Over the last decade, solid-state high-order harmonic generation (HHG) has garnered significant attention in the fields of strong-field and condensed matter physics. Since its discovery in ZnO single crystals [1], non-perturbative HHG has been observed in a wide range of materials, including wide-bandgap media [2,3], semi-metals [4–7], and artificial metamaterials [8–10]. The aforementioned studies have shown the remarkable sensitivity of HHG on material properties and suggested potential applications in the field of materials research, as well as in the development of controllable broadband HHG sources and all-optical switches [11–13].

The active control dynamics processes involved in HHG are essential for various applications [14,15]. Two fundamental dynamic processes in solid-state HHG that contribute to the intraband and interband harmonics are the intraband acceleration and interband polarization of carriers, respectively [16]. It is widely recognized that interband polarization primarily contributes to high-energy (above-bandgap) harmonics, while intraband acceleration is predominant for low-energy (below-bandgap) harmonics [16,17]. Both mechanisms have the potential to actively regulate HHG. Research has demonstrated that intraband harmonics in single-layer transition metal dichalcogenide (TMD) can be enhanced by approximately 20% using pre-excited incoherent carriers [18]. An orthogonal-polarized control laser field can significantly reduce interband harmonics by approximately one order of magnitude through the suppression of electron-hole collisions [13]. However, these studies have been limited by their reliance on the single-particle model within a frozen band structure, which restricts their applicability. The single-particle model is only valid when the control laser can be considered a perturbation [19]. A more powerful control laser has the capability to induce diabatic effects, such as band renormalization and phase transitions [20]. These effects extend beyond the regime of static systems and weak electron interactions. However, they may offer a more reliable approach to controlling HHG due to its high sensitivity to band structure and related factors [21,22].

Vanadium dioxide (VO2), a typical strongly correlated material, can serve as an ideal platform for understanding complex correlation physics [23–26] and various applications [27,28] owing to the substantial alterations in its physical characteristics upon external excitation on an ultrafast timescale. Previous research has suggested VO2 for applications in dynamically controllable integrated optoelectronic devices [29–31]. Recently, intraband harmonics in VO2 have demonstrated the capability to serve as probes for ultrafast solid-state dynamics with the modulation of light emission in the infrared region [32]. Interband harmonics can naturally generate high-energy coherent light sources, and controlling them is expected to extend all-optical control of HHG to the visible and even ultraviolet ranges.

In this work, we conducted experimental investigations on HHG and its control in VO2 films. Non-perturbative interband harmonics spanning visible to ultraviolet regions were measured using a reflection geometry setup. Additionally, we demonstrate that temperature and photo-carrier doping can effectively modify HHG with a high modulation depth over several orders of magnitude (extinction ratio ≥40dB) and transient resolution in the hundreds of femtoseconds. Our quantitative analysis revealed that the photo-induced carrier dynamics and insulator-to-metal transition (IMT) are the driving forces that dynamically control the interband harmonics. Finally, we showed that the metallic phase fraction can be quantitatively extracted from the time-resolved (tr)-HHG signals during the IMT process.

The sample was purchased from a commercial company (Nanjing MKNANO). By utilizing reactive ion beam sputtering deposition, a polycrystalline VO2 film is deposited onto a double-sided polished sapphire substrate (0006). The X-ray diffraction (XRD) pattern in Fig. 1(b) shows peaks corresponding to various crystal face indices, indicating the polycrystalline structure of the VO2 film. The sample is subsequently positioned on a temperature-regulated rack, which maintains stability within ±50mK, and is subjected to annealing in a vacuum environment at 450 K for a duration of 30 min prior to our HHG measurement.

