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Nitrogen molecular ions (N2+) in air plasma pumped by femtosecond laser pulses give rise to superradiant emission at 391.4 nm in the presence of an external seed pulse at proper wavelength. Due to the transient alignment of the nitrogen molecular ions, the superradiance signal presents a strong modulation as a function of the temporal delay between the pump and the seed pulses. Through Fourier transformation with high frequency resolution, we distinguished the contribution of the finely separated rotation levels of the upper and lower states. It was found that the population density of certain rotational levels in the upper state is higher than that in the lower one, indicating that population inversion of the rotation levels of the two involved states is a key enabling factor for this superradiant emission.
© 2017 Optical Society of America
1. Introduction
Air plasma pumped by intense ultrafast laser pulses emits coherent radiations in both forward and backward directions. These coherent radiation sources based on the main constitutions of ambient air, coined as “air laser”, have attracted great interest in recent years [1–13]. Since the air plasma created by intense laser pulses can be produced tens of meters, even kilometers away from the pump laser, the “air laser” holds unique potential to emit a coherent radiation from the sky toward the ground. This backward lasing radiation may be employed to probe the pollutants or hazards trace gas in atmosphere, which is expected to bring about tremendous improvement of detection sensitivity due to its coherent detection nature [5,11]. Among different schemes for “air laser”, the underlying physical mechanisms for the emission of atomic oxygen [2] and neutral nitrogen molecules [9–11,13] have been well understood, while the coherent radiation from nitrogen molecular ions N2+ remains mysterious. This emission manifests as a coherent forward pulse and it occurs mainly at 391.4 and 428.2 nm [3], corresponding to the transition B2Σu+(ν' = 0) → X2Σg+(ν = 0,1) of the singly ionized nitrogen molecules, where ν' and ν are the vibration quantum number of the upper and lower states. Recently, it is revealed that the coherent emission at 391 nm generated by 800 nm femtosecond laser is of the nature of superradiance, a kind of collective spontaneous emission [14,15].
Up to now, several different mechanisms have been proposed for this phenomenon. D. Kartashov et al. noticed the slight different revival period of the B2Σu+ and X2Σg+ state of nitrogen molecular ions, and proposed laser without inversion occurs during transient temporal windows [16]. In another two independent works, it was suggested that steady state population inversion between the B2Σu+ and X2Σg+ states is achieved through laser-induced population transfer among different electronic states of nitrogen molecular ions in the case of 800-nm pump laser [17,18]. Based on the common assumption that the optical gain can be achieved only under the condition of population inversion, Wang et al. concluded that the net population inversion is much smaller than the absolute population of the upper state by simultaneously measuring the fluorescence emission spectra and the transmission spectra [19]. Because population inversion is not an absolute prerequisite for optical gain, it is still in hot debate whether the population inversion between N2+ (B2Σu+) and N2+ (X2Σg+) is achieved for N2+ lasing. Very recently, Azarm and associates compared the high-resolution spectrum of the sideway fluorescence and the forward lasing emission at 428 nm obtained in ambient air pumped by 1.5 μm pulses [20]. It was found that the rotation level of the forward lasing is shift to higher quantum number J, compared to the sideway fluorescence. Through best fit of the forward lasing spectrum, it was proposed that population inversion of certain rotation levels of the upper and lower states can be responsible for this superradiant emission, while total population inversion of the two electronic states may be not necessary. Therefore, it is highly desired to evaluate experimentally the relative population distribution in the quantum rotation levels of the two electronic states.
In this work, we employed a pump-seed experimental configuration with sufficient temporal delay between the two pulses. By taking Fourier transformation of the strongly modulated superradiant emission owning to transient alignment of the N2+ for varying temporal delay, the rotational levels of the upper (B2Σu+) and the lower (X2Σg+) energy state are individually identified, thanks to the high frequency resolution in our experiments. The population density in the upper level (B2Σu+) was found to be higher than that of the lower (X2Σg+) level for certain quantum rotational levels. This manifests as a direct evidence that population inversion in the rotation levels of the upper and lower lasing states is achieved for the superradiant emission of N2+.
