1. Introduction

High-order harmonic generation (HHG) in atoms and molecules has been intensively explored in the past decade. Many new physical phenomena in the high-field interaction are discovered, and a robust ultrafast coherent radiation sources in the XUV region has been developed [1–3]. Moreover, HHG provides an approach to probe the electronic and nuclear dynamics of atoms and molecules with the unprecedentedly fast temporal resolution, and also offers an insight into the transient molecular structure [4–8] in sub-nanometer scale, since the harmonic emission depends on the molecular structure. For example, Itatani et al. [9] proposed a tomographic reconstruction of the highest occupied molecular orbit (HOMO) of the nitrogen molecule. Liu and Wei [10,11] demonstrated that the two-center interference in HHG from aligned CO₂ molecules could be controlled by fine changing the driving laser intensity.

One of the important differences between the molecular and the atomic HHG is that the molecular HHG is further influenced by the nuclear vibration [12–16]. Lein [14] shows that HHG is sensitive to the laser-induced vibrational motion according to the numerical solution of the time-dependent Schrödinger equation for vibrating hydrogen molecules, which represents that the more intense harmonics are generated in the heavier isotopes and the differences become more obvious with the higher harmonic frequency. The calculations performed by Bandrauk et al. [15] also show that the harmonic yield from the fixed nuclear is more intense than from the moving nuclear in H₂ and D₂ molecules. Baker et al. [16] also propose a technique that uses the harmonic yield to probe the nuclear dynamics and the structural rearrangement in hydrogen and methane molecules with subfemtosecond time resolution. Recently, with the development of high-energy and broadband-tunable infrared parametric source for HHG [17–20], the driving laser wavelength can be tuned to the infrared absorption of molecule near the vibrational energy levels, and it is possible to investigate and even to control the proton dynamics in the molecular HHG by tuning the infrared wavelength of the driving laser.

In this paper, we experimentally investigate the wavelength effects on the molecular HHG (CH₄) with nuclear vibration and on the atomic HHG (Xe) without nuclear vibration driven by a tunable infrared parametric source. We tune the wavelength of the driving laser to approach the vibration absorption of CH₄ molecules (1670nm), and unambiguously observe that the yield of the molecular HHG is much sensitive to the infrared wavelength while the yield of the atomic HHG is not. The results can be attributed to the nuclear resonance between the driving infrared laser and the vibrational energy levels, which can excite the higher molecular vibration state. The nuclear resonance is sensitive to the infrared wavelength and the molecular HHG is sensitive to the nuclear vibration, which lead to that the molecular HHG is sensitive to the infrared wavelength. The results indicate that the infrared wavelength can be used to control the proton vibration in the molecular HHG.

2. Experiment and discussion

2.1 Experimental setup

A home-build infrared optical parametric amplifier (OPA) is used in this work, which is pumped by a commercial Ti:sapphire based chirped pulse amplification laser (Coherent Inc.), and the detail of the OPA is described in the references [19,20]. The OPA system can produce ~45fs/1kHz output pulses. The output pulses are tunable from 1.5 µm to 1.9 µm, and the maximum output pulse energy is >1.7mJ at 1.6 μm. The infrared output pulses are focused in a gas cell (the focal length 150mm, and the length of gas cell ~2.5mm) located in a high-vacuum interaction chamber. The output power of the OPA keeps ~1.2mJ for the deferent working wavelengths and it can be controlled by the pump energy of the 800nm laser. The size of the focal spot keeps ~150µm and it can be controlled by the size of the iris which lies in the output beam from the OPA. The Raleigh length is ~5mm, and the average intensity is estimated to be ~1.5 × 10¹⁴ W/cm² in the interaction region within the gas. The stagnation pressure of the gas is around 100 torr. The generated high-order harmonics are detected by a home-made flat-field grating spectrometer equipped with a soft-x-ray charge-coupled device camera (CCD, Princeton Instruments, SX 400), and Al foil with 500nm thickness is used in the spectrometer to stop the driving laser. The distance from the gas cell to the XUV grating is ~1.0m, and the distance from the XUV grating to the CCD plane is ~0.24m. The entire spectrum is imaged to the CCD array and averaged over multiple laser pulses, and it is not necessary to scan the grating or the position of the CCD. The experimental setup is shown in Fig. 1 .

 

Fig. 1 The experimental setup. OPA: optical parametric amplifier. The infrared output pulses from OPA are focused into a gas cell located in a high-vacuum interaction chamber. The generated high-order harmonics are detected by a home-made flat-field grating spectrometer equipped with a soft-x-ray charge-coupled device camera (CCD).

