Nitrogen fluorescence emission pumped by femtosecond optical vortex beams

An experimental investigation on nitrogen fluorescence emissions pumped by a single 800 nm fs optical vortex (OV) beam with different topological charges (TC) is reported. The intensity of the two prototype emission lines from neutral nitrogen molecules (N2) and molecular nitrogen ions (N2 +), i.e., 337 nm and 391 nm, respectively, shows different TC dependences: the former slightly decreases as the TC increases, while the latter sharply decreases as the TC changes from zero to a non-zero value. The dependences of the 337-nm and 391-nm emission intensity on pulse energy are also different: the former shows a linear variation for different TCs, while the latter has an abrupt change in the slope when changing the TC. Furthermore, the dependence of the 337-nm emission intensity on gas pressure exhibits a plateau which is universal for different TCs. In contrast, the dependence of the 391-nm emission intensity on gas pressure shows an apparent hump which is respective of the TC. These actual new results will facilitate further theoretical study on the formation dynamics of the nitrogen fluorescence emissions induced by the OV beam, and inspire that such beam can been taken as a unique pure optical tool to manipulate the transitions between different electronic-vibrational states.


Introduction
Since its discovery a few decades ago [1], femtosecond laser filamentation, which is formed by a dynamic competition between the self-focusing of the laser beam and the plasma defocusing caused by the ionization of air molecule or its major components (N 2 and O 2 ), has been continuously advancing our understanding of molecular ionization, dissociation, excitation and other dynamical processes through intriguing emissions such as fluorescence [2], lasing action [3][4][5][6], supercontinuum [7], and terahertz [8,9]. Among them, the prototype nitrogen fluorescence emissions from the excited N 2 and N 2 + molecules with a predominate line at 337 nm and 391 nm, respectively, can provide valuable clues to identify the formation mechanism of the molecular excited states for increasing the efficiency of population inversion, and thus the intensity of the remote cavity-free laser which holds great potential for the remote sensing and weather control [10][11][12].
The fluorescence emissions at 337 nm and 391 nm have been assigned to the transitions of N 2 (C 3 Π u , ]′ 0) → N 2 (B 3 Π g , ] 0) and N + 2 (B 2 Σ + g , ] 0) → N + 2 (X 2 Σ + g , ]′ 0), respectively. Two main types of experimental scenarios have been carried out to control the formation of N 2 (C 3 Π u ) and N + 2 (B 2 Σ + g ). The first type is to adjust the intrinsic characteristic parameters of the laser such as pulse energy [2], wavelength [4] and OPEN ACCESS EDITED BY Huipeng Kang, Innovation Academy for Precision Measurement Science and Technology (CAS), China polarization [13], and even to employ a multiple-beam configuration for taking external pulses as seed [14][15][16], including the pump-probe technology. The pulse energy can directly influence molecular ionization rate, while the wavelength and polarization are related to the photon energy and spin angular momentum, respectively, which can influence photonic excitation and thus the transition selection rules. The second type is to control the macroscopic environment of the interaction region between nitrogen molecules or ions and laser by altering focusing condition [17,18], pulse repetition [19], and gas pressures [17] or gas mixtures (e.g., nitrogen-argon mixture and nitrogen-oxygen mixture) [20]. The fluorescence emissions at 337 nm and 391 nm can be generally observed and controlled in these scenarios, and from which alternative schemes have been derived for explaining the formation of the N 2 (C 3 Π u ) and N + 2 (B 2 Σ + u ). The former is attributed to three main possible schemes: collision-excitation [5,13,14,[21][22][23], collision-assisted intersystem crossing [13,24,25] and dissociative recombination through the reactions of N + 2 + [26][27][28], while the latter is attributed to two main possible schemes: one is multi-photon ionization of the inner-valence electrons of N 2 [29]; the other is collision ionization of N 2 with a high energy electron [5,13,30]. Additionally, the second harmonic emission as well as supercontinuum emission can serve as a self-seeding pulse to start and enhance the lasing in N + 2 molecules [17,31]. However, a conclusive agreement on the formation mechanism of N 2 has not yet been reached, and thus further understanding and clarification of the mechanism behind the possible schemes requires, from an experimental point of view, alternative evidence by resorting to a unique technology.
