Introduction

Coherent Raman scattering (CRS) techniques are now indispensable for obtaining structural information on materials at the molecular level through vibrational resonances. CRS can provide much stronger vibrationally selective signals than spontaneous Raman scattering. For this reason, CRS techniques have gained popularity in recent days as alternatives to spontaneous Raman spectroscopy. CRS spectroscopies, such as coherent anti-Stokes Raman scattering (CARS) and stimulated Raman scattering (SRS), have many applications in gas-phase1,2, molecular dynamics in condensed phases3,4,5, and molecular imaging6,7,8,9. In the CRS processes based on four-wave mixing, two incident laser pulses coherently drive a particular Raman transition. The vibrational coherence enhances the Raman signal by several orders of magnitude with respect to the spontaneous Raman process, which allows fast acquisition of CRS signals compared to spontaneous Raman. Among various CRS techniques, CARS and SRS spectroscopy have been prominent as powerful imaging tools with high speed. CARS and SRS microscopy offer label-free and non-invasive three-dimensional visualization of the chemical composition of the sample6,7,10,11,12,13,14. However, the present CRS techniques provide only information on Raman active vibrations, identical to spontaneous Raman scattering in principle. One needs other types of vibrational spectroscopy to obtain further vibrational information unobtainable from Raman/CRS spectroscopy.

Herein, we report a new coherent Raman spectroscopy, coherent anti-Stokes hyper-Raman scattering (CAHRS) spectroscopy experimentally for the first time. The CAHRS process is based on the fifth-order nonlinear susceptibility and six-wave mixing, giving spectral information identical to the spontaneous hyper-Raman (HR) process and different from the usual Raman one. In the HR process, two incident photons are absorbed and one photon is emitted, while one photon is absorbed and another is emitted in the usual Raman process15,16. One of the most important peculiarities of HR spectroscopy is its different selection rules from Raman spectroscopy. In principle, all the infrared active modes are HR active. Besides, HR spectroscopy can detect “silent modes” that are both inactive in Raman and IR spectra17,18. Thus, HR spectroscopy can offer additional information on vibrational spectra due to the distinct selection rules from IR and Raman spectroscopy. Indeed, recent HR measurements have shown that HR spectroscopy gives information on molecular structures and molecular dynamics unobtainable by IR and Raman spectroscopy19,20,21,22,23,24. Despite its potential importance for studying molecular systems, very weak HR signals due to small cross-sections have prevented one from applying HR spectroscopy to many fields. Under typical experimental conditions, HR signals are 10−4 to 10-5 times weaker than Raman signals, resulting in long measurement times, hours to days.

One possible method to make HR measurements faster is to employ a CRS process like conventional CRS techniques. As mentioned previously, in CRS processes, multiple laser pulses induce vibrational coherences, enhancing the scattered signal compared to the spontaneous Raman scattering. Theoretically, CAHRS spectroscopy has been proposed in both electronic resonant and non-resonant cases several decades ago25,26,27. However, CAHRS has yet to be performed experimentally, even though CAHRS spectroscopy is desired to obtain HR signals/spectra in a short measurement time. In this study, we successfully observed CAHRS signals from solution samples. Our results show that our observed signals surely come from the CAHRS process and suggest that CAHRS spectroscopy gives different information on molecular vibration from Raman spectroscopy. CAHRS spectroscopy affords an improved way of obtaining hyper-Raman spectra.

Results and Discussion

Principle of CAHRS

Figure 1a shows the energy diagrams of spontaneous HR, CARS, and CAHRS processes. In the CARS process, a pump beam (ω1) and a Stokes beam (ω2) are used to interact with a molecule. When ω1− ω2 matches the frequency of a Raman active vibrational mode, vibrational resonance happens28,29. In contrast, in the case of CAHRS, when 2ω1− ω2 matches the frequency of a hyper-Raman active vibrational mode, vibrational coherence is induced. To probe the vibrational coherences, another ω1 beam is used in CARS, but two ω1 beams are necessary in the CAHRS process. The CAHRS signal polarization is given by

$${P}_{{{\rm{CAHRS}}},\,i}^{\left(5\right)}= \, {{{\rm{\chi }}}}_{{ijklmn}}^{\left(5\right)}\left({4\omega }_{1}-{\omega }_{2};{\omega }_{1},{\omega }_{1},{\omega }_{1},\,{\omega }_{1},\right. \\ \left. -{\omega }_{2}\right){E}_{j}\left({\omega }_{1}\right){E}_{k}\left({\omega }_{1}\right){E}_{l}\left({\omega }_{1}\right){E}_{m}\left({\omega }_{1}\right){E}_{n}^{*}\left({\omega }_{2}\right),$$
(1)