Download Full Size | PDF

2.2 Experimental results

We choose CH₄ molecules and Xe atoms as the investigative objects due to three reasons. First, 1670nm is one of the infrared absorption peaks due to the vibration absorption of C-H. Second, the proton (the lightest nuclear) can be easily induced by the driving laser, and the carbon (the heavy parent body) can be considered to be static in the HHG process. Third, their ionization potentials are similar (12.7eV for CH₄, 12.1eV for Xe), and it is reasonable to neglect the differences in phase-matching conditions for the harmonic generation in the two cases [16]. Additionally, the molecular HHG has been proved to be sensitive to the laser-induced nuclear vibration [14–16] (the less intense harmonics is generated in the faster moving nuclear), and the atoms without nuclear vibration are adopted contrastively as the reference of the harmonic intensity from “static” nuclear.

First, we measure the harmonic spectra driven by the 800nm laser beyond the molecular vibration absorption. The harmonic spectra from CH₄ molecules and Xe atoms are measured at the equal gas density and at the same laser condition shown in Fig. 2(a) . Contrastively, we also measure the harmonic spectra driven by the infrared parametric source at the 1670nm working wavelength within the vibration absorption shown in Fig. 2(b). We unambiguously observe that the integrated yield of the molecular HHG is much lower 20 times than the yield of the atomic HHG at the 1670nm working wavelength in Fig. 2 (b), while their harmonic yields are similar at the 800nm working wavelength in Fig. 2 (a).

 

Fig. 2 Measured angle-integrated spectra from CH₄ molecules and Xe atoms at equal gas density, driven by the same laser condition with the working wavelengths of (a) 800nm and (b) 1670nm.

Download Full Size | PDF

In order to ensure that the harmonic yields from both gases are measured at the optimal condition, we also measure the harmonic yields at the different focus locations, and find that the optimal harmonic yields from both gases are at the same focus location due to their similar ionization potentials. By the way, the HHG of Xe atoms and CH₄ molecules are also measured with Zr filter (the Al filter transmission with 500nm thickness is about 18 - 72eV, while the Zr filter transmission with 500nm thickness is about 70 - 200eV), and all the harmonic signals are too weak to identify the existence. Therefore, the main plateau of CH₄ and Xe should lie in the transmission range of Al filter, and the cut-off energies of them should be near the absorption edge of Al filter, when the pump wavelength is near 1600nm.

The differences between the molecular HHG and the atomic HHG, beyond or within the wavelength of the vibration absorption, can be attributed to the nuclear resonance between the driving infrared laser and the vibrational energy levels. The driving laser with the resonant working wavelength for the molecule can excite the higher molecular vibration state even dissociation, and leads to that the less intense harmonics are generated in the faster moving nuclear.

Using the wavelength effect on the molecular vibrational dynamics, which can be identified by the harmonic yield, we think that the proton vibration can be controlled by tuning the infrared wavelength of the driving laser and the atomic HHG can be used as the reference of the harmonic intensity from “static” nuclear. The harmonic yields can be compared through the spectrum peak and the spectrum integration. In Fig. 3 (a), the harmonic yields from CH₄ molecules are weak and different (the spectrum peaks are: 7.0 for 1550nm, 1.9 for 1670nm, 2.1 for 1800nm, and 1.0 for the background; the spectrum integrations are: 3100 for 1550nm, 1800 for 1670nm, 1900 for 1800nm, and 1000 for the background). In Fig. 3 (b), the harmonic yields from Xe atoms are strong and similar (the spectrum peaks are: 104 for 1550nm, 100 for 1670nm, 101 for 1800nm, and 1.0 for the background; the spectrum integrations are: 49500 for 1550nm, 50000 for 1670nm, 49000 for 1800nm, and 1000 for the background) in our observing window 18 - 42nm. Therefore, the harmonic yields from CH₄ molecules are weaker and more sensitive than that from Xe atoms. For CH₄ molecules shown in Fig. 3 (a), the harmonic yield decreases monotonously and rapidly when the pump wavelength is scanned from 800nm to 1670nm. When the pump wavelength is near or above 1670nm, the harmonic yield is too weak to identify the cut-off energy and the spectrum peak (the magnitudes of the harmonic signal and the background are almost similar). However, for Xe atoms shown in Fig. 3 (b), all the harmonic yields are strong and the wavelength effects on the HHG are normal and expected. They are shown that the yield of the molecular HHG is sensitive to the infrared wavelength, while the yield of the atomic HHG is not sensitive to the wavelength at the same laser condition. These phenomena can be attributed to the laser-induced nuclear resonance. The nuclear resonance is sensitive to the infrared wavelength and the molecular HHG is sensitive to the nuclear vibration, which lead to that the molecular HHG is sensitive to the infrared wavelength. The results indicate that the infrared laser can excite the higher molecular vibration state and can be used to control the proton vibration in the molecular HHG.

 

Fig. 3 Measured angle-integrated spectra at the different infrared wavelengths of the driving laser from (a) CH₄ molecules and (b) Xe atoms, respectively.

