As articulated by the Kramers–Heisenberg–Dirac dispersion theory [1,2], emission of radiation in a vast class of scattering phenomena is inseparable from absorption. Even though the emission part of scattering is easier to detect and appreciate, its absorption counterpart is equally important for the correct, complete physical picture of scattering, as well as for a control of scattering. Raman scattering offers one of the most striking examples of how the absorption side of scattering not only provides much needed physical insights, but also broadens the impact of this process as a method for spectroscopy and microscopy. Very much like studies into other types of scattering, such as the Compton effect [3], the early-era Raman research was entirely focused on the emission of frequency-shifted radiation [4,5]. It was not until the advent of lasers and the emergence of nonlinear optics that the first observation of Raman-induced loss—inverse Raman scattering—was reported [6].

Recognized as a useful spectroscopic tool in the early era of nonlinear optics [7–12], in more recent times, the inverse Raman effect has largely stayed in a shadow of a high renaissance of coherent anti-Stokes Raman scattering (CARS) [13–16], spearheading a breakthrough in high-speed chemically selective bioimaging [17,18]. Within the past few years, however, both stimulated Raman gain (SRG) and stimulated Raman loss (SRL) were making their comeback as powerful and practical concepts of high-resolution, high-sensitivity spectroscopy [19,20] and microscopy [21–23], offering new resources for bioimaging and remote sensing. As one promising approach, chemically specific SRG/SRL spectroscopy can be implemented [19,20] with a coherent, backward propagating 337-nm pump, provided by lasing atmospheric nitrogen driven by a short-pulse mid-IR laser [24–26].

A rapid progress of laser sources capable of generating ultrashort high-peak-power pulses expands the realm of nonlinear optics. In broadband laser–mater interaction processes driven by such pulses, canonical nonlinear-optical effects no longer show up as their textbook silhouettes. Instead, they fuse into an intricate nonlinear dynamics that involves cascades of strongly coupled spatial, temporal, and spectral transformations, giving rise to ultrabroadband field-waveform transients with complex spectra, pulse shapes, and phase profiles [27–29]. Manifestations of Raman scattering in such scenarios may be also very different from mere spectral sideband generation, and may include, as perhaps most striking effects, continuous frequency downshifting and generation of extremely short, single-cycle or even sub-cycle field transients [30–32]. Combination of stimulated Raman scattering (SRS) with high-order harmonic generation (HHG) provides a powerful spectroscopic probe for ultrafast molecular dynamics and complex molecular potentials [33].

Here, we present an experimental setting that combines HHG with the inverse Raman effect. In this setting, ultrashort mid-infrared pulses are used to drive HHG in a Raman-active gas. The spectral analysis of such a high-harmonic output reveals well-resolved signatures of SRG and SRL, showing up near the frequencies of prominent vibrational transitions of molecules. When tuned on a resonance with the $v^\prime = 0 \to v^{\prime\prime} = 0$ pathway within the ${B^3}{\Pi _{\rm g}} \to {C^3}{\Pi _{\rm u}}$ second positive system (2PS) of molecular nitrogen (${{\rm{N}}_2}$), the eleventh harmonic of a 3.9 µm, 80 fs laser driver is shown to acquire a distinctive antisymmetric spectral profile with red-shifted bright and blue-shifted dark features as indicators of stimulated Raman gain and loss.