Interestingly, the OV beam, possessing a spiral phase structure and thus exhibiting a unique ring-shaped transverse intensity profile, carries orbital angular momenta (OAM) which equals to a quantized TC [32] and can add a new degree of freedom to study strong-field physics [33,34]. Indeed, it has been found that the intrinsic photon OAM can participate in the couple with the rotational and electronic motion, and makes the transitions forbidden by selection rules become possible when using the OV beam [35][36][37][38], while the bound electron can absorb the photon carrying an OAM [34,37,[39][40][41][42][43][44]. On the other hand, the unique ring-shaped spatial distribution of the OV beam makes it can solely manipulate atoms or ions like a tweezer [45][46][47]. Therefore, the OV beam seems can not only affect the population of vibrational levels of electronic states, the transition probabilities and thus the emissions, but also affect the interaction between electrons, molecules and ions through the adjustable TC which is related to the size of the intensity ring, and accordingly, it offers a unique alternative to study nitrogen fluorescence emissions and to revisit the mechanism behind the aforementioned possible schemes. However, it still lacks direct experimental evidence on whether and how the OAM and ring-shape intensity profile are involved in the formation of N 2 (C 3 Π u ) or N + 2 (B 2 Σ + u ). In this paper, using OV beams with different TCs, we systematically study the evolutions of the 337-nm and 391-nm emission intensity with pulse energy and gas pressure. Considering the advantages of the OV beam, a simultaneous control on the intrinsic process and the macroscopic region of the interaction between molecules and the laser is expected. It is found that the 391-nm emission sharply decreases as the TC increases while the 337-nm emission slightly depends on the TC. Moreover, the 337-nm emission exhibits a similar linear variation with the pulse energy for different TCs, while the evolution of the 391-nm emission with the pulse energy changes as the TC changes. For different TCs, the two emissions also exhibit different dependences on the gas pressure. These observations suggest that the OV beam is a unique and flexible toolkit to manipulate nitrogen fluorescence emissions.

Methods
In our experiments, femtosecond pulses generated by a commercial Ti:sapphire laser system (Astrella, Coherent, Inc.) are focused by an f = 400 mm convex lens into a gas chamber with a base pressure below 10 -5 Pa, as shown in the left-hand panel of Figure 1. The pulse's central wavelength, duration and repetition of the pulse are 800 nm, 45 fs and 1 kHz, respectively. The variation of the pulse energy is achieved by a gradual neutral density filter (NDF) with a diameter of 50 mm. Spiral phase plates (SPP) with a high damage threshold are employed for generating femtosecond OV with different TCs of n. A beam splitter (BS) with a high splitting ratio of 99:1 is used to splitter the OV beam and steer the weak one into a CCD camera which can measure and monitor the spatial profile of the pulses. The measured transverse intensity profiles of the beams display rings with different radii, see the right-hand panels of Figure 1. The beam for n = 0 is a regular Gaussian beam. In special, the radius of the intensity ring increases as n increases, which is consistent with theoretical results showing the radius is proportional to |n| √ [48]. The uncertainty of the pulse energy is estimated to be less than 10%, which will not affect the comparison of data at different TCs and the consequent conclusion.
The chamber is filled with pure nitrogen gas at different pressures by a fine valve, and visible filaments with lengths of 10 mm-35 mm are formed. The fluorescence emissions produced from the chamber after the filament generation area are filtered by a combination of an 800 nm notch filer followed by a two-color filter (BG 40). The combination transmits the spectral components shorter than 400 nm but blocks the other accompanying emissions and attenuates largely the fundamental pulse as its intensity is too high.