Download Full Size | PDF

2.3 Discussion

Considering the complexity of CH₄ molecule, a rough classical one dimension oscillator model is introduced to try to interpret the wavelength effect on the nuclear vibration. Compared with the light proton, the heavy parent body can be considered to be “static”, so the laser-induced proton vibration can be written as:

 

Fig. 4 Calculated proton motions without considering the molecular potential, (a) the internuclear separation R/R_e and (b) the additional kinetic energy △E/E₀), are compared between two different driving laser wavelengths. The thin lines are the electric field in one optical cycle. (c) Calculated proton vibrations with Morse potential at the different driving laser wavelengths, the thin dashed lines are the proton vibrations, and the thick dotted solid lines are their amplitudes (stars for 800nm, triangles for 1550nm, circles for 1670nm, and squares for 1800nm).

Download Full Size | PDF

On the other hand, the molecular potential should also pay a key role in such vibration dynamics, because the nuclear resonance between the driving infrared laser and the vibrational energy levels can excite the higher molecular vibration state. The accurate potential of CH₄ molecules is complex and unprepared, and Morse potential $V(R)=D_e[e^{-2\alpha (R-R_e)}-2e^{-\alpha (R-R_e)}]$ [21] is adopted as the approximate potential for qualitative explanation in our calculation, where D_e is the dissociation energy, and α is the Morse coefficient defined as $\sqrt{\left(\mu {\omega }_e^2\right)/2D_e}$, in which μ is the reduced nuclear mass and ω_e is the resonant frequency (1670nm for CH₄ in our discussion). So the driving force of the potential can be calculated as:

The proton vibration with Morse potential at the different wavelengths of the driving laser can be introduced roughly by numerically solving the Eq. (1). The proton vibrations and their amplitudes driven by the different infrared wavelengths are represented by the dashed lines and the dotted solid lines in Fig. 4(c), respectively. From the calculational results, we can see that the proton vibration is sensitive to the infrared wavelength of the driving laser. For the proton driven by 800nm laser (black solid line), its vibration is much weaker than that driven by the infrared laser near vibration absorption, because the photon energy of 800nm is very far away from the molecular vibrational energy. Therefore, the harmonic yield of CH₄ molecules is similar to the harmonic yield of Xe atoms, and this is observed in our experiment shown in Fig. 2 (a). For the proton driven by 1670nm laser (green dashed line), its amplitude is the fastest enlarged due to the resonance between the photon energy of 1670nm and one of the molecular vibrational energies. For the proton driven by 1800nm laser (red dashed line), its amplitude is gradually larger than others due to that the proton acceleration in the laser field of 1800nm is longer than others. According to the calculation of the nuclear motion effect on the molecular high-order harmonics [14–16], one knows that the harmonic yield from “static” nuclear is more intense than the harmonic yield from moving nuclear, and the yield from the fast motion (leads to longer internuclear separation) is less intense than the yield from the low motion. Actually, we have observed these phenomena in our experiment shown in Fig. 2 and Fig. 3. For CH₄ molecules, there are both quantum yield effect and resonant effect which are both dependent on the pump wavelength. For the resonant effect, the harmonic yield is lower, when the pump wavelength is more close to 1670nm. For the quantum yield effect, the harmonic yield is lower when the pump wavelength is longer. Therefore, the harmonic yield decreases monotonously and rapidly when the pump wavelength is scanned from 800nm to 1670nm, due to that the two effects are consistent. When the pump wavelength is larger than 1670nm, the harmonic yield will be weaker and complex, due to that the two effects are opposite. In our experimental condition, the harmonic yield is too weak to identify the cut-off energy and the spectrum peak when the pump wavelength is larger than 1670nm. Therefore, the harmonic yield seems weakly depends on the pump wavelength when the pump wavelength is larger than 1670nm. For Xe atoms, the wavelength effect on the harmonic yield is normal and expected, and the small change in the case of Xe can be explained by the theoretical result [22–24]. Therefore, the differences between CH₄ and Xe are obvious when the pump wavelength is near or above 1670nm, and the results can be attributed to the nuclear motion induced by the driving laser field.

In this experiment, we mainly compare the yield of CH₄ with the yield of Xe at one certain driver wavelength, because they are at the same laser condition. The cut-off wavelength for the molecular HHG should be similar to the atomic HHG, though the yield of the molecular HHG near or above 1670nm is too weak to identify the cut-off wavelength clearly. By the way, our simple theoretical model is just a qualitative explanation of these phenomena, and a more comprehensive theory of HHG in molecules that includes the nuclear wavepacket and the molecular potential is necessary for fully account for the underlying physics.

3. Summary

In conclusion, we experimentally investigate the wavelength effect on the harmonic yields of CH₄ molecules and Xe atoms driven by an infrared parametric source, and observe that the yield of the molecular HHG is much sensitive to the infrared wavelength while the yield of the atomic HHG is not. The results can be attributed to the nuclear resonance between the driving infrared laser and the vibrational energy levels, which can excite the higher molecular vibration state. Because the nuclear resonance is sensitive to the infrared driving laser wavelength, it becomes possible to control the proton vibration in the molecular HHG by tuning the infrared wavelength of the driving laser.