Serving as a source of a high-peak-power mid-IR driver in our experiments (Fig. 1) is a pulse-compressed output of a three-stage optical parametric chirped-pulse amplifier (OPCPA) [34,35], delivering mid-IR field waveforms with a central wavelength ${\lambda _0} \approx {3.9}\; \unicode{x00B5}{\rm m}$, a pulse width ${\tau _0} \approx {{80}}\; {\rm{fs}}$, and a pulse energy up to ${E_0} \approx {{35}}\; {\rm{mJ}}$ [35,36].The mid-IR OPCPA output is focused in a two-compartment gas cell with a 30-cm-focal-length lens (Fig. 1). The gas pressure $p$ inside the first compartment of the gas cell is variable from ${10}^{- 6}$ up to 1.0 bar, with high-vacuum-side pressures provided via a rotary variable displacement dry-vacuum pump (roots pump, RVP in Fig. 1). Spectral analysis of the mid-IR part of SC radiation is performed with a homebuilt scanning monochromator and a cryogenically cooled HgCdTe detector. The spectrum of the HHG output with wavelengths down to 200 nm is analyzed with an ultraviolet-to-near-infrared (UV–NIR) high-resolution HR4000 OceanOptics spectrometer (UV–NIR HRS, Fig. 1). To perform spectral analysis of harmonics of higher orders, the harmonic beam is reflected off a 17-cm-focal-length spherical holographic diffraction grating (DG in Fig. 1) to be detected with a microchannel plate with a phosphor screen, used jointly with a CCD camera (MCP and CCD, Fig. 1). The diffraction grating and the MCP detector are installed in the second compartment of the gas cell, which is separated from the first compartment by a CaF2 window (Fig. 1) and is kept at a gas pressure of ${\rm{3\cdot1}}{{{0}}^{- 10}}\; {\rm{bar}}$, sustained by a turbomolecular vacuum pump (TMP in Fig. 1).

 

Fig. 1. Experimental setup: HRS, high-resolution spectrometer; ND, neutral-density filter; MCP, microchannel plate with a phosphor screen; RVP, roots vacuum pump; TMP, turbomolecular vacuum pump; FM, flip mirror; L, focusing lens; DG, diffraction grating; GC, gas cylinder; W1, W2, gas-cell windows; UVW, ${\rm{Ca}}{{\rm{F}}_2}$ window separating two compartments of the gas cells.

Download Full Size | PDF

Typical spectra of high-order harmonics (HHs) generated in a gas cell filled with molecular nitrogen are presented in Figs. 2(a) and 2(b). As a general tendency, these spectra display well resolved peaks centered at frequencies $m{\omega _0}$, with odd integer $m$ and ${\omega _0} = {{2}}\pi c/{\lambda _0}$, corresponding to odd-order harmonics of the driver. Harmonics with $m$ as high as $m = {{31}}$ are observed near the short-wavelength cutoff of the MCP detection range [Fig. 2(b)], suggesting that harmonic spectra extend beyond the cutoff of the detection range in this experiment.

 

Fig. 2. Typical spectra of high-harmonic radiation from an ${{\rm{N}}_2}$-filled gas cell at gas pressures as specified in the legend measured with (a) a UV–NIR high-resolution spectrometer and (b) an MCP-based spectrometer in experiments with a laser driver with ${\lambda _0} \approx {3.9}\; \unicode{x00B5}{\rm m}$, ${\tau _0} \approx {{80}}\; {\rm{fs}}$, and ${E_0} \approx {{17}}\; {\rm mJ}$. Enclosed within the dashed-line box is the dispersive feature $\sigma (\lambda)$ centered at the wavelength of the $v^\prime = 0 \to v^{\prime\prime} = 0$ transition within the ${B^3}{\Pi _{\rm g}} \to {C^3}{\Pi _{\rm u}}$ second positive system of ${{\rm{N}}_2}$.

Download Full Size | PDF

Figure 3(a) zooms in on the 330–365 nm region within the high-resolution HH spectra, capturing a peak, $\xi (\lambda)$, at the frequency of the 11th harmonic generated in an ${{\rm{N}}_2}$-filled gas cell at different pressures of ${{\rm{N}}_2}$ Immediately notable in the high-frequency wing of this peak is a prominent dispersive feature $\sigma (\lambda)$ centered at the wavelength of the $v^\prime = 0 \to v^{\prime\prime} = 0$ transition within the ${B^3}{\Pi _{\rm g}} \to {C^3}{\Pi _{\rm u}}$ 2PS of ${{\rm{N}}_2}$, ${\lambda _\Pi} \approx {{337}}\; {\rm{nm}}$ [37]. In Fig. 3(b), we present the spectra of the differential signal $\Delta (\lambda) = \sigma (\lambda) - \xi (\lambda)$ plotted for different gas pressures $p$. Both the $\sigma (\lambda)$ feature in the high-frequency wing of the 11th harmonic and the differential signal $\Delta (\lambda)$ display a well-pronounced dip on their high-frequency side and an equally well-pronounced peak on their low-frequency side, indicating, respectively, a loss and a gain of 11th harmonic energy.

