1. Introduction

Supercontinuum (SC) generation with ultra-broadband spectra covering the spectral range from near infrared to ultraviolet (UV) has been intensively investigated in different optical media [1], and has stimulated important applications in various fields [2–5]. The SC generation is attributed to the involved nonlinear processes [6–8] such as self-phase modulation (SPM), stimulated Raman scattering, four-wave parametric process and temporal self-steepening. The first SC generation with an ultrabroad spectrum covering the spectral range from infrared to UV was obtained in high pressure gases [9]. Significant extension of spectrum in UV was achieved by the strong interaction between the intense third harmonic and fundamental pulses [10], or self-focusing of few-cycle pulse [11]. For diatomic molecules, the relative orientation between the molecular axis and field polarization can be manipulated through impulsive rotational Raman excitation [12] by ultrashort pump pulse, which leads to periodic revivals of molecular alignment after the excitation of pump pulse. The molecular alignment has been extensively studied for high harmonic generation [13, 14], ultrashort pulse compression [15], and filaments [16–18] with additional spatiotemporal phase modulation [19, 20].

In this paper, we investigate the SC generation by femtosecond filamentation in prealigned diatomic molecules of O₂ and N₂. Due to the different polarizabilities of O₂ and N₂, there is a noticeable discrepancy of the spectral UV extension in these two molecular gases. The UV extension of the SC in the spectrum of the probe pulse is mainly attributed to the additional cross-focusing effect resulted from the molecular alignment revivals, and can be manipulated by tuning the relative delay between the pump and probe pulses. The dependences of the SC generation on the pump intensity for molecular alignment and the gas pressure are studied.

2. Experiment setup

As shown in Fig. 1, our experiments were carried out with a Ti:sapphire amplified laser system (1 kHz, 800 nm, 50 fs). Both the pump and probe pulses with orthogonal polarizations were down-collimated with two separated telescope systems to obtain a large interaction volume, which were re-combined collinearly by using a thin film polarizer (TFP). The delay between the s-polarized pump pulse and the p-polarized probe one was tuned by using a motorizing translation stage in the probe arm. The collinearly recombined pump and probe pulses were then focused by using a lens with a focal length of f=60 cm into a gas cell of 85 cm, which was filled with pure molecules of O₂ or N₂ with a maximum gas pressure of 2 atm. At the exit of the gas cell, the spectral and spatial profiles of the probe pulse were measured simultaneously by using a photomultiplier (PMT) based spectrometer (SpectraPro 750) and charge-coupled device (CCD) after an a-BBO polarizer (extinction ratio ~ 1:10^-6). By using a variable attenuator in the pump arm, the pulse energy of the pump could be adjusted from 0.1 to 0.57 mJ, while the probe one was fixed to 1.5 mJ.

 

Fig. 1. The schematic of experimental setup. BS: beam splitter; VA: variable attenuator; HWP: half-wave plate; TFP: thin film polarizer; CCD: charge coupled device. The inset is the typical spatial profile of the probe pulse when the maximum UV extension of SC in parallel aligned O₂ molecules was obtained.

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3. Results and discussion

Figures 2(a) and 2(c) show the measured molecular alignment revival signal of O₂ and N₂ proportional to (<<cos ² θ _||>>-1/3)² by using the weak field polarization technique [21] to reveal the polarization modulation of the probe pulse, where θ _|| is the angle between the molecular axis and the pump polarization. In order to do that, the polarization of the pre-attenuated probe pulse was firstly rotated by 45° and then steered to cross the pump pulse non-collinearly at a small crossing angle. The field component with polarization perpendicular to the incident probe polarization was selected by an α-BBO polarizer, which was then sent to a photodiode and analyzed by a Lock-in amplifier (SR830, Stanford). Since the pump and probe pulses were set to have orthogonal polarizations in our experiment, we calculated the corresponding molecular alignment revival <<cos ² θ _⊥>>=(1-<<cos ² θ _||>>)/2 along the filed polarization of the probe pulse as shown in Figs. 2(b) and 2(d), where θ _⊥ is the angle between the molecular axis and the probe polarization. The refractive index seen by the probe pulse reads δn _⊥ = (2πρ₀Δα/n₀)(<<cos ² θ _⊥>>-1/3), where ρ ₀ is the initial molecular density, Δα=α _||-α _⊥ is the polarizability difference [22], n ₀ is the linear refractive index. By considering the Gaussian-shaped transverse profile of the pump with more significant molecular alignment in the beam center than its periphery, the probe pulse experiences an additional cross-(de)focusing effect depending on the transient molecular orientation. The alignment-induced additional cross-(de)focusing competes the beam diffraction as δn _⊥ >(k ₀Z₀)^-1 , where k ₀ and Z₀ are respectively the wave-number and Rayleigh range of the probe beam [16]. For a pump intensity of 4.3×10¹³ W/cm² with (<<cos ² θ _⊥>>-1/3)~0.032, the refractive index variation is estimated to be δn _⊥ ~1.2×10^-5 for molecular O₂ with a polarizability difference of Δα=1.2 ų at a gas pressure of 2 atm. For a pump beam waist of ~50 μm, the beam diffraction of the probe pulse is estimated to be (k ₀Z₀)^-1 ~1.2×10^-5 ~δn _⊥, indicating an important role of the alignment-induced cross-(de)focusing effect in our experiments. Meanwhile, an additional time-dependent frequency shift due to the accumulated phase modulation from molecular alignment revivals as δω(t)~-∂δn _⊥ (t)/∂t is introduced to the delayed probe pulse [19, 20]. The succeeding filamentation dynamics as well as the consequent SC generation is therefore dominated by the spatiotemporal phase modulation of the molecular alignment.