2. Experimental setup
The schematic experimental setup is presented in Fig. 1. Femtosecond laser pulses at 800 nm wavelength from a commercial Ti: Sapphire laser system (30 fs, 1 kHz, 3.6 mJ, Elite DUO, Coherent Ltd) are split into two beams by a beam splitter (70%: 30%). The strong linearly polarized beam with single pulse energy of 2 mJ is steered into a gas chamber filled with nitrogen gas and acts as the pump pulse. The weak beam, after passing through an optical delay line of ultra-precision linear translation stage, is frequency doubled by a 150 μm thick β-barium borate (BBO) crystal and then filtered by a narrow-band-pass filter around 390 nm. The spectrum of this pulse extends from 385 nm to 395 nm and serves as the seed pulse in our experiments. The pump and the external seed pulses are recombined collinearly by a dichroic mirror, which has high reflectivity around 400 nm and high transmission around 800 nm. The time delay between the pump laser and the external seed can be scanned by the program-controlled translation stage (Newport, XMS100). The two pulses are focused with an f = 300 mm convex lens into the gas chamber filled with pure nitrogen gas at different pressures. A visible plasma column with length of ~15 mm is generated with 2 mJ pump pulse in 4 mbar nitrogen gas. To separate the forward lasing emission around 391 nm from the fundamental pump pulse at 800 nm, another pair of dichroic mirrors were used. The coherent lasing emission around 391 nm is focused by a fused quartz lens into a fiber spectrometer (AvaSpec-2048-SPU) with a spectral resolution of 0.2 nm. In our experiment, the pressure of nitrogen gas is in the range of several millibars, which enables that the coherent 391 nm emission can be effectively generated in a long range of time delay between the pump and seed pulses.
Fig. 1 Experimental setup. DL: delay line; BBO: β-barium borate crystal; BPF: Band-pass filter; DM: dichroic mirror; BS: beam splitter; M: reflective mirror; HWP: half wave plate; Lens: fused silica lenses.
3. Results and discussion
Figure 2(a) shows a typical spectrum of the coherent emission around 391 nm recorded in the presence of both the pump laser and the external seed with an optimized delay. The experiment is conducted in the gas pressure of 2 mbar. For comparison, the spectrum of the seed pulse is also presented (blue line). In our experiments, we deliberately avoid the self-seeded 391 nm emission by limiting the nitrogen gas pressure below 4 mbar [21]. It can be seen that the weak external seed is significantly amplified in terms of energy, manifesting as a series of strong emission lines with narrow bandwidth. The intensity of the coherent emission is one order of magnitude higher than that of the external seed at 391.4 nm. These observations are consistent with previous reports [22–25], which has been ascribed to the seed-triggered collective spontaneous emission, i.e. superradiance [14,15]. These emission lines centered at 391.4 nm and 388.5 nm have been respectively assigned to the P branch and the R branch of the electronic transition of N2+ (B2Σu+, ν' = 0, J') → N2+ (X2Σg+, ν = 0, J) with ΔJ = J' - J = −1 for P branch and ΔJ = J' - J = + 1 for R branch [22–25]. As shown in Fig. 2(a), we identified rotational transitions in the R-branch emission and the rotation quantum number J' of the upper level is also denoted. It is revealed that the R branch is consisted of many rotational states ranging from J' = 13 to J' = 23.
Fig. 2 (a) Typical spectrum of the coherent emission around 391 nm (red line) recorded in the presence of both the pump laser and the external seed with an optimized delay. For comparison, the spectra of the seed pulse (blue line) and pump pulse (green line) are also presented. (b) Superradiance intensity around 391 nm as a function of the time delay between the pump laser and the seed for the gas pressure of 4 mbar (red line), 2 mbar (green line) and 1 mbar (blue line).
Figure 2(b) presents the superradiant 391nm signal as a function of the temporal delay between the pump and seeding pulse for different gas pressures. It can be seen that the superradiance intensity is sensitive to the gas pressure. Besides, it can be found that the superradiance cannot be generated efficiently when the time delay is longer than 70 picoseconds in the gas pressure of several millibars. This time scale is almost three orders of magnitude shorter than the spontaneous lifetime of the N2+ (B2Σu+) as 60 ns [26,27]. The ultrashort decay time of the optical gain can be attributed to the fast decay of N2+ (B2Σu+) by the collision of free electrons in the filament. Finally, there are strong periodic modulations for the superradiance intensity as a function of the time delay between the pump laser and the external seed, which is consistent with the conclusion that the coherent emission at 391 nm is the superradiance trigged by the external seed [15]. For the superradiance, the coherence is built by means of absorbing and emitting by the seed pulse [6]. And the dipole coupling between N2+ (B2Σu+) and N2+ (X2Σg+) depends on the molecular axis relative to the laser polarization direction. It becomes maximum when the axis of nitrogen molecular ions is parallel to the polarization of the external seed. Thus, the periodic modulation of time-dependent superradiance reflects the evolution of the molecular axis, i.e. the time-dependent molecular alignment.