where \({P}_{{{\rm{CAHRS}}}}^{(5)}\) is the fifth-order nonlinear polarization, the subscripts of the fifth-order nonlinear susceptibility χ(5) refer to the axes of the cartesian coordinate system along with the variously polarized electric fields, E(ω1) and E(ω2) are the electric fields of the ω1 and ω2 lasers, respectively. As a result, the CAHRS intensity is proportional to the absolute square of χ(5) of the sample, I1, and I2 denoting the intensities of the ω1 and ω2 beams, respectively, in the homodyne detection. This means that the signal strongly depends on ω1 rather than the CARS signal, which proportional to |χ(3) | 2 I12 I2. While CARS detects the four-wave mixing signal at ωCARS = 2ω1-ω2, CAHRS does the six-wave mixing process at ωCAHRS = 4ω1−ω2, as shown in Fig. 1a.

Fig. 1: Concept and experimental layout of CAHRS spectroscopy.
Fig. 1: Concept and experimental layout of CAHRS spectroscopy.
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a Energy diagrams for CAHRS, CARS, and spontaneous HR, and possible diagrams for the non-resonant background (NRB) b Phase-matching geometries for CAHRS and CARS satisfying kCAHRS = 4k1−k2 and kCARS = 2k1−k2, where k1 and k2 are the wavevectors of the ω1 and ω 2 beams, respectively. θ1 and θ2 are the angles of the ω 1 and ω2 beams with respect to the CAHRS/CARS beam, respectively. c Experimental schematics for CAHRS spectrometer. OPA, pol, HWP, and LP denote optical parametric amplifier, polarizer, half-wave plate, and long-pass filter, respectively.

In addition to the difference in the selection rules and the pump power dependence, CAHRS spectroscopy shows the different phase-matching conditions from CARS spectroscopy. The beam geometry needs to satisfy the phase-matching condition to generate signals efficiently. The phase-matching condition of the CAHRS signal can be expressed as kCAHRS = 4k1−k2, shown in Fig. 1b, while that of the CARS signal is kCARS = 2k1−k2, where k1, k2, kCARS, and kCAHRS are the wavevectors of ω1, ω2, the CARS signal28,29, and the CAHRS signal, respectively. Table 1 shows the calculated incident angles of ω1 and ω2 with respect to the generated signal (Fig. 1b) for neat liquid samples of chloroform and benzene with the use of their refractive indices30,31. For simplicity, we assume the wavelengths of ω1 are 1030 nm and 515 nm for CAHRS and CARS, respectively, and the target molecular vibration is 1000 cm-1. In the case of CAHRS, θ 1 and θ 2 are larger than 10° and 15°, respectively, and their difference is ~5°. The difference in incident angles of ω1 and ω2 in CAHRS is much larger than those in CARS ( < 2°). This is because the difference in frequencies between ω1 and ω2 in the case of CAHRS is much larger than of CARS. This calculation suggests that it is difficult to generate CAHRS signals in the collinear geometry without a tight focusing that is sometimes employed in CARS spectroscopy. To generate CAHRS signals in the collinear geometry, a high numerical aperture that relaxes the phase-matching condition may be necessary. Moreover, the differences in the incident angles between benzene and chloroform are much larger in CAHRS (θ 1: 3° and θ 2: 5° for CAHRS) than in CARS (θ 1: 0.2° and θ 2: 0.3° for CARS) should be noticed, meaning that the optimal beam geometry for CAHRS strongly varies depending on the sample. Indeed, we needed to employ different beam geometries to approximately satisfy the phase-matching conditions for CAHRS when we measured chloroform solvent and benzene.

Table 1 Calculated phase-matching angles of ω1 and ω2 with respect to the generated signal (θ 1 and θ 2) for CAHRS and CARS from chloroform and benzene solvents
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Experimental observation of CAHRS signals

Figure 1c shows our CAHRS spectroscopic system based on an fs Yb: KGW laser (for details, refer to Methods). The system stretches the fundamental output of the laser from 200 fs to ps by using a 4 f spectral filter, by which we can tune the spectrum and the pulse width of ω1. Typically, we set the spectral bandwidth and the center wavelength of ω1 to be 5 cm-1 and 1027 nm, respectively. We employ the tunable and fs output of an optical parametric amplifier pumped by the fundamental laser as ω2, whose wavelength is set depending on the vibrational frequency of a target molecule. Note that the ω2 laser with a bandwidth of ~100 cm-1 combined with a CCD camera for a detector provides us a multiplex detection scheme, in which we can directly observe spectra from the samples.