 

Fig. 2. (a) and (c) The measured molecular alignment signal of O₂ and N₂ by weak field polarization technique. (b) and (d) The calculated molecular alignment metric <<cos ² θ _⊥>> versus pump-probe delay.

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Figure 3 shows the measured output spectra of the probe pulse as its temporal peak was tuned to various revival times [labeled in Fig. 2(b)] of the prealigned O₂ molecules with a pressure of 2 atm. As shown in Fig. 3(a), the spectrum of the probe pulse (dashed curve) was significantly broadened (from 525 to 900 nm) as compared with the input one (solid curve) when the molecules were randomly orientated (without pump). Here, the SPM, including contributions from time-dependent field intensity (~∂I/∂t) and electron density (~∂ρ/∂t) [23], plays an important role for the observed spectral broadening with a noticeable blue-shift, which is also closely related with the self-steepening and space-time focusing occurring in the filamentation process of the probe pulse. When the pump pulse was turned on, for instance at delay-A as shown in Fig. 3(b), the spectrum was slightly narrowed with weakened SPM process for the additional cross-defocusing effect from the perpendicularly orientated molecules with (<<cos ² θ _⊥>>-1/3)<0. As shown in Fig. 3(c), the narrowest spectrum was observed around delay-B with most significant perpendicular molecular alignment. The output spectrum of the probe pulse was almost the same as the case of randomly orientated molecules when the temporal peak of the probe pulse was tuned to delay-C [Fig. 3(d)], where the molecular alignment degree, <<cos ² θ _⊥>>~1/3, is close to the case without molecular alignment and hence lead to negligible cross-(de)focusing effect. However, as shown in Fig. 3(e) for delay-D, SC with noticeable extension in UV spectral region (cutoff at 370 nm) was observed for additional cross-focusing effect from the parallel molecular alignment revival, which hence enhanced the involved SPM. The final pulse energy of the generated SC was measured to be 1.2 mJ at the end of gas cell with a stable self-cleaned single core beam profile as shown in the inset of Fig. 1. The extension in the UV spectral region of the generated SC decreases rapidly as the probe pulse was tuned away from the optimal parallel revival of the molecular alignment shown in Fig. 3(f) for delay-E as example.

Both spatial and temporal phase modulations by molecular alignment revivals were introduced to the probe pulse to influence its succeeding filamentation dynamics [18] and SC generation. The SC generation with maximum UV extension around the maximum parallel molecular alignment revival indicated that the additional cross-focusing effect from spatial phase modulation played a more important role than the frequency modulation from temporal phase modulation, since the cross-focusing effect reached its maximum value for the maximum parallel revival (around delay-D) where the frequency modulation induced by the temporal phase modulation was close to zero [19, 20]. The frequency modulation proportional to |∂δn _⊥ (t)/∂t | reached its maximum value around the transition time from parallel to perpendicular (or perpendicular to parallel) revivals with negligible spatial cross-(de)focusing effect, where almost no additional extension of SC generation was observed (delay-C) in our experiment. Therefore, the additional cross-focusing effect from the parallel revival of the molecular alignment enhanced SPM as well as self-steepening and space-time focusing effects to broaden the spectrum of the probe pulse, resulting in considerable UV extension of the generated SC observed in our experiments.

 

Fig. 3. The spectra of the probe pulse at the end of O₂ cell for (a) randomly orientated molecules (dashed curve) and (b)-(f) when it is tuned to various molecular alignment revivals as labeled in Fig. 2 (b). The dashed and solid curves stand for the output spectra of the probe pulse when the molecules are randomly orientated and prealigned, respectively. The solid curve in (a) is the input spectrum of the probe pulse.

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The SC generation and extension by additional cross-focusing from the maximum parallel revival of molecular alignment (delay-D) was further proved by tuning the intensity of the pump pulse for molecular alignment as shown in Fig. 4(a), which directly changed the molecular alignment degree and hence the cross-focusing effect. The gas pressure of oxygen was set to be 2 atm. The extension of the spectrum in the UV region decreased gradually as the decreasing pump energy from 0.57 to 0.4 mJ, which corresponds to a variation of the pump intensity from 4.3×10¹³ to 3.0×10¹³ W/cm² around the geometric focus and molecular alignment degree |<<cos ² θ _⊥>>-1/3| from 0.032 to 0.022. Almost no additional spectral extension at short wavelengths was observed at pump intensities smaller than 2.6×10¹³ W/cm² for the negligible influence from molecular alignment.

