Backward nitrogen lasing actions induced by femtosecond laser filamentation: influence of duration of gain

The pump-probe experimental setup for investigating the gain dynamics of nitrogen lasers generated in a gas mixture of N₂/Ar is schematically illustrated in figure 1, which is similar to that used in our previous works [17, 18]. Briefly, femtosecond laser pulses (1 kHz, 800 nm, ∼40 fs) from a commercial Ti: sapphire laser system (Legend Elite Cryo PA, Coherent, Inc.) were divided into two paths with an 80/20 beam splitter (BS). One beam with a pulse energy of ∼10.5 mJ served as the pump and the other with a pulse energy of ∼2 mJ was used to produce wavelength-tunable seed pulses. In our case, the pulse with energy of 2 mJ was first reduced to ∼3 mm in diameter by a telescope system and its spectrum was broadened using a piece of 20 mm-long BK7 glass. Then, the 800 nm pulse was frequency doubled using a 2 mm-thickness ${\beta }-{\rm barium}$ borate crystal (BBO), which acted as the seed pulse to generate seed-amplification-based nitrogen laser emissions. The center wavelength of seed pulse can be continuously tuned in a broad range around 357 nm by rotating the angle of BBO crystal. Both the pump and seed pulses were linearly polarized and their polarization directions were perpendicular to each other. The time delay between the pump and seed pulse was controlled by a motorized linear translation stage with a temporal resolution of ∼16.7 fs. After being combined by a dichroic mirror (with high reflectivity at ∼800 nm and high transmission at ∼400 nm), the pump and seed pulses were collinearly focused into a gas chamber filled with N₂/Ar mixture by a 150 cm focal-length lens. After interaction with the gas mixture in the chamber, the exiting pulses were first collimated by a 150 cm focal-length lens and then passed through two dichroic mirrors to remove the intense 800 nm pulses. Furthermore, to remove the strong supercontinuum white light generated during the propagation of the intense pump pulses in the gas chamber, a Glan–Taylor prism was used to completely separate the pump beam and 357 nm N₂ laser because of their different polarization directions. Lastly, the forward spectra of the N₂ laser were recorded using a 1200 grooves/mm grating spectrometer (Andor Shamrock 303i) which has a spectral resolution of ∼0.06 nm.

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Figure 2(a) shows a typical forward 357 nm (${C}^{3}{\Pi }_{u}(\nu =0)\to {B}^{3}{\Pi }_{g}(\nu \prime =1)$ of N₂) laser spectrum (blue solid curve) generated by focusing both the pump and seed pulses into the gas chamber which was filled with a mixture of 300 mbar N₂ gas and 900 mbar Ar gas. For comparison, both the spectra of the injected seed pulse and of the ASE laser at 357 nm wavelength produced by only the pump pulses are plotted with the red dashed and black dash-dotted curves, respectively. The inset in figure 2(a) clearly indicates that the 357 nm N₂ laser generated with the seed pulse has a nearly perfect linear polarization. Similar to the previously reported seed-amplification-based nitrogen lasers, the polarization direction was again measured to be parallel to that of the seed pulses [14]. Meanwhile, we also recorded the backward 357 nm ASE laser spectrum generated with only the pump pulses, as shown in figure 2(b). Here, we choose the 357 nm nitrogen laser for this investigation because its signal is significantly stronger than that of the 337 nm (${C}^{3}{\Pi }_{u}(\nu =0)\to {B}^{3}{\Pi }_{g}(\nu \text{'}=0)$ of N₂) nitrogen laser, although both lasing lines have been observed in our experiment. On the other hand, due to the different experimental conditions, the 337 nm nitrogen laser generated in the mixture of N₂/Ar is stronger than the 357 nm nitrogen laser when a mid-infrared pump laser is used [6].