We measured a para-nitroaniline (PNA) solution as a test sample to ensure that the spectroscopic system we built can detect CAHRS signals. Previous studies showed that PNA gives relatively intense HR signals because of its large hyperpolarizability under the electronic (pre-) resonant conditions32,33. Figure 2a, b show raw observed spectra from the 10 mM PNA solution in chloroform (red lines) and the neat chloroform solvent (black lines) in the spectral ranges from 1200 to 1500 cm-1 and from 700 to 1000 cm-1, respectively, corresponding to the wavelengths around 480 nm and 492 nm, blue-shifted from those of the incident laser and the second-harmonics of the ω1 light. When we set the input laser powers of the ω1 pulse and the ω2 pulse to 60 mW and 5 mW, the peak intensity of the observed signal from the PNA solution was about 10,000 CCD counts/s, readily detectable. Spectra from the neat chloroform solvent in Fig. 2a, b are smooth and featureless, representing the spectral profiles of the ω2 laser, due to the so-called “non-resonant background” attributed to the instantaneous electronic response (Fig. 1a). In contrast, spectra from the PNA solution in Fig. 2a, b show dispersive line shapes. To correct spectral distortions originating from the spectral distribution of the Stokes light, we divide the raw spectra from the PNA solution by those from the neat chloroform solvent. In the following, we discuss the intensity-corrected spectra.

Fig. 2: CAHRS spectra of PNA solution.
Fig. 2: CAHRS spectra of PNA solution.
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a, b Raw observed spectra from PNA solution (red lines) and neat chloroform solvent (black lines). c, d Intensity-corrected spectra of PNA solution by dividing the raw spectra of PNA solution by those of neat chloroform. e, f Spontaneous HR spectra of the PNA solution. Spectral ranges of a, c, and e are around 1350 cm−1, and b, d, and f are around 850 cm−1. In the CAHRS measurements, the powers of the ω1 and ω2 lights were 60 and 5 mW, the exposure times were 1 s, and 10 exposures were averaged. In the spontaneous HR measurements, the power of the excitation light was 50 mW, the exposure time was 10 s, and 10 exposures were averaged.

We found dispersive and asymmetric lineshapes around 1350 and 850 cm-1 in the intensity-corrected spectra from the PNA solution (Fig. 2c, d). These spectral features result from the interference between the non-resonant and vibrational resonant terms of the fifth-order nonlinear optical susceptibility of PNA solution, ensuring that the observed signals from PNA originate from vibrational resonances of PNA. The vibrational frequencies of the dispersive signals in Fig. 2c, d are determined to be 1323 and 850 cm-1, which we ascribed to the NO2 symmetric stretching and NO2 in-plane deformation (scissors) modes, respectively34. The fact that these peak frequencies are consistent with those in spontaneous HR spectra (Fig. 2e, f for around 1350 and 850 cm-1, respectively) means that the observed signals are indeed due to the hyper-Raman resonances.

Also, we found that the observed signal has a laser-like character in the direction satisfying the phase-matching condition. This feature agrees that the detected signal was generated through a coherent Raman process. Considering all the observations above, we conclude that the observed signals are generated through the CAHRS process.

Time dependence of CAHRS signals from PNA solution

Figure 3a shows the intensity-corrected spectra from the PNA solution with various time-delay Δt (the ω1 pulse was time-delayed by Δt from the ω2 pulse) from −1.3 ps to +1.3 ps. As Δt increases, the spectral line shapes around 1325 cm-1 become sharper and stronger, meaning that the spectral resolution improves35. As a result, a small vibrational band around 1310 cm-1, due to the NO2 symmetric stretching mode, appears with Δt. The spectral change observed is ascribed to the change in the ratio between the fifth-order nonlinear susceptibilities for CAHRS and the non-resonant background. The vibrational coherence prepared by the pump and Stokes pulses is typically picoseconds, while the non-resonant background is extremely short-lived because the non-resonant background originates from the instantaneous electronic response. This difference in the response to two laser pulses enables us to control the relative weights of vibrationally resonant and non-resonant signals by changing Δt. Namely, for positive Δt, the relative contribution of the CAHRS signal to the whole signal increases and that of the non-resonant background decreases, improving the spectral resolution, as shown in Fig. 3a. Thus, we confirmed that the time-delayed measurement allowed us to suppress the contribution of the non-resonant background signals and to improve the signal to background ratio, as shown in previous studies using CARS spectroscopy35,36

Fig. 3: Delay-time dependence.
Fig. 3: Delay-time dependence.
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a Intensity-corrected spectra from PNA solution with various Δt from −1.3 to +1.3 ps. b Delay-time dependence of the non-resonant background signals corresponding to the cross-correlation of the ω1 and ω2 pulses at 4ω1−ω2. The FWHM was determined to be 1.3 ps.