We performed all HHG experiments using a reflection geometry configuration in a vacuum environment [Fig. 1(a)] to eliminate propagation effects and environmental influences. The mid-infrared (MIR) probe laser (0.35 eV, 100 fs, 15 μJ) was generated through collinear differential frequency generation (DFG) between the signal and idler laser of an optical parametric amplifier (OPA) pumped by a Ti:sapphire-based regenerative amplifier (1.55 eV, 35 fs, 1 kHz, 5 mJ). The signal laser of the OPA (0.95 eV, 60 fs, 5 μJ) is directed through a 9:1 beam splitter, with the majority of the light being utilized to generate the MIR probe laser, while a smaller portion serves as the pump laser. The pulse energy of the pump and MIR probe lasers can be continuously adjusted by incorporating a combination of half-wave plates and linear polarizers, respectively, placed in their individual optical paths. Subsequently, the pump and probe lasers are focused non-collinearly (θ≈10°) onto the sample surface using CaF2 lens (f=500mm for the pump laser and 200 mm for the probe laser). The diameters of the laser spot (e−2) on the sample measured using the knife-edge method are 200 μm for the pump laser and 100 μm for the probe laser. A nanoscale precision linear translation stage (Newport) is used to meticulously control the time delay between the pump and probe lasers. All pump-probe data are derived by directly comparing the harmonic intensity in the presence and absence of the pump, thus allowing for monitoring potential sample damage. Finally, all harmonic signals are recorded by a home-built spectrometer, which is composed of a slit, a 300gmm−1 grating, and a charge-coupled device (CCD) camera.

Figure 2(a) displays the representative harmonic spectrum obtained from a polycrystalline VO2 film on a sapphire substrate. The spectrum was generated by a linearly polarized MIR laser (0.35 eV, 100 fs) in a reflection geometry setup at room temperature. The 5th–11th order harmonics, ranging from visible to ultraviolet and exceeding the 0.6 eV bandgap of insulating VO2, were recorded. It is noted that the even-order harmonics are absent owing to the inversion symmetry and polycrystalline nature of the VO2 film [33]. The integral intensity of the harmonic scale as a function of laser power is shown in Fig. 2(b), revealing a clear division into two distinct regions at 0.5TW/cm2. For weaker lasers, HHG remained within the perturbative regime. Beyond this power threshold, all harmonics exhibited deviations from the scaling law characteristic of the perturbative regime (dotted line), indicating a transition to non-perturbative light–matter interaction where the dynamics are governed by the dynamic laser field. It is noteworthy that the cutoff of the HHG scaled linearly with the driving laser field, as shown in Fig. 2(c), which is inconsistent with the previous theoretical prediction of cutoffs in strongly correlated systems but remarkably consistent with single-electron pictures. The cutoff of HHG in strongly correlated systems was predicted to be determined solely by the correlation strength rather than by the laser field [34]. The discrepancy between theoretical predictions and experimental results may be attributed to the assumption of a fixed correlation strength in the theoretical calculation. Simulations using time-dependent density functional theory revealed that, instead of being constant, the Coulomb repulsion in strongly correlated systems dynamically oscillated with the laser field, with an amplitude approximately proportional to the strength of the laser field [35]. These findings further underscore the necessity of exploring HHG in strongly correlated systems.

Figure 3 illustrates the temperature-dependent normalized intensity of the 5th-order harmonic. A distinct step pattern exhibiting intensity variations spanning over four orders of magnitude is observed around 340 K, indicating that the harmonic modulation arises from the IMT [28]. The observed hysteresis aligns with the first-order nature of the phase transition [36,37]. At approximately 340 K, IMT occurred, leading to the collapse of the subband split by the strong electron correlation. The significant decrease in harmonic intensity was attributed to a strong non-radiative electron transfer in the metal and a considerable change in the dielectric environment of VO2 [29,38]. It was noted that a significantly high modulation depth (extinction ratio >60dB) of IMT in HHG can be attained, comparable to that of conductivity [28,39] and more notable than changes in transmittance based on linear optics [40,41]. The significant modulation of IMT for interband harmonics indicates its potential for dynamically controlling HHG, particularly considering previous research showing induction of IMT in VO2 using all-optical techniques [42,43].