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In our experiments, we found that the N₂ laser signal sensitively depends on the gas pressures. In particular, under the conditions of our pump laser and focal system, the strongest laser signal was observed at the gas pressures of 300 and 900 mbar of N₂ and Ar gases, respectively. Figure 3(a) shows the dependences of the forward (blue squares curve) and backward (red triangles curve) 357 nm laser signals on the Ar gas pressure. The reason that we mainly investigated the laser signal as a function of Ar gas pressure is that the concentration of Ar gas can strongly influence the duration of gain in the N₂ molecules as a consequence of the excitation mechanism of N₂ laser [19]. This feature has also been confirmed by our observations. It can be seen that the lasing action is initiated when the Ar gas pressure is increased to ∼550 mbar. Then, the laser signal first grows rapidly with the gas pressure until the Ar gas pressure reaches ∼900 mbar. Afterwards, the laser signal drops with the gas pressure and eventually vanishes at an Ar gas pressure of ∼1600 mbar. We speculate that the quenching of the laser signal should be due to depletion of the excited N₂ molecules through a collisional quenching reaction ${N}_{2}({C}^{3}{\Pi }_{u})+Ar\to {N}_{2}({B}^{3}{\Pi }_{g})+Ar$ which becomes more severe at the Ar gas pressures higher than ∼900 mbar [20].

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Figure 3(b) shows the normalized intensity of 357 nm N₂ laser as a function of the time delay between the pump and seed pulses measured at a fixed gas pressure of 300 mbar of N₂ gas and varied pressures of 600, 900 and 1200 mbar of Ar gas. At zero time delay, the relative intensities of the N₂ laser measured under these gas conditions can be evaluated from the data labeled with A, B, and C in figure 3(a). Here, the zero time delay between the pump and seed pulses was determined by observing the beginning of plasma defocusing of the seed pulses induced by the pump pulses, and the positive delay means that the seed pulse is behind the pump pulse. It can be seen that at all the gas pressures of Ar, lasing actions (i.e., amplification of the seed pulses) occurred at time delay of ∼3 ns between the pump and seed pulses. We roughly evaluated the duration of gains (full width at half maximum, FWHM) at the Ar gas pressures of 600 mbar, 900 mbar, and 1200 mbar with the least-square fitting curves as shown in figure 3(b), which are ∼3 ns, ∼3.4 ns and ∼2.3 ns, respectively. The longest duration of gain is observed at the Ar gas pressure of 900 mbar, which is consistent with the strongest nitrogen laser signal generated under this condition.

It should be noted that the optimal gas mixture (300 mbar N₂ and 900 mbar Ar) for generating the strongest lasing signal presented in figure 3(a) is different from that (1 bar N₂ and 5 bar Ar) using 3.9 μm mid-infrared pumping [6]. One possibility leading to the difference is that according to the calculation in [16], the electron energy will be higher and distributed in a broader range with the 3.9 μm pump laser, which can lead to more efficient collisional excitation. Also, we speculate that at the longer wavelength, higher gas pressure can be used due to the reduced ionization effect (i.e., the same electron kinetic energy can be achieved at much lower laser intensity for the long wavelength driver laser, which reduces photoionization rate), which further leads to the enhancement of lasing.

The results in figure 3(b) indicate that pumping N₂ molecules with excited metastable Ar atoms can lead to a much longer duration of gain than that achievable with the electron collisional excitation in pure N₂ gas, even intense, ultrashort laser pulses are used in both cases [14, 16, 19]. The difference in turn leads to essentially different laser behaviors, i.e., the former scheme has successfully generated strong ASE N₂ laser in both forward and backward directions, whereas with the latter scheme only forward laser signals can be generated with a decent pulse energy. To quantitatively reveal the role of the duration of gain, we design the following experiment to generate nitrogen lasers with variable duration of gain in the nitrogen molecules, and investigate how the backward laser behavior relies on it.