Figure 3b shows the delay-time dependence of the non-resonant background signal from neat chloroform solvent. As short-lived, the non-resonant background plot corresponds to the cross-correlation of the ω1 and ω2 pulses. The full-width at half maximum (FWHM) is determined to be 1.3 ps, corresponding to the time resolution of our experimental equipment. Since the CAHRS process involves four photons of the ω1 pulse and one photon of the ω2 pulse, the pulse width of the picosecond ω1 pulse dominates the time resolution of our experimental equipment rather than the femtosecond ω2 pulse.

In the present setup, we can tune the pulse width of ω1 from picoseconds to sub-picoseconds using a 4 f pulse shaper. When we set the pulse width of ω1 to picoseconds, we expect to detect much more vibrational bands thanks to the improvement of the spectral resolution. If we set the pulse width of ω1 to sub-picoseconds, we can expect an application of CAHRS spectroscopy to time-resolved measurements, which provides information on ultrafast molecular dynamics through hyper-Raman active vibrations.

The fifth-order nonlinear Raman spectroscopy has been extensively explored in the time and frequency domains to investigate inter- and intramolecular vibrational dynamics in the condensed phase. Even though the real direct fifth-order signal was observed in previous studies37,38,39, it turns out that cascading lower-order signals, such as third-order signals, frequently overwhelm the weak fifth-order signal40,41,42. The concentration dependence of the signal has been evaluated to make a distinction between the real fifth-order and the cascading process41,42,43,44,45. For the intramolecular modes, the signal electric field of the fifth-order process is linear to the molecular density. In contrast, the electric field of the cascading third-order process is proportional to the absolute square of the third-order nonlinear susceptibility and, thus, is proportional to the square of the molecular density. We examined the concentration dependence of the signal from PNA in chloroform (see details in Supplementary Information section 1 and 2). The result clearly shows that the observed signal originates from the real fifth-order process.

Power dependence of CAHRS signals from PNA solution

A further proof of our measurement of CAHRS signals is the power dependence. As we described previously, the observed signals are expected to be proportional to the fourth powers of the ω1 intensity and linearly proportional to the ω2 intensity, respectively (\({I}_{{{\rm{CAHRS}}}}\propto {I}_{1}^{4}{I}_{2}\)).

Figure 4a, b show the power dependence of observed signals against the intensities of the ω1 and ω2 pulses, respectively. The laser intensities of the ω1 and ω2 pulses were set to be ~1011 W/cm2, smaller than the damage threshold of common solvents (1012 ~ 1013 W/cm2)46,47. The line shapes of the observed spectra were almost the same within the range of the laser intensities of the ω1 and ω2 pulses for this measurement. It should be noted that when more intense lasers were introduced into the sample than the experimental condition described above, the line shapes were distorted and broadened. This result indicates that other higher nonlinear optical processes simultaneously contribute to the observed signals with higher incident powers. For this reason, we introduced laser pulses in moderate conditions to not deform the line shapes.

Fig. 4: Incident-power dependence.
Fig. 4: Incident-power dependence.
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Integrated signal intensities from 1200 to 1450 cm−1 were plotted against the laser power of the ω1 light (a) and against the laser power of the ω2 light (b). The inset of (a) is the ω1 intensity dependence in the small laser power range.

Figure 4b describes that the integrated intensities of the observed signals are proportional to the fourth powers of the ω1 intensity and linearly proportional to the ω2 intensity, respectively. Both results are consistent with \({I}_{{{\rm{CAHRS}}}}\propto {I}_{1}^{4}{I}_{2}\), further supporting that the generated signal comes from the CAHRS process.

Polarization property of CAHRS signals

Figure 5 shows the polarization dependence of the CAHRS signals from the PNA solution. We measured CAHRS spectra under the eight possible polarization combinations by setting the polarizations of ω1, ω2, and the signal to be vertical (V) or horizontal (H) to the scattering plane.

Fig. 5: Polarization dependence.
Fig. 5: Polarization dependence.
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CAHRS spectra from PNA solution of CHCl3 around 1320 cm−1 under the eight polarization combinations, a VVV, b HHH, c VHV, d HVH, e VHH, f HVV, g VVH, and h HHV. The first letter refers to the polarization of the CAHRS signal, the second letter to that of the ω1 beam, and the third letter to that of the ω2 beam, respectively.