The filtered pulses passing through a replaceable band-pass filter are coupled into a fiber spectrometer (Ocean Optics, HR4000) by means of an f = 50 mm fused silica lens followed by another f = 100 mm fused silica lens placed on a two-dimension moving stage. To circumvent the saturation of the spectrometer when the fluorescence intensity is too high, another neutral density filter is mounted at the entrance to the spectrometer. Depending on the fluorescence intensity, different laser shots are performed for each individual measurement to reduce the error and ensure a sufficiently high statistical accuracy. By choosing appropriate pulse energy range as well as the gas pressure range in our measurement, the supercontinuum is carefully controlled to emerge beyond a high pressure.

Results and Discussions
In this paper, we concentrate on the measurements of the two typical emissions at 337 nm and 391 nm. We first confirm that the length of filaments formed in nitrogen gas increases as the pulse Frontiers in Physics frontiersin.org energy increases in the case of n = 0, i.e., for a Gaussian beam. Then, according to the fact that the lasing signal is linear polarization and only propagates along the forward direction while the fluorescence signal is usually random polarization [4,6], we have checked the polarizations of the forward emissions and found that the 391-nm emission for n = 0 is lasing signal while it is fluorescence signal for n = 1 or n = 2. Moreover, the measured 337-nm emissions for different TCs (i.e., n = 0, one and 2) are all from the fluorescence signal. For n = 0, the 337-nm emission intensity, as shown in Figure 2A, increases nearly linearly with the increasing the pulse  Frontiers in Physics frontiersin.org energy, while the 391-nm lasing intensity first increases slowly with increasing the pulse energy, and then increases fast when the pulse energy is above 1.25 mJ, exhibiting an apparent knee point, see Figure 2C, which is consistent with the results presented in Ref. [17]. The significant increase of the 391-nm lasing intensity is due to that ionization rate increases exponentially with increasing the pulse energy which can directly affect the formation of N + 2 (B 2 Σ + u ). For the 337-nm emission, the evolutions of the number of N 2 (C 3 Π u ) and thus the fluorescence intensity with pulse energy proposed the aforementioned three possible schemes are similar [4]. Thus, the pulse energy is a simple but effective parameter which is used to influence the number of N 2 (C 3 Π u ) or N + 2 (B 2 Σ + u ). Different features are also found from the evolutions of the 337nm and 391-nm emission intensity with the gas pressure ranging from 250 Pa to 3,000 Pa at the pulse energy of 1.25 mJ, see Figures 2B, D. The 337-nm emission first increases fast until 900 Pa, and then decreases slowly and reaches its minimum at around 2,100 Pa, exhibiting an almost plateau-like tendency. Then, it increases fast again and exhibits a second increasing stage, as shown in Figure 2B. This stage can be attributed to the effective generation of supercontinuum which emerges at high pressures and takes over the 337-nm spectrum. In contrast, the 391-nm emission reaches its maximum at around 1,300 Pa, and then decreases significantly, leading to an obvious hump, as shown in Figure 2D, which is similar to the results presented in Ref. [17]. The significant decrease of the 391-nm lasing intensity beyond the pressure of 1,300 Pa is due to that the population inversion between the two involved states [i.e., N + 2 (B 2 Σ + g , ] 0) and N + 2 (X 2 Σ + g , ]′ 0)] decreases at higher pressures, while the 428-nm lasing emission, which is from the transition of N + 2 (B 2 Σ + g , ] 0) → N + 2 (X 2 Σ + g , ]′ 1), takes over as the generation of supercontinuum gradually approaches 428 nm with increasing pressure [17].
