without surface molecule, there are only structureless broad bands in the SFG and DFG spectra (pink lines). For the spectra with ODT SAM, the resonant bands are superimposed on the Au broadband signals as dips/valleys for SFG and peaks for DFG because of their different perturbation processes illustrated in Fig. 1. And, the red lines present the fitting result of the spectra with Eq. (6) and the black spectra represent resonant SFG or DFG contributions obtained from fitting. At τ = 3.7 ps, both SFG and DFG bands appear as peaks without the presence of the non-resonant contributions as shown in Fig. 2(b). The resonant bands are the symmetric stretching (${\mathrm{\nu }_{\textrm{SS}}}({ - \textrm{C}{\textrm{H}_3},\,\textrm{ODT}} )$, ∼2880 cm–1), Fermi resonance (${\mathrm{\nu }_{\textrm{Fermi}}}({ - \textrm{C}{\textrm{H}_3},\,\textrm{ODT}} )$, ∼2940 cm–1) and asymmetric (${\mathrm{\nu }_{\textrm{AS}}}({ - \textrm{C}{\textrm{H}_3},\,\textrm{ODT}} )$, ∼2965 cm–1) stretching of the terminal $- \textrm{C}{\textrm{H}_3}$ group of ODT. The spectral peak positions of these vibrations are listed in Table 1. The frequency difference between the DFG and SFG bands is ∼13 cm–1 at 0 ps and ∼4 cm–1 at 3.7 ps.
Fig. 2. SFG and DFG spectra of ODT/Au SAM at (a) delay τ = 0 ps (blue dots for experimental data, red lines for fitting, black lines for resonant signals, pink lines for clean Au surface) and (b) τ = 3.7 ps. Vertical black lines for the resonant DFG band positions.
Table 1. Raman shifts of resonant SFG and DFG bands
To verify that the frequency deviation between the SFG and DFG band positions is from the VIS, extra spectral features are added in the incident IR pulse as a frequency marker by inserting a polyethylene film (PE) in the IR light path as shown in Fig. 3(a) the spectra at τ = 0 ps. With the PE film, the intensity is reduced at 2857, 2925 and 2956 cm–1 because of absorption of ${\mathrm{\nu }_{\textrm{SS}}}({ - \textrm{C}{\textrm{H}_2} - ,\,\textrm{PE}} )$, ${\mathrm{\nu }_{\textrm{AS}}}({ - \textrm{C}{\textrm{H}_2} - ,\,\textrm{PE}} )$ and ${\mathrm{\nu }_{\textrm{AS}}}({ - \textrm{C}{\textrm{H}_3},\,\textrm{PE}} )$ of PE.
Fig. 3. SFG and DFG spectra of ODT/Au SAM at 0 ps (a) and absorption spectra of PE calculated from SFG and DFG spectra (b), and delay time-dependent band position of νSS($- $CH3, ODT) and νSS($- $CH2$- $, PE) (c) (red for bands in DFG, blue for bands in SFG, and green for average).
As demonstrated previously [24], the IR absorption spectrum can easily be calculated from the SFG spectra of a reference Au surface at 0 ps with and without the absorber. Even with an ODT SAM on the Au surface, the IR absorption spectra can still be calculated through the division of the SFG or DFG spectra with and without the PE film as shown in Fig. 3(b). The frequency difference for the calculated PE absorption bands is ∼13 cm–1, the same as that of the resonant ODT SFG and DFG bands.