In an isotropic sample like liquid/solution, symmetry restricts the forms of \({{{\rm{\chi }}}}_{{ijklmn}}^{(5)}\) 48. Assuming symmetric permutation of the indices for the pump pulse (j, k, l, and m) and that for the probe and Stokes pulses (i and n), one can show that four tensor components, namely, \({{{\rm{\chi }}}}_{111111}^{(5)}\), \({{{\rm{\chi }}}}_{211112}^{(5)}\), \({{{\rm{\chi }}}}_{111122}^{(5)}\), and \({{{\rm{\chi }}}}_{111221}^{(5)}\) are nonzero, while other components, such as \({{{\rm{\chi }}}}_{211111}^{(5)}\) and \({{{\rm{\chi }}}}_{111112}^{(5)}\), vanish in the dipole approximation. With Kleinman symmetry, we can further reduce the tensor elements to \({{{\rm{\chi }}}}_{111111}^{(5)}\) and \({{{\rm{\chi }}}}_{211112}^{(5)}\), which satisfy \({{{\rm{\chi }}}}_{111111}^{(5)}=\) \({5{{\rm{\chi }}}}_{211112}^{(5)}\). Because all the four ω1 fields in the CAHRS process are degenerated in our experiment, the polarizations of the CAHRS signal and the ω2 laser should be the same to generate the signal originating from the tensor element \({{{\rm{\chi }}}}_{111111}^{(5)}\) or \({{{\rm{\chi }}}}_{211112}^{(5)}\); otherwise no signal is detected. In our measurements, the VVV (V-polarized signal, V-polarized ω1, and V-polarized ω2) and HHH polarization combinations correspond to \({{{\rm{\chi }}}}_{111111}^{(5)}\), the VHV and HVH combinations correspond to \({{{\rm{\chi }}}}_{211112}^{(5)}\), the HVV and VHH combinations correspond to \({{{\rm{\chi }}}}_{211111}^{(5)}\), and the VVH and HHV combinations correspond to \({{{\rm{\chi }}}}_{111112}^{(5)}\).

Our results shown in Fig. 5 indeed follow this rule. Namely, we successfully detected the CAHRS signals under the VVV (Fig. 5a), HHH (Fig. 5b), VHV (Fig. 5c), and HVH (Fig. 5d) polarization combinations. In contrast, the other polarization combinations (Fig. 5e–h) give no signals, approximately 10-3 times smaller than those under the VVV/HHH combinations. We also found that the VHV (HVH) signal from the non-resonant background is ~6 times weaker than the VVV(HHH) signal. Theoretically, in the case of the non-resonant background, \({{{\rm{\chi }}}}_{111111}^{(5)}\) is equal to five times \({{{\rm{\chi }}}}_{211112}^{(5)}\) with Kleinman symmetry, meaning that the VHV (HVH) signal should be 25 times less than the VVV (HHH) signal in the homodyne detection. The experimental deviation from the theoretical value suggests the breaking of Kleinman symmetry, requiring a further study.

CAHRS spectra from neat benzene liquid

Next, we will discuss CAHRS signals of Raman inactive modes of benzene liquid. Because a benzene molecule has centrosymmetry, the mutual exclusion principle between Raman and hyper-Raman spectroscopy is operative, as well as that between IR and Raman spectroscopy (see Supplementary Information section 3). Namely, Raman active vibrations are hyper-Raman (IR) inactive, and hyper-Raman (IR) active vibrations are Raman inactive. Figure 6a, b show the observed spectra of liquid benzene from 550 to 750 cm-1 and from 900 to 1100 cm-1, respectively. The observed spectra were divided by those of deuterated benzene (benzene-d6) as the non-resonant background for the intensity correction. The former spectral region from 550 to 750 cm-1 includes an HR active mode with the largest HR intensity (a2u; CH bending mode at 670 cm-1, see Supplementary Information section 4)49. The latter spectral region includes not only an HR active mode with the second largest HR intensity (e1u; CH bending mode at 1038 cm-1) but also a well-known Raman active mode with the largest Raman intensity (a1g; totally symmetric breathing mode at 992 cm-1)49. As expected, we found vibrational bands around 670 and 1040 cm-1 attributed to HR active modes mentioned above, while no signals around 992 cm-1 in the spectrum despite the largest Raman intensity. The absence of CAHRS signals due to the 992 cm-1 Raman band represents that the observed signal is not derived from an optical process, including the Raman excitation. Thus, we can rule out the possibility that the observed signal comes from a cascading χ(3) process based on the Raman excitation, which often overwhelms a χ(5) signal, ensuring that the signals come from the CAHRS process.