 

Fig. 4. (a) The evolution of the probe pulse spectra at the end of O₂ cell with different pump intensities for molecular alignment. (b) The UV extension of SC of the probe pulse in prealigned (labeled as a) and randomly orientated (labeled as r) O₂ molecules with different gas pressures.

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Besides the degree of molecular alignment, the additional cross-focusing effect also closely depends on the number density of the involved molecules. As shown in Fig. 4(b), for parallel molecular alignment revival at delay-D, the extension of the generated SC at short wavelengths decreased gradually as the gas pressure changed from 2.0 to 1.6 atm, with a fixed pump energy of 0.57 mJ and molecular alignment degree of |<<cos ² θ _⊥>>-1/3|~0.032. However, when the molecular alignment was turned off without pump pulses, the output spectra of the probe pulses were almost unchanged for the decrease of the gas pressure from 2.0 to 1.6 atm, indicating a negligible influence of the variation of the material nonlinearities (estimated to be 20% by considering a linear dependence on the number density) on the spectral broadening of the probe pulse in our experiments. Obviously, molecular alignment with additional cross-focusing effect from parallel revival played a significant role for the observed SC extension at short wavelengths as a result of the consequently enhanced SPM and self-steepening effect during the succeeding filamentation.

For various diatomic molecules with different polarizability differences and nonlinearities, the influence of the molecular alignment revivals on the SC generation and extension is different. For example, in comparison with the above studied O₂ molecules with a polarizability difference of Δα=1.2 ų and nonlinear refractive index of n₂=10.2 ×10^-19 cm²/W at 2 atm, N₂ molecules shows a polarizability difference of Δα=1.0 ų and nonlinear refractive index of n₂=4.6×10^-19 cm²/W at 2 atm [24, 25]. The smaller polarizability difference of N₂ [Fig. 2(c)] as compared with O₂ [Fig. 2(a)] could be seen clearly from the relative magnitudes of the measured molecular alignment signals for the same experimental conditions. Therefore, aligned N₂ molecules are expected to produce weaker effects on the extension of the generated SC than prealigned O₂ molecules. Figure 5 shows the spectral evolution of the probe pulse when its temporal peak was tuned to various revivals of the molecular alignment of N₂ [labeled as A-E in Fig. 2(d)]. Similar to O₂ molecules as shown in Fig. 3, the output spectra of the probe pulse were narrowed for the perpendicular molecular alignment revival of N₂ molecules [Figs. 5(b) and 5(c)], and SC generations with noticeable extension in the UV region was observed for the parallel molecular alignment revival [Fig. 5(e)]. However, the UV extension of the generated SC for the maximum parallel revival around delay-D with aligned N₂ molecules was not as much as that of the aligned O₂ molecules, which was originated from the relative smaller polarizability difference (Δα) of N₂.

 

Fig. 5. The spectra of the probe pulse at the end of N₂ cell with same presentation as Fig. 3.

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The relatively weaker influence of aligned N₂ molecules on the SC generation and extension in the UV spectral region were also confirmed by tuning the pump intensity and gas pressure around the maximum parallel revival, which are shown in Fig. 6. The changes of the output spectra versus the gas pressure and pump intensity were similar for both O₂ and N₂ molecules as considered, while the variation of the spectral range was smaller for N₂ (Fig. 6) than O₂ (Fig. 4). For N₂ molecules at 2 atm, as shown in Fig. 6(a), the spectral UV extension was vanished when the pump intensity is around 0.6×10¹³ W/cm², which is estimated to be 2.6×10¹³ W/cm² for molecular O₂. It indicates a more closer dependence of SC generation and extension on the alignment degree of O₂, which was consistent with its larger value of polarizability difference. For the relative small nonlinear refractive index of N₂ molecules, as shown in Fig. 6(b), the spectra of the probe pulse narrowed gradually as the decreasing of the gas pressure for the both cases with and without molecular alignment, which differed from O₂ molecules as shown in Fig. 4 (b).

 

Fig. 6. (a) The evolution of the probe pulse spectra at the end of N₂ cell with different pump intensities for molecular alignment. (b) The UV extension of SC of the probe pulse in prealigned (labeled as a) and randomly orientated (labeled as r) N₂ molecules with different gas pressures.

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4. Conclusion

In summary, we have studied the UV extension of SC generation by filaments in prealigned diatomic molecules of O₂ and N₂ with various pump intensities, gas pressures and molecular alignment revivals. The experimental results showed that the additional cross-focusing effects resulted from the spatial modulation of the refractive index by the parallel aligned molecules dominated the UV extension of SC, which closely depended on the polarizability difference (Δα) and nonlinear refractive index (n ₂) of the involved molecules. It therefore could be used as a flexible method to manipulate the UV extension of SC generation in molecular gases.