In order to control the excitation, ionization and collision occurring in the femtosecond filament which is related to the formation of N 2 (C 3 Π u ) or N + 2 (B 2 Σ + u ), we have repeated the same experiments using OV beams with different TCs. As mentioned above, the OV beam exhibits a ring-shaped intensity profile with a radius increasing with the TC, as depicted in right-hand panels of Figure 1. The OV beam is an effective tool to control the interaction region between the laser and nitrogen molecules, and influence the dynamics process. On the other hand, the OV beam carries an OAM scaled by the TC, which is related to the OAM-dependent absorption of light by a bound electron and may influence the transitions between different states, resulting in that the ionization process for the formation of N + 2 (B 2 Σ + u ) can also be controllable. Thus, focusing on the role of the TC in the two protype transitions, we have extended the measurements to the OV beams with a higher TC, i.e., n = 1 and n = 2. Figure 3A displays the variation of spectra induced by the OV with the TC when the incident pulse energy is 1.25 mJ. It is obvious that the 337-nm emission intensity exhibits a weak dependence on the TC, see the inset in Figure 3A, while the 391-nm emission dominates in the case of n = 0 but decreases significantly for a higher TC. The former is further confirmed by the evolutions of the 337-nm emission intensity with the pulse energy for different TCs at the nitrogen gas pressure of 1,200 Pa, as shown in Figure 3B. As an overall view, the 337-nm emission intensity increases nearly linearly with increasing the pulse energy for different TCs and their slopes keep almost constant. In other words, the 337-nm emission intensity shows an identical change tendency for different TCs, exhibiting a less dependence on the TC which determines the spatial distribution of the pulse. As a result, the 337-nm emission intensity is influenced by the pulse energy, but it is irrespective of the spatial distribution.
In particular, the 337-nm emission intensity gradually decreases as the TC increases for a same pulse energy though the intensity gap is not large. This can be due to the ring-shaped energy distribution of the OV beam for a non-zero TC. The OV beam with a non-zero TC has an apparent hole in its center, which makes the peak intensity of the pulse decrease though the energy is the same as that in the case of n = 0, i.e., for a Gaussian beam. The peak intensity influences the formation of N 2 (C 3 Π u ) whose population becomes less as the peak intensity decreases, leading to a weak N 2 fluorescence emissions (337 nm, etc.) for a higher TC. On the other hand, in contrast to the 337-nm emission, the intensity of the N + 2 fluorescence emissions (391 nm, etc.) which is directly related to the ionization process for the generation of N + 2 (B 2 Σ + u ) shows a distinctly different dependence on the pulse energy: it increases significantly first, and then exhibits an apparent change of the slope when the pulse energy exceeds  Figure 3C. Interestingly, for n = 1, the 391-nm emission intensity exponentially decreases, which is more than one order of magnitude lower than that of n = 0, while it becomes obscure when n increases up to two for the pulse energy range tested. The 391-nm emission becomes weaker for a non-zero TC, indicating that the discrepancy between the Gaussian beam and OV beam will influence the intensity of the N + 2 forward emissions, which can be understood from two aspects. First, the special spatial distributions of the OV beam makes the peak intensity of the pulse become weaker for a higher TC as the pulse energy is distributed along a bigger circle, resulting in a lower population of N + 2 (B 2 Σ + u ). Because the ionization process for the generation of N + 2 (B 2 Σ + g ) has a rate depending exponentially on the instantaneous electric field of the laser, the 391-nm emission will be greatly suppressed due to the decrease in the maximum electric field when the spatial distribution of the pulse changes from the Gaussian to the OV. As a result, the 391-nm emission intensity decreases with increasing the TC, exhibiting a tendency similar to that observed at 337 nm. Second, the interaction region between the OV beam and the molecules becomes larger as the TC increases, which should also influence the formation of N + 2 (B 2 Σ + u ) and thus the 391-nm emission intensity. Furthermore, by qualitatively comparing the gap between the fluorescence intensity for n = 1 and n = 2 with that between the case of n = 0 and n = 1, we can find that the former is not obvious while the latter is large, see Figure 3C, which reveals that the exponential decrease of the ionization rate is mainly due to the decrease of the peak intensity of the laser, rather than the increase of the interaction region for a higher TC. It should be noted again that because the spiral phase profile of the OV field endows the photon with an OAM that equals to the TC, the OAM-dependent multiphoton absorption of a bound electron should be allowed by the transition selection rules, while the effect of photon OAM on photoionization is already trivial [49,50], which will influence the plasma density and thus the intensity of the second harmonic [51]. The second harmonic can be taken as a seed to influence the lasing emission at 391 nm [17]. As we mentioned above, the 391-nm emission for n = 0 is lasing signal while that for n = 1 or n = 2 is fluorescence signal, which suggests that the lasing action at 391 nm is suppressed by the OV field, indicating that the TC can be taken as a novel additional parameter to control the transition responsible for the 391-nm emission and even the corresponding lasing action. As a whole, our experimental observations herein are the first-hand data for further theoretical study on nitrogen fluorescence emissions in the OV fields.