Fig. 6: Selection rules verified by measurements of benzene.
Fig. 6: Selection rules verified by measurements of benzene.
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CAHRS spectra of neat benzene in 550 ~ 750 cm−1 (a) and in 900 ~ 1100 cm−1 (b). Spectra are intensity corrected by using the non-resonant background signals from neat benzene-d6. Spontaneous HR spectra of benzene in 550 ~ 750 cm−1 (c) and in 900 ~ 1100 cm−1 (d). In the CAHRS measurements, the powers of the ω1 and ω2 lights were 60 and 5 mW, the exposure times was 1 s, and 10 exposures were averaged. In the spontaneous HR measurements, the power of the excitation light was 30 mW, the exposure time was 10 s, and 10 exposures were averaged.

The 670 cm-1 signal has a corrected intensity of ~40 at the peak maximum with a Lorentzian-like but slightly asymmetric and dispersive line shape, meaning that the vibrationally resonant component of χ(5) is much larger than that of the non-resonant background. In contrast, the corrected intensity of the 1040 cm-1 band is about two at the peak maximum, and its lineshape is dispersive, suggesting the magnitudes of the vibrationally resonant and non-resonant background are comparable. It is safe to say that our observations in the CAHRS spectra semi-quantitatively account for the relative intensities in the spontaneous HR spectra, in which the intensity of the 670 cm-1 band is about ten times larger than that of the 1040 cm-1 band49.

In addition, it is worth noting that the 670 cm-1 and 1040 cm-1 bands observed in the CAHRS spectra are not Raman active but IR active. The result means that CAHRS spectroscopy enables us to detect IR active and Raman inactive vibrations through the hyper-Raman process. The detection of IR active modes by CAHRS spectroscopy is important in its application to microscopy. As explained previously, all the IR active modes are, in principle, HR active, meaning that CAHRS spectroscopy using visible and near-infrared light sources can yield equivalent information to IR spectroscopy. The spatial resolution of IR microscopy is limited to the order of several micrometers due to the diffraction limit of IR light. On the other hand, because CAHRS spectroscopy is based on a high-order nonlinear process with visible/near-infrared light, the spatial resolution of CAHRS microscopy is expected to be as high as conventional CRS microscopy, which is much higher than IR microscopy. IR-photothermal microscopy50,51 and third-order sum-frequency generation microscopy52 have been developed to obtain information on IR active modes. CAHRS spectroscopy relies on a higher-order nonlinear process than those techniques, meaning that CAHRS spectroscopy requires higher pulse energy to generate sufficient signals. Nevertheless, CAHRS spectroscopy has an advantage for detecting IR modes in the low-frequency region. Generally, it is difficult to generate IR light longer than 10 μm, corresponding to <1000 cm-1. In contrast, because CAHRS spectroscopy uses near-infrared and visible lights, there is no limitation on the frequency range of the target vibration. The 670 cm-1 band from benzene and the 850 cm-1 band from PNA that we observed correspond to 14.9 and 11.8 μm, respectively. In addition, a CAHRS signal due to the 490 cm-1 band from deuterated benzene was successfully obtained (see Supplementary Information section 5), corresponding to the mid-IR light with >20 μm. These experimental results ensure that CAHRS spectroscopy can address low-frequency vibrations that are not readily accessed by IR-based techniques. Also, while IR-based techniques suffer very strong water absorption in the infrared region, CAHRS spectroscopy is not seriously influenced by water.

Comparison between CAHRS and spontaneous HR spectra

In this section, we briefly compare CAHRS spectra with spontaneous HR spectra from the PNA solutions and benzene shown in previous sections. Table 2 summarizes the experimental conditions, including the incident laser powers and exposure times. It should be emphasized that the CAHRS and HR signals are measured with the same light source, polychromator, and CCD camera, suggesting we can fairly compare the signals of two spectroscopies. We focus on the 1323 cm-1 band of the PNA solution (Fig. 2c, e) and the 670 cm-1 band of benzene (Fig. 6a, c), the strongest HR band from each sample. The signal-to-noise (SN) ratios of these bands in the CAHRS and spontaneous HR spectra are contained in Table 2. The SN ratios of the 1323 cm-1 band of PNA are 103 and 30 in the CAHRS and spontaneous HR spectrum, respectively. In the case of the 670 cm-1 band of benzene, the SN ratios are 103 and 10 in the CAHRS and spontaneous HR spectrum, respectively. In both cases, our evaluation indicates that CAHRS spectroscopy gives much higher SN ratios than spontaneous HR spectroscopy by a factor of 102. We recognize that CAHRS and spontaneous HR spectroscopy differ in the number of incident lights: the CAHRS process requires two-color laser beams, while one for spontaneous HR scattering. However, the much higher SN ratios in the CAHRS spectra with shorter exposure times than spontaneous HR spectra suggest the possibility of CAHRS spectroscopy for acquiring HR spectra at high speed.