The experimental setup is schematically shown in figure 4, in which the same femtosecond laser system was employed. Again, the femtosecond laser beam was split into two to generate a dual-pulse source. The first pulse was used as the pump pulse to generate the population inversion in N₂ molecules which can enable generation of the backward ASE laser. The time-delayed second pulse was used to quench the lasing action, which is referred to as the quenching pulse in the following. The center wavelength of both pulses was ∼800 nm. The energies of pump and quenching pulses were measured to be ∼4.2 mJ and ∼0.35 mJ before the focal lens, respectively. The peak intensity of quenching pulses is significantly lower than that of the pump pulses because for the N₂ molecules at excited states, their ionization potentials are much lower than that of the N₂ molecules at the ground state. Both the pump and quenching pulses were linearly polarized and their polarization directions were parallel to each other.

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The time delay between the two pulses was controlled using a motorized linear translation stage. After combined by a beam splitter with 70% reflectivity and 30% transmission at 800 nm, the pump and quenching pulses were collinearly focused by a 150 cm focal-length lens into the chamber filled with the gas mixture of N₂/Ar. It should be mentioned that by using such a beam combining scheme, energy loss of light is inevitable. However, since our pump pulses were sufficiently energetic, both forward and backward laser signals were generated using the illustrated dual-pulse pump scheme. We inserted a dichroic mirror (with high reflectivity at ∼400 nm and high transmission at ∼800 nm) in the probe beam path to extract the backward N₂ laser emissions. The same grating-based spectrometer was used to record the spectra of the backward laser at 357 nm wavelength.

Figure 5(a) shows the 357 nm N₂ laser spectra measured in the backward direction with (red dash-dotted curve) and without (blue solid curve) the second pump pulse. In this specific case, the time delay between the pump and quenching pulses was set at ∼2.3 ns when a complete quenching of the backward laser was observed. The gas pressures of N₂ and Ar were 300 mbar and 900 mbar, respectively.

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In figure 5(b), we present the measured intensity of the backward N₂ laser signal as a function of the time delay between the pump and quenching pulses (red dashed curve). For comparison, the forward gain dynamics in the N₂ molecules measured under the same pump conditions was indicated by the blue dotted curve. The two curves together reveal the crucial role played by the duration of gain on the generation of backward N₂ ASE laser. From the blue dotted curve showing the gain dynamics, one can see that the population inversion was established ∼3.2 ns after the pump pulse. Besides, it was found in the red dashed curve that when the time delay between pump and quenching pulses reached ∼4 ns, the backward laser signal started to appear. This observation implies that when the quenching pulse arrives earlier (i.e., in a time window between ∼3.2 ns and ∼4 ns behind the pump pulse), the population inversion will be destroyed before the ASE could be effectively established in the population inverted N₂ molecules. We determine that the difference between the above two times, which is ∼0.8 ns, indicates the minimum duration of gain required for generating the backward ASE nitrogen laser.

To further confirm the above physical understanding, we performed the same measurement at a different gas pressure of N₂ (500 mbar), as shown in figure 5(c). We found that under the gas condition, the population inversion was established ∼2.1 ns after the arrival of pump pulse and the backward laser signal started to appear when the time delay between pump and quenching pulses reached ∼2.9 ns. Therefore, the minimum duration of gain required to generate the backward ASE nitrogen laser under this condition is estimated to be ∼0.8 ns, which is very close to the result indicated in figure 5(b). Moreover, both figures 5(b) and (c) show that for sufficiently long time delays between the pump and quenching pulses, the backward laser signals grow with the increasing time delay, and finally become saturated. The saturation is simply due to the fact that when the quenching pulse arrives too late, i.e., after the generation of backward ASE N₂ laser has been completed, the quenching pulse will no longer be able to disturb the backward ASE signal.

It should be noted that the duration of gains measured in pure N₂ gas excited by ultrafast laser pulses are typically one order of magnitude shorter (i.e., a few tens of picoseconds), which are sufficient for generating forward ASE lasers but insufficient for generating an intense backward ASE laser [11, 14]. Our result suggests that for generating backward ASE nitrogen laser from N₂ molecules, the minimum duration of gain should be on a timescale of ∼1 ns.