Figure 3(c) display the time-dependent band positions of ${\mathrm{\nu }_{\textrm{SS}}}({ - \textrm{C}{\textrm{H}_3},\,\textrm{ODT}} )$ and ${\mathrm{\nu }_{\textrm{SS}}}({ - \textrm{C}{\textrm{H}_2} - ,\textrm{PE}} )$ (red for bands in DFG, blue for bands in SFG, and green for average). At negative delays, there is a ∼8 cm-1 difference between the band positions of ${\mathrm{\nu }_{\textrm{SS}}}({ - \textrm{C}{\textrm{H}_3},\,\textrm{ODT}} )$ in the SFG spectra ${\omega _{\textrm{SFG}}}({{\mathrm{\nu }_{\textrm{SS}}},\,\textrm{} - \textrm{C}{\textrm{H}_3}} )$ and that in the DFG spectra ${\omega _{\textrm{DFG}}}({{\mathrm{\nu }_{\textrm{SS}}},\,\textrm{} - \textrm{C}{\textrm{H}_3}} )$. ${\omega _{\textrm{SFG}}}({{\mathrm{\nu }_{\textrm{SS}}},\,\textrm{} - \textrm{C}{\textrm{H}_3}} )$ undergoes redshift with delay time and ${\mathrm{\omega }_{\textrm{SFG}}}({{\mathrm{\nu }_{\textrm{SS}}},\,\textrm{} - \textrm{C}{\textrm{H}_3}} )$ is blue shifting. This band position difference reaches maximum at time zero, ∼13 cm-1, then decreases with delay time, and flat out after 2 ps at a value of ∼4 cm-1. The band positions of ${\mathrm{\nu }_{\textrm{SS}}}({ - \textrm{C}{\textrm{H}_2} - ,\,\textrm{PE}} )$ calculated from the SFG spectra ${\omega _{\textrm{Abs} - \textrm{SFG}}}({{\mathrm{\nu }_{\textrm{SS}}},\,\textrm{} - \textrm{C}{\textrm{H}_2} - } )$ and that from the DFG spectra ${\omega _{\textrm{Abs} - \textrm{DFG}}}({{\mathrm{\nu }_{\textrm{SS}}},\,\textrm{} - \textrm{C}{\textrm{H}_2} - } )$ display very similar time-dependent trend as that of SFG and DFG bands. In our experiment geometry, the PE absorption is embedded in the IR pulse itself, the band position or center frequency of the absorption peaks should be the same in SFG and DFG spectra at the same delay times, and can serve as frequency markers in the measured spectra. Therefore, the delay time-dependent behavior of the PE absorption bands suggests that the band position shifting is form the ‘read’ out step with dispersive VIS pulse.
For each vibration, SFG and DFG are generated from the same vibrational transition 0→1, should appear with the same Raman shift from the VIS (the 1→2 hot band will show frequency difference but with much weaker spectral intensity, and often appears as shoulders of the 0→1 spectral bands [16]). Although experimental inaccuracy, such as calibration error in the spectrograph, may lead to apparently different band positions, the scope is much smaller than that in the 0 ps SFG and DFG spectra in Fig. 2, and only causes frequency offset but not time-dependent shifting.
As illustrated in Fig. 1, the SFG/DFG frequency is determined by and EVIS. With complicated molecular interactions, the frequency of the induced polarization ${P^{(1 )}}$ may shift during the dephasing process [16]. However, if the frequency shift is from ${P^{(1 )}}$, the resonant band positions of DFG and SFG should move in the same direction with the delay time, not in opposite directions as we observed.
Because of the asymmetric temporal profile of ${P^{(1 )}}$ (sharp rise and slow decay), only the VIS field tailing the IR pulse, labeled as EVIS,act in Fig. 1(c), reads out ${P^{(1 )}}$ and generates SFG/DFG signal at t > 0. However, the frequency value of SFG and DFG band positions is from the Raman shift with respect to the VIS center frequency, which implies that the whole electric field of the VIS, EVIS,whole is used in the calculation. If there is any uncompensated dispersion in the VIS pulse, the average frequency of EVIS,whole will be different from that of the EVIS,act. In practice, ωVIS,act is difficult to measure, ωVIS,whole is used to calculate the vibrational frequency (Raman shift) in SFG and DFG spectra. Therefore, the SFG and DFG band positions from the same vibration will present with apparently different frequency in the spectra. With delay time increasing, EVIS,act is closer to EVIS,whole, then the apparent frequency difference between SFG and DFG bands will decrease. In other words, the frequency difference of SFG and DFG band positions is time-dependent. Additionally, if ωVIS,act < ωVIS,whole, the calculated SFG Raman shift, ωSFG – ωVIS,whole, is smaller than the ‘real’ vibrational frequency, ωIR = ωSFG – ωVIS,act, and the calculated DFG Raman shift, ωVIS,whole – ωDFG, is larger than ωIR = ωVIS,act – ωDFG. The other way around if ωVIS,act > ωVIS,whole. The time-dependent band positions in Fig. 3(c) indicate that ωVIS,act < ωVIS,whole around 0 ps in our experiment.