Table 2 Experimental conditions and SN ratios of CAHRS and spontaneous HR signals
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Magnitude of χ(5) for CAHRS signals

Furthermore, we determined the magnitude of \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\) of the sample giving rise to the CAHRS signal. According to the theory of four- and six-wave mixing processes1,53,54,55, the power of a CAHRS signal \({{\mathcal{P}}}\)CAHRS is expressed as

$$ {{{\mathcal{P}}}}_{{{\rm{CAHRS}}}} \\ ={\left(\frac{{{8\pi }^{3}\omega }_{{{\rm{CAHRS}}}}}{{n}_{{{\rm{CAHRS}}}}{c}^{3}}\right)}^{2}\times {|5{{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}|}^{2}{L}^{2}{{{\mathcal{P}}}}_{1}^{4}{{{\mathcal{P}}}}_{2}\frac{{A}_{{{\rm{CAHRS}}}}}{{A}_{1}^{4}{A}_{2}}{{{\rm{sinc}}}}^{2}\left(\frac{\Delta {kL}}{2}\right)\times {10}^{28}\left[{{\rm{W}}}\right],$$
(2)

where ωCAHRS is the angular frequency of the CAHRS signal, nCAHRS is the refractive index of the sample at ωCAHRS, c is the speed of light, \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\) is the CAHRS susceptibility in esu, L is the interaction length, Ai is the cross-sectional area of each laser beam, \({{\mathcal{P}}}\)i is the power of each laser beam in watt, and Δk = |kCAHRS – (4k1−k2)|, respectively. Considering the experimental conditions (for details refer to Table 3 in Methods) and the signal intensities in CCD counts, we calculated the magnitude of \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\). Note that we assume the phase-matching condition is fully satisfied (Δk = 0) in the present experiments.

Table 3 Parameters used in the determination of \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\)
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First, the magnitude of \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\) of liquid benzene is determined to be 4 × 10-28 esu (6 × 10−45 m4/V4). Although there is an uncertainty in \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\) due to the high nonlinearity of the CAHRS process, \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\) of benzene we determined might be used as a reference of \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\). We compared the magnitude of \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\) with that of \({{{\rm{\chi }}}}_{{{\rm{CARS}}}}^{\left(3\right)}\), third-order nonlinear susceptibility giving a CARS signal. \({{{\rm{\chi }}}}_{{{\rm{CARS}}}}^{\left(3\right)}\) from benzene was reported to be ~10-13 esu (~10-21 m2/V2)9,56,57. The ratio \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}\left[{{{\rm{m}}}}^{4}/{{{\rm{V}}}}^{4}\right]\,/\,{{{\rm{\chi }}}}_{{{\rm{CARS}}}}^{\left(3\right)}\left[{{{\rm{m}}}}^{2}/{{{\rm{V}}}}^{2}\right]\) from benzene was obtained as ~10-24 [m2/V2]. In nonlinear optics, the ratio between the ith and i+1th nonlinear susceptibilities is often estimated, assuming that the ith-order polarization P(i) would be comparable to the i+1th-order polarization P(i+1) when the characteristic atomic electric field Eat = 5×1011 [V/m] is applied58. In this case, the ratio χ(i+1)/χ(i) is estimated to be 1/Eat. According to this estimation, the ratio \({{{\rm{\chi }}}}^{\left(5\right)}/{{{\rm{\chi }}}}^{(3)}\) is expected to be the order of (1/Eat)2 ≈ 10-24 [m2/V2], fairly agreeing with the experimental value of \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{\left(5\right)}/{{{\rm{\chi }}}}_{{{\rm{CARS}}}}^{\left(3\right)}\) from benzene.

We also discuss the enhancement of CAHRS signals due to the electronic resonance effect by comparing \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{(5)}\) per molecule of benzene liquid with that of PNA. The electronic absorption of PNA is at 390 nm in solution, while that of benzene liquid is in the deep ultraviolet region. Thus, CAHRS signals of PNA should be pre-resonantly enhanced under the experimental condition, while benzene should not. \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{(5)}\) per molecule of PNA in chloroform and benzene were calculated to be 5 ×10−50 and 1 ×10−46 esu cm3/molecule, respectively. This result means that the two-photon electronic (pre-) resonance effect enhances \({{{\rm{\chi }}}}_{{{\rm{CAHRS}}}}^{(5)}\) per molecule by a factor of 103 ~ 104. The signal enhancement due to electronic resonance improves sensitive detection, enabling various applications demonstrated in conventional CRS spectroscopy.