 

Fig. 3. (a), (b) Spectra of (a) the 11th harmonic of the mid-IR driver and (b) differential signal $\Delta (\lambda)$ for an ${{\rm{N}}_2}$-filled gas cell at gas pressures as specified in the legend. (c) Maximum gain at the center of the bright Raman feature (blue dots with error bars, left axis) and the maximum loss at the center of the dark Raman feature (pink dots with error bars, right axis) as functions of $p$ against their best ${p^{2.5}}$ fits (dashed lines). (d) Energy of the 11th harmonic as a function of $p$. All measurements are performed with a laser driver with ${\lambda _0} \approx {3.9}\; \unicode{x00B5}{\rm m}$, ${\tau _0} \approx {{80}}\; {\rm{fs}}$, and ${E_0} \approx {{17}}\; {\rm{mJ}}$. Shown in the inset is the differential SRS signal $\Delta P$ as a function of the power of the 11th harmonic.

Download Full Size | PDF

This spectral distribution of loss and gain is consistent with a physical picture of stimulated Raman scattering of a broadband pump with a central frequency ${\omega _{\rm p}} = {{11}}{\omega _0} + \delta$, in the high-frequency wing ($\delta \gt {{0}}$) of the 11th harmonic of the mid-IR driver. In this process [Figs. 4(a)–4(d)], the pump centered at ${\omega _{\rm p}}$ experiences a Raman gain of its low-frequency part and Raman loss in its high-frequency part [Figs. 4(a)–4(c)] via ${\omega _{\rm {a,s}}} = {\omega _{\rm p}} \pm {\Omega _{\rm R}}$ Raman scattering through the rotational pathways within the $v^\prime = 0 \to v^{\prime\prime} = 0$ manifold of ${{\rm{N}}_2}$, thus acquiring bright Stokes and dark anti-Stokes features centered at ${\omega _{\rm s}} = {\omega _{\rm p}} - {\Omega _{\rm R}}$ and ${\omega _{\rm a}} = {\omega _{\rm p}} + {\Omega _{\rm R}}$ [Figs. 4(a)–4(d)].

 

Fig. 4. (a), (b) Raman (a) gain and (b) loss via (a) direct and (b) inverse Raman scattering, giving rise to bright Stokes and dark anti-Stokes features in the wing of the 11th harmonic of the mid-IR driver ${\omega _0}$. (c), (d) High-harmonic-driven Raman gain and loss. A broadband signal with a central frequency ${\omega _{\rm p}}$ experiences a Raman gain of its low-frequency part and Raman loss in its high-frequency part via ${\omega _{\rm {a,s}}} = {\omega _{\rm p}} \pm {\Omega _{\rm R}}$ Raman scattering (c), acquiring bright Stokes and dark anti-Stokes features centered at ${\omega _{\rm s}} = {\omega _{\rm p}} - {\Omega _{\rm R}}$ and ${\omega _{\rm a}} = {\omega _{\rm p}} + {\Omega _{\rm R}}$ (d).