There is a small offset between the SFG and DFG bands even at long positive delays in Fig. 3(c). As shown in Eqs. (1) and (2), SFG and DFG is proportion to P(1)(t)EVIS(t) and the VIS dispersion is weighted by P(1)(t) discriminately in SFG and DFG spectra. At long delay time, although the whole VIS is used in the reading out step, the dispersion in VIS still causes asymmetric line shapes in the SFG and DFG which led to small offset in the band positions.
With time-resolved SFG and DFG spectra, the VIS pulse can be retrieved with PCGP algorithm [24]. The retrieved amplitude and phase of the VIS field are displayed in Figs. 4(a) and (b). The spectral band width of the retrieved VIS (blue in Fig. 4(a)) is smaller than the measured VIS (red in Fig. 4(a)). Both the spectral profile and phase of the VIS are deviated from Gaussian (the phase of a Gaussian pulse is constant.). The time-dependent frequency distribution of a pulse can be diagnosed by slicing along its temporal evolution. Figure 4(c) presents the calculated VIS from Eq. (8) by a simulated Gaussian splicing pulse (Eq. (7)). The center frequency of the VIS is shifting very similarly as that of the DFG resonant bands, but opposite to that of the SFG bands.
Fig. 4. Retrieved (a) field intensity (red for measured) and (b) phase of VIS from PCGP algorithm. (c) Temporal slice of the VIS pulse. (The x-axis of the VIS spectra presented in ωVIS – ωVIS,c, where ωVIS,c was the center frequency of the measured VIS spectrum.)
With the PCGP algorithm, the surface SFG and DFG responses, $P_{\textrm{SFG}}^{(1 )}$ and $P_{\textrm{DFG}}^{(1 )}$, can be retrieved as shown in Fig. 5(a). $|{P^{(1 )}}{|^2}$ is equivalent to the retrieved SFG or DFG spectrum. The resonant SFG (valleys) and DFG (peaks) bands are narrower compared to those in Fig. 2, because PCGP treatment removes the broadening from VIS (the convolution effects of EVIS in Eqs. (3) and (4)). Spectral distortion from the VIS, such as the shoulder SFG peak around 2900 cm–1 in Fig. 2(a), disappears in ${|{P_{\textrm{SFG}}^{(1 )}} |^2}$ as well. These results suggest that PCGP is capable to remove line-shape distortion (most if not all) and improve the overall spectral profile. The band position difference between $P_{\textrm{SFG}}^{(1 )}$ and $P_{\textrm{DFG}}^{(1 )}$ (2876 and 2884 cm-1) was reduced to ∼8 cm-1, smaller than the 13 cm-1 measured value at 0 ps (Table 1). As above discussed, the 5 cm-1 offset is from the asymmetric line shapes of the SFG and DFG bands introduced by the dispersion in the VIS. The rest 8 cm-1 can be attributed to center frequency difference in EVis,act and EVis,whole, which cannot be removed by PCGP treatment. (Additionally, calibration error of the spectrometer may also contribute 1∼2 cm-1 frequency deviation to the total band position difference.)
Fig. 5. The retrieved surface response ${P^{(1 )}}$ (a) and the time slice of $P_{\textrm{SFG}}^{\left( 1 \right)}$ (b) and $P_{\textrm{DFG}}^{\left( 1 \right)}$ (c).