To get further insight into the role of molecular ion alignment in the superradiance, we compared the seeding pulses with its polarization parallel and orthogonal to that of the pump laser pulse. The results are shown in Fig. 3. It is noticed that the delay time corresponding to the peak (dip) in the parallel case is exactly the delay time corresponding to the dip (peak) in the perpendicular case. This observation is the characteristic feature of the molecular alignment and origins from the evolution of molecular rotational wave packet. In addition, the superradiance is stronger when the polarization of the external seed is parallel to that of the pump laser. In our experiment, the orientations of the neutral nitrogen molecules are isotropic before laser irradiation. In contrast, the orientation distribution of the nitrogen molecular ions becomes anisotropic due to the anisotropic angular dependence of the ionization probability. According to molecular ADK theory, N2+ (B2Σu+) and N2+ (X2Σg+) can be generated through tunneling ionization from the highest occupied molecular orbital (HOMO) and the second lower-lying orbital (HOMO-2) of nitrogen molecules in strong femtosecond laser fields. The maximum of the ionization rate is achieved when the laser polarization is parallel to the molecular axis for the tunneling ionization from both HOMO and HOMO-2 [28]. As a result, the preferential ionization leads to the fact that the axes of most of N2+ (B2Σu+) and N2+ (X2Σg+) are parallel to the laser polarization at the moment of generation. In the meantime, the laser-molecule interaction generates a rotational wave packet, which leads to the transient molecular alignment [29–31]. After the laser pulse, the transient alignment can periodically be revived as long as the coherence of the rotational wave packet remains. At the same time, a permanent alignment parallel with the pump polarization presents due to that the absolute value of M is much smaller than that of J [29–31], where J and M are quantum numbers related to the angular momenta and the projection of the angular momentum onto the polarization direction of the pump laser, respectively. The existence of permanent alignment leads to the different angle between the molecular axis and the laser polarization direction when the polarization of the external seeding pulse is parallel or perpendicular to that of the pump laser. The seed laser experiences higher alignment degree of molecular ions when the polarization of the external seed is parallel with the polarization of the pump laser. Because the electronic transition moment between N2+ (B2Σu+, ν' = 0) and N2+ (X2Σg+, ν = 0) is parallel to the molecular axis, the transition efficiency in the parallel case is higher than that in the perpendicular case. As a result, the superradiance is stronger when the polarization of the external seeding pulse is parallel to that of the pump laser, which totally agree with our experimental observations.
Fig. 3 Superradiance intensity as a function of the time delay between the pump laser and the seed with the polarization of the pump laser being parallel (red line) or perpendicular (blue line) to that of the seed.
It is known that the Fourier transform spectrum of the evolution of the rotational wavepacket contains a series of beat frequencies ω between adjacent J states, which are given by:
where B0 is the rotational constants of N2+ . The amplitude of the beat frequency is determined by the relevant rotational population in the rotational wave packet. Figure 4 shows the Fourier transform spectrum of the time-dependent superradiance intensity shown in Fig. 2 (b) in the case of 2 mbar. The frequencies can be well identified by the equation (4J + 6) BB and (4J + 6) BX with BB = 2.085 cm−1 and BX = 1.932 cm−1 being the rotational constants of N2+ (B2Σu+) and N2+ (X2Σg+) [32]. Consequently, the contribution from both N2+ (B2Σu+) and N2+ (X2Σg+) is clearly separated in the frequency domain. The rotational states of N2+ (B2Σu+) mainly distribute 13 < J < 23 and those of N2+ (X2Σg+) mainly distribute 14 < J < 24, which also agrees well with the emission lines in the R branch, presented in Fig. 2(a). Due to that the amplitude of the Fourier transform spectrum is determined by the rotational populations in the rotational wave packet, it can be inferred from Fig. 4 that the population of N2+ (B2Σu+) is 2.5 times higher than that of N2+ (X2Σg+) within the rotation states from J = 13 to J = 23. Therefore, this experimental observation directly show that population inversion of certain rotation level between the B2Σu+ and X2Σg+ states occurs for the forward 391 nm superradiant emission. As only parts of rotational states participate in N2+ superradiance, the present measurement cannot judge whether net population inversion is achieved between the excited and ground electronic states of the nitrogen ions, which is under hot debate now.Fig. 4 Fourier transformation of the time-dependent superradiance around 391 nm. Here J' and J are the rotation quantum number of the upper and lower states of the transition. The rotational coherence was clearly exhibited for both the excited state and the ground state of nitrogen molecular ions.
4. Conclusion
In summary, we observed strong superradiant emission around 391 nm from singly ionized nitrogen molecules when intense 800 nm femtosecond laser pulses was focused together with a delayed seeding pulse in nitrogen gas. Due to the field-free transient alignment of the nitrogen molecular ions by the pump pulse, periodic modulations of the superradiance were observed as a function of the time delay between the pump and the external seed pulses. The quantum rotational levels of the upper and lower lasing states were identified, by taking Fourier transformation of the temporal signal. It was found that population inversion between some rotation levels of the upper and lower states of nitrogen ions is achieved for this superradiant emission.
Funding
This work is supported by the National Natural Science Foundation of China under Grants No.11625414, No. 21673006, No. 11474009, and No. 11434002.
Acknowledgments
The authors acknowledge stimulating discussion with Yi Liu of University of Shanghai for Science and Technology.
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