In summary, we have developed a new CRS spectroscopy, CAHRS spectroscopy, which enables us to measure HR active vibrational modes, based on a χ(5) process. We provided fundamental information on CAHRS spectroscopy by measuring test samples for future applications in various fields associated with high-order nonlinear optical processes, in particular, ultrafast spectroscopy and imaging. We have provided the fundamental basis for CAHRS spectroscopy, by examining the spectral profiles, the time dependence, the pump power dependence, and the polarization dependence of the CAHRS signals from the PNA solution. In the previous paper describing the theory of coherent HR spectroscopy, it is written that it may be impossible to perform coherent hyper-Raman experiments with liquid samples because a liquid is likely to suffer a dielectric breakdown at the high fields. However, using proper light sources with a high repetition rate and proper pulse widths, we have successfully demonstrated CAHRS spectroscopy of liquid samples without suffering a dielectric breakdown. Besides, the CAHRS signals from the benzene solution show that CAHRS spectroscopy can detect an HR active mode that is Raman inactive. We show that CAHRS spectroscopy offers spectral information on low-frequency vibrations below 1000 cm−1 (down to ~500 cm−1), which is difficult for IR-based techniques to approach. The comparison of the CAHRS signals of the samples with the spontaneous HR signals suggests that CAHRS spectroscopy can give us identical information on spectra at a higher speed than spontaneous HR spectroscopy. Our results imply that the present laser technology can bring enough CAHRS signals from various systems and make CAHRS spectroscopy hold promise to be a powerful tool for investigating many systems, complementary to the present CRS techniques.

Methods

Experimental setup of CAHRS spectrometer

The schematic of the CAHRS spectrometer is shown in Fig. 1c. A femtosecond Yb: KGW laser (Light Conversion, Pharos PH2−10W, wavelength: 1030 nm, pulse width: ~200 fs, repetition rate: 50 kHz, pulse energy: 200 μJ) was used to drive the whole setup. A 40 μJ portion of the output of the laser was introduced into a homemade 4 f spectral filter consisting of a transmission grating (1800 lines/mm, blazed wavelength: 1030 nm), a cylindrical lens, an adjustable slit, and a mirror to obtain the narrowband ω1 beam (wavelength: 1027.36 nm, bandwidth: ~10 cm−1). The remaining 160 μJ was introduced into an optical parametric amplifier (OPA, Light Conversion, Orpheus). An idler light from the output of the OPA (wavelength: 1060 ~ 1120 nm) was frequency-doubled in a type-I β-barium borate (BBO) crystal to produce the tunable ω2 beam (wavelength: 530 ~ 560 nm, pulse width: ~200 fs, bandwidth: ~100 cm−1). The wavelength of the tunable ω2 beam was adjusted to satisfy 2ω1-ω2 = Ω (Ω is a vibrational frequency). Filters were used to eliminate the idler light passing through the BBO crystal. Polarizations of the narrowband ω1 and the tunable ω2 beams were controlled independently by using polarizers and half-wave plates. Two beams were focused into a sample cuvette by lenses (ω1: f = 50 mm and ω2: f = 150 mm) at the angles satisfying the phase-matching conditions. At the focal position, the diameters of the ω1 and ω2 beams are estimated to be 50 and 90 μm, respectively, from the knife-edge method. The CAHRS signals from the samples were collected with an achromatic lens (f = 30 mm, ϕ = 25.4 mm). After the lens, the CAHRS signals passed through an aperture and filters to remove the ω1 and ω2 pulses spatially and spectrally, an analyzer to select their polarization, and a depolarizer to suppress the polarization dependence of a polychromator. Finally, the CAHRS signals were introduced into the polychromator (Horiba, iHR320, 1200 lines/mm, blazed wavelength: 500 nm) and detected by a CCD camera (Andor, DV420A-OE). Each spectra shown is an average of 10 exposures.

Experimental setup of spontaneous HR spectrometer

The narrowband ω1 beam in the CAHRS setup was used as an excitation light source. The ω1 beam was reflected by a short-pass dichroic mirror and focused into the sample with an achromatic lens (f = 30 mm, ϕ = 25.4 mm). Stokes HR signals in the backward direction were collected by the same lens. Then, the Stokes HR signals were passed through the dichroic mirror to remove the ω1 beam, introduced into the polychromator, and detected by the CCD camera. The polychromator and the CCD camera were the same as the CAHRS spectrometer. Each spectra shown is an average of 10 exposures.

Materials

Chloroform, para-nitroaniline (PNA), and benzene liquid were purchased from Nacalai Tesque and used as received. Deuterated benzene-d6 (99.50% D) was purchased from Eurisotop and used as received. All samples were filled in the quartz cuvette (double transparent, optical path length: 5 mm). In this paper, we set the concentration of PNA/chloroform solution to 10 mM.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.