Download Full Size | PDF

The probability of a Raman process in which absorption of the pump at ${\omega _{\rm p}}$ is accompanied by emission at ${\omega _{\rm {a,s}}} = {\omega _{\rm p}} \pm {\Omega _{\rm R}}$ [Fig. 4(a)] is [6,38,39] ${\wp _{\rm {a,s}}} \propto \int |\mu{|^2}{\rho _{\rm p}}[{\rho _{\rm {a,s}}} + ({{2}}\hbar /\pi){({\omega _{\rm {a,s}}}/c)^2}]{\rm{d}}{\omega _{\rm p}}$, where $\mu$ is the pertinent two-photon dipole moment matrix element, ${\rho _{\rm p}}$ is the energy density of the pump, ${\rho _{\rm {a,s}}}$ is the energy density of emission at ${\omega _{\rm {a,s}}}$, and $c$ is the speed of light in vacuum. The probability of the inverse Raman process, that is, a process in which radiation absorption at ${\omega _{\rm {a,s}}} = {\omega _{\rm p}} \pm {\Omega _{\rm R}}$ gives rise to emission at ${\omega _{\rm p}}$ [Fig. 4(a)], is [6,38,39] ${\wp _{\rm p}} \propto \int |\mu{|^2}{\rho _{\rm {a,s}}}[{\rho _{\rm p}} + ({{2}}\hbar /\pi){({\omega _{\rm p}}/c)^2}]{\rm{d}}{\omega _{\rm {a,s}}}$.

To provide a quantitative measure for the HHG-driven Raman gain and loss, we search for the maximum of $\Delta (\lambda)$ within the bright Stokes feature, and the minimum of $\Delta (\lambda)$ within its anti-Stokes dark-feature counterpart. When plotted as functions of the gas pressure $p$, ${\max}(\Delta)$ and $|{\min}(\Delta)|$ display a strongly correlated behavior [cf. blue and pink dots in Fig. 3(c)], closely following a ${p^{2.5}}$ scaling [dashed lines in Fig. 3(c)]. Such a correlated behavior of ${\max}(\Delta)$ and $|{\min}(\Delta)|$ is fully consistent with the equations for ${\wp_{\rm {a,s}}}$ and ${\wp_{\rm p}}$. That the pressure dependence of ${\max}(\Delta)$ and $|{\min}(\Delta)|$ is neither linear nor quadratic in $p$ is not unexpected since the Raman effect in our setting is driven via a highly nonlinear process of 11th harmonic generation, where $p$ enters not only via the density of molecular species, but also via the phase-matching factor, yielding a strongly nonlinear function of $p$ [Fig. 3(d)].

Combining the stimulated Raman, $\propto {\rho _{\rm p}}{\rho _{\rm {a,s}}}$ terms of ${\wp_{\rm {a,s}}}$ and ${\wp_{\rm p}}$ for a system at thermal equilibrium yields a Raman gain at ${\omega _{\rm s}}$ and a Raman loss or, else, inverse Raman effect, at ${\omega _{\rm a}}$. The Raman gain coefficient at frequency $\omega$, $G(\omega) = \Delta P(\omega)/P(\omega)$, induced by a pump with frequency ${\omega _{\rm p}}$ is expressed in terms of the imaginary part of the relevant third-order susceptibility ${\chi ^{(3)}}(\omega ; \omega , {\omega _{\rm p}}, - {\omega _{\rm p}})$ as [9,10] $G(\omega) \propto {{96}}{\pi ^2}{n^{- 1}}{c^{- 3}}\omega {\omega _{\rm p}}{\rm{Im}}[{\chi ^{(3)}}(\omega ; \omega , {\omega _{\rm p}}, - {\omega _{\rm p}})]P({\omega _{\rm p}})$, where $n$ is the refractive index, and $P(\Omega)$ is the radiation power at frequency $\Omega$. Thus, unlike, e.g.,  the CARS signal, the Raman-gain-induced $\Delta P(\omega) = G(\omega)P(\omega) \propto \omega {\omega _{\rm p}}{\rm{Im}}[\chi ^{(3)}(\omega ; \omega , {\omega _{\rm p}}, - {\omega _{\rm p}})]P({\omega _{\rm p}})P(\omega)$ is linear with both the pump and probe power. This prediction agrees well with our experiments [the inset in Fig. 3(d)]. Such a scaling of the differential signal $\Delta P$ with the driver power makes the SRG and SRL reliably detectable even at very low levels of pump power, enabling, as shown by earlier work [9,10,40], spectroscopy with cw laser sources.