We conducted photo-carrier doping experiments using a two-color pump-probe setup to demonstrate the all-optical control of HHG. The experimental schematic diagram is shown in Fig. 4(a). The pump laser (0.95 eV, 60 fs) serves as the primary excitation source for the sample through single-photon absorption. Concurrently, a time-delayed MIR laser is employed as a probe to induce the generation of harmonics. According to theoretical predictions, interband harmonics are suppressed, while intraband harmonics are increased when incoherent carriers are stimulated [18,44,45]. We observed that all harmonics in Fig. 4(b) were suppressed, thus limiting our discussion to interband harmonics. Quantitative analysis showed a positive correlation between the decrease in harmonic intensity and harmonic order. Specifically, the 5th-order harmonic intensity was reduced by 38%, with the higher 11th-order suppressed by 79%. This order-dependent harmonic reduction provides evidence that scattering-induced dephasing, rather than the phase-space filling effect, is the primary mechanism that suppresses HHG. According to semi-classical theory, higher-order interband harmonics from the so-called “short trajectory” possess a longer excursion time and are more sensitive to dephasing owing to increased scattering events [16,45]. The tr-HHG signals obtained after the photoexcitation by scanning the time delay between the pump and probe pulses are shown in Fig. 4(c). A positive time delay indicates that the pump laser arrived at the sample before the probe laser. All the harmonic intensities experience an initial abrupt decay followed by a gradual recovery. The tr-HHG signals were accurately fitted using the following convolutional exponential decay function: I(t)=I0+(Afaste−t/τfast+Aslowe−t/τslow)⊗[1τ0πe−(t/τ0)2],(1)where I0 represents the harmonic intensity without pumping. Afast,slow and τfast,slow denote the amplitudes and lifetimes of the fast and slow processes, respectively. The Gaussian factor 1τ0πe−(t/τ0)2 describes the response function related to the pulse durations of the pump and probe. The fitting results [solid curve in Fig. 4(c)] closely match the experimental data [COD(R2)≥0.999], including a rapid process of approximately 300 fs and a slow process of approximately 7 ps. The fast term aligned well with the fast relaxation of carriers predicted by the quantum Boltzmann equation methodology [46], whereas the slow term was consistent with slow relaxation in the insulating phase VO2 [47]. These results indicate that a pump laser can control the interband harmonics over a wide energy range in VO2 on an ultrafast timescale.

Additional details of the time-resolved normalized 5th-order harmonic intensity for various pump powers are shown in Fig. 5(a). It was observed that the harmonic intensity decreased as the pump power increased at any positive time delay. Furthermore, it was noted that the harmonic was completely suppressed within 100 fs after pumping when the pump power exceeded a threshold, corresponding to a modulation depth [modulation depth=1−Imin(norm.)] close to 100%, as shown in Fig. 5(b).

In order to achieve a deeper understanding of the role of the photo-carrier in such robust all-optical control, we employed a quantitative analysis of tr-HHG signals across various pump powers. Equation (1) effectively fitted all tr-HHG signals in Fig. 5(b). The fitting parameters Afast, τfast, Aslow, and τslow are summarized in Figs. 6(a)–6(d), which are dependent on pump powers. The amplitudes and lifetimes of the fast and slow processes were observed to be divided into two distinct regimes at approximately 12mJ/cm2. The lifetimes of the fast and slow processes in the weaker pumps showed a slight correlation with the pump power. However, the strong pump had a significant impact on the lifetimes of both processes. In particular, the slow process exhibited greater sensitivity and demonstrated a ten-fold increase in lifetime compared to weaker pumps, as shown in Fig. 6(c). Regarding the amplitudes representing the weights of the corresponding dynamics, it was observed that both the fast and slow terms were uniformly proportional to weak pumps. When a strong pump was employed, the fast process approached saturation [Fig. 6(b)], while the slow process underwent an additional up-warping-like increase [Fig. 6(d)]. These findings suggest that the photo-carrier controls HHG via distinct processes, with a power threshold of 12mJ/cm2. We have identified that the photo-induced IMT drives tr-HHG at high pump powers based on the transmission spectrum. Figure 6(e) shows the MIR transmittance at 3.5 μm (∼0.35eV) for the VO2 film at various pump powers with a time delay of 1 ps between the pump and probe pulse. The MIR transmittance exhibited a clear decrease at approximately 12mJ/cm2, which is an indicative of IMT in VO2 [40,48]. This threshold closely aligns with the pump power at which the abrupt pump-dependent HHG change occurs and the IMT threshold of VO2 as measured using ultrafast electron diffraction technology [48].