Figures 5(b) and (c) are the temporal slices of ${P^{(1 )}}$. The $P_{\textrm{SFG}}^{(1 )}$ and $P_{\textrm{DFG}}^{(1 )}$ are calculated with Eq. (8), where the slicing pulse is expressed as Eq. (7) and FT is Fourier Transform.
There is no significant band frequency shift for the νSS and νAS SFG and DFG bands in the temporal slices of ${P^{(1 )}}$ as shown in Figs. 5(b) and (c). Although ${P^{(1 )}}$ is decaying with time, the resonant band positions are not significantly shifting when ‘read’ out with ideal pulse (ISlice is a replica as a fully compensated pulse). Which suggests that the band position shifts in νSS and νAS shown in Fig. 3 are mainly from the dispersed VIS, not the induced polarization ${P^{(1 )}}$ itself.
As discussed above, the deviation of vibrational band position determined from the measured Raman shift of BB-SFG/DFG resonant bands is from the ‘read’ out step with the dispersed VIS. In fact, the dispersion in the VIS pulse could originate from its generation (from OPA, Etalon, band pass filter, or grating + slit) and the linear or nonlinear refraction when it propagates in bulk media (lens, crystals, polarizers and filters), and commonly exists in the ps VIS pulses used in BB-SFG/DFG spectroscopy. Stiopkin et al. [19] reported the SFG spectra with VIS pulses generated from a 4-f stretcher, and found that the trend of the delay-dependent SFG frequency varied with the VIS linewidth. In a 4-f stretcher, the broadband pulse was dispersed by a grating to generate a narrow pulse with a slit. If the dispersion from the grating was not compensated perfectly, the delay time-dependent frequency shift may also be observed. Thus, the small frequency deviation may be common in SFG or DFG spectroscopy.
As shown in Fig. 3(c), the average vibrational band position from the measured Raman shifts of the resonant SFG and DFG bands is almost constant and very close to the inherent vibrational frequency, |ωDFG/SFG – ωVIS,act| and can be expressed as,
5. Conclusion
From the time-dependent BB-SFG/DFG spectra of ODT SAM on Au surface, the resonant SFG and DFG bands corresponding to the same ODT vibration appear with different Raman shift (calculated from |ωDFG/SFG – ωVIS|) in the measured spectra. And the SFG and DFG bands are significantly deviated from the natural vibrational frequency. As illustrated in Fig. 1, only part of the VIS pulse which reaches the sample surface after the IR pulse, EVIS,act, contributes to the SFG and DFG signal generation. However, the Raman shift presented in the SFG and DFG spectra is calculated with the center wavelength of the VIS pulse (EVIS,whole). Therefore, the SFG and DFG band positions inevitably deviate from its natural vibrational frequency with a dispersive VIS pulse and present delay time-dependent shifting in the measured spectra. In most cases, mechanisms which cause deviation of a spectral band from its natural frequency in IR and Raman spectroscopies can lead to similar frequency deviation in SFG and DFG. However, time-resolved spectroscopy as SFG and DFG is more sensitive to the dispersion in pulsed light sources. Unfortunately, the uncompensated dispersion in ultrashort pulse is a common phenomenon, and more attention should be paid to the measured band positions of SFG and DFG spectroscopies.
As our results demonstrated, the spectral properties retrieved from PCGP treatment can help to remove the resonant band position deviation and provide more accurate vibrational frequency. Additionally, simply using (ωSFG – ωDFG)/2 as the measured vibrational frequency will be more reliable and accurate than any of the measured ωSFG and ωDFG. These results demonstrate a practical way to accurately and precisely identify the vibrational frequency through the combination of SFG and DFG measurement and PCGP algorithm, which could be not only significant for the analysis of in situ SFG and DFG spectroscopies of buried interfaces, but also helpful for other time-resolved vibrational spectroscopies.
Funding
National Natural Science Foundation of China (21902134, 22072121); Key Laboratory of Spectrochemical Analysis and Instrumentation (Xiamen University), Ministry of Education (SCAI2007).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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