Experiments presented here show that SRG and SRL can be extended to a completely new setting, allowing HHG and other concepts and tools of strong-field optics to be integrated with Raman-based methodology as a route toward ultrafast time-resolved spectroscopic studies and high-brightness chemically specific imaging. Moreover, operating through the celebrated 337 nm lasing pathway of ${{\rm{N}}_2}$, this setting of stimulated Raman scattering suggests a physical mechanism whereby mid-IR-driven air lasing [24,41] and laser filamentation [34,42,43] can be integrated with SRG/SRL spectroscopy to open new avenues in highly sensitive standoff trace-gas detection. One of the important questions to be addressed by further studies is whether the rotational coherence prepared in the 2PS of ${{\rm{N}}_2}$ by HHs of a mid-IR driver could help enhance ${{\rm{N}}_2}$ lasing in mid-IR driven laser filaments.

Since the HH radiation is highly sensitive to the orientation and structure of molecules, it provides an ultrafast spectroscopic probe [44], which utilizes laser-driven photoelectrons rescattered by their parent ions, thus integrating laser spectrochronography with ultrafast electron diffraction. Because this process is extremely fast and because the de Broglie wavelength ${\lambda _e}$ of the recolliding electrons can become very short, HHG spectroscopy provides a unique combination of attosecond resolution in time and ${\lambda _e}$-scale resolution in space [33]. Now, that molecular rotations have been found to manifest themselves via an SRS of HHs, the Raman features in HH spectra can add a meaningful readout to detect elements of symmetry in molecular modes, thus helping map out the molecular potential and reconstruct molecular orbitals. Moreover, the Raman signatures of molecular rotations, such as those observed in the HH spectrum in Figs. 3(a) and 4(a), can help better define molecular orientation and clock the phases of molecular alignment in laser-pump–HH-probe spectrochronography.

As electron recollisions recur every field half-cycle, ${T_0}/{{2}}$, high-frequency radiation is emitted as ${T_0}/{{2}}$-periodic sequences of extremely short, attosecond pulses trains [45]—the time-domain field structure that translates into spectra with prominent odd-order HH peaks in the frequency domain. This extremely short duration of individual bursts of HH radiation is, however, difficult to sustain over any sensible propagation distance outside a vacuum chamber. The finding that HHs can efficiently couple to the Raman modes of molecules can help address this problem. While suitable solutions in the class of soliton transients are still to be identified and carefully analyzed, the existing coupling between the HH field and Raman-active molecular modes is the key to suppressing the dispersion-induced pulse stretching via coupled-state field-evolution scenarios [32], where extremely short optical field waveforms drive Raman-active molecular modes, which, in their turn, modulate the phase of the driver field to yield soliton transients capable of emitting ultrabroadband, multidecade supercontinua and sustaining their extremely short pulse widths over large propagation distances [46].

The HH-field–Raman-mode coupling is in no way limited to the 2PS of ${{\rm{N}}_2}$. Deeper into the UV region, a similar SRG/SRL feature is observed in the high-frequency wing of the 15th harmonic as a result of SRS via $v^\prime = 0 \to v^{\prime\prime} = 2$ transitions within the $\gamma$ system of nitrogen monoxide. The HH-field–Raman-mode coupling scenarios that could be targeted with harmonics in the EUV and x-ray ranges include Raman scattering by core electrons [47] as a route toward element-specific spectroscopy of the electronic structure and highly excited states in atomic systems.

To summarize, the spectral analysis of HH generated by ultrashort mid-IR pulses in ${{\rm{N}}_2}$ reveals signatures of inverse Raman scattering, showing up near the frequencies of prominent vibrational transitions of ${{\rm{N}}_2}$. This HH setting extends the inverse Raman effect to a vast class of strong-field light–matter interaction scenarios.