In Figs. 6(f) and 6(g), we have graphically summarized the schematic pictures of the modulation at various pump powers. When a weak pump was applied, tr-HHG exhibited typical semiconductor-like responses, as shown in Fig. 6(f). Incoherent carriers suppress harmonics by scattering-induced dephasing, characterized by attenuation proportional to the harmonic order in Fig. 4(b), whose modulation depth was determined by the initial excitation density and subsequent dynamics [45,49]. In the experiment, incoherent carriers were generated via single-photon excitation and subsequently relaxed through Auger-Meitner recombination (fast relaxation) and electron-phonon interactions (slow relaxation), ultimately reverting to the ground state [50]. These processes shaped the linear scales on the pump observed in Figs. 6(b) and 6(d) and the temporal profile of the harmonics in Fig. 6(b) [19]. For a strong pump [Fig. 6(g)], a large number of photo-carriers in VO2 shield the electron-electron interactions, resulting in IMT [51]. The up-warping of the amplitude of the slow process away from linear scaling and the dramatic expansion of its lifetime shown in Figs. 6(c) and 6(d) are clear indications of IMT.

Finally, we aimed to demonstrate the effectiveness of tr-HHG in materials research by analyzing the phase fractions throughout the IMT in VO2. The tr-HHG in VO2 during the IMT can be expressed as follows: Itot(t)=εIm(t)+(1−ε)Ii(t),(2)where subscripts m and i represent the metallic and insulating phases of VO2, respectively. The metallic phase fraction, denoted by ε, varies between 0 and 100%. The left-hand term in Equation (2) was explicitly measured and is shown in Fig. 5(a). In contrast, the two terms on the right can be determined by employing strong and weak pumps. As shown in Fig. 6, tr-HHG is characterized by the presence of incoherent carriers and their relaxation dynamics under a weak pump. The application of a strong pump leads to a complete transition of VO2 from the insulating to the metallic phase (ε=100%), resulting in tr-HHG exhibiting prolonged suppression without significant recovery over hundreds of picoseconds (≫150ps). By utilizing Eq. (2) to fit the data in Fig. 5, the metallic phase fraction ε can be depicted in Fig. 7 as a function of pump power. The pump-dependent phase fraction arises from the naturally occurring inhomogeneous IMT in VO2 polycrystalline films [52]. These findings are consistent with numerical simulations conducted on polycrystalline NiO2 [53] and indicate that tr-HHG is a robust all-optical technique for directly capturing IMT features.

In summary, we have demonstrated the efficient control of interband harmonics in VO2 films by systematically changing the temperature and photoexciting incoherent carriers. We observed that temperature-induced IMT can reduce interband harmonics by four orders of magnitude. Additionally, we achieved an all-optical modulation to HHG with a modulation depth of nearly 100% (extinction ratio ≥40dB) and 100 fs response speed using photo-carrier doping, making it an ideal candidate for all-optical switches and controllable broadband coherent light sources. Two mechanisms contributed to efficient control: scattering-induced dephasing, occurring upon the excitation of a few electrons, and photo-induced IMT, resulting from significant photo-carrier doping. Finally, we demonstrated that tr-HHG can be used as a powerful ultrafast all-optical probe for IMT by extracting the metallic phase fraction without requiring complex numerical simulations. Furthermore, our experiment revealed linear scaling between the cutoff of the HHG and the laser field, beyond the previous HHG theory in strongly correlated systems. Future theoretical models are expected to provide comprehensive insights into correlated electron dynamics. Our research shows that plentiful photo-carrier dynamics and phase transitions in strongly correlated systems offer attractive knobs for controlling HHG, holding potential for applications in all-optical devices.