In order to provide more information for the benefit of exposing the characteristics of nitrogen fluorescence emissions, we plot the 337-nm emission intensity as a function of nitrogen gas pressure for different TCs with the pulse energy of 1.5 mJ in Figure 4. Since the evolution of the 337-nm emission intensity with the gas pressure in the case of n = 0 has been discussed above, we will focus on comparing the discrepancy of the evolutions between different TCs. As shown in Figure 4A, the evolutions of the 337-nm emission intensity with the pressure in both cases of n = 1 and n = 2 behave similarly to that of n = 0: it first increases fast and then decrease slowly, exhibiting an almost plateau-like tendency for a large pressure range, and then it increases fast again. This means that the change of the spatial distribution does not affect the evolution of the 337-nm emission. A similar but much smoother plateau-like tendency emerges for different energies in the cases of n = 0, n = 1 and n = 2, as shown in Figures 4B-D), respectively. Overall, the 337-nm emission intensity evolves similarly with the pressure for different TCs, and exhibits a plateau for a large pressure range. The plateau is irrespective of the TC and pulse energy, and seems to be universal. It should be noted that at the pressures above 2,400 Pa, the 337-nm emission intensity for n = 0 and n = 1 almost coincide and a similar second increasing state appears in all cases, which can be attributed to the effective generation of supercontinuum which dominates at high pressures and gradually suppresses the 337-mm emission.
In contrast to the 337-nm emission, the evolution of the 391-nm emission intensity with the gas pressure, as presented in Figure 5A, shows a clear TC dependence: an apparent hump emerges in the case of n = 0, while it disappears in the case of n = 1 or n = 2. Similar humps are also observed at other pulse energies for n = 0, as shown in Figure 5B. Figure 5A also shows that, compared to the case of n = 0, the 391-nm emission intensity for a non-zero TC exponentially decreases for the gas pressure range tested. It should be noted that, in our measurements, the supercontinuum emission is absent for most pulse energies or pressures, apart from for the pressures above 2,500 Pa at the highest pulse energy of 1.5 mJ for the case of n = 0. The latter covers a very small part which cannot influence the main trends of the curve for n = 0 in Figure 5 and thus the subsequent analysis. Furthermore, the results presented in Figures 5C, D show that the 391-nm emission intensity gradually increase as the gas pressure increases in the case of n = 1 or n = 2. In particular, the 391nm emission intensity of n = 1, as shown in Figure 5C, exhibits an abrupt hump and a second increasing stage when the pulse energy is 1.5 mJ. The latter, similar to the 337-nm results presented above, can also be attributed to the influence of the supercontinuum which dominates at higher pressures. Overall, the 391-nm emission has a strong dependence on the TC, which suggests that the OV beam is a unique toolkit to control the transitions between different electronic-vibrational states and thus the fluorescence emissions.

Conclusion
In our study, employing OV beams with different TCs (i.e., 0,1 and 2), the evolutions of the 337-nm and 391-nm emission intensity with pulse energy and gas pressure are experimentally investigated. It is found that the 337-nm emission intensity slightly decreases as the TC increases, while that at 391 nm sharply decreases as the TC changes from zero to a non-zero value. Meanwhile, the dependences of the 337-nm intensity on pulse energy show similar behaviors (i.e., a linear variation) for different TCs, while the Frontiers in Physics frontiersin.org dependences of the 391-nm intensity on pulse energy have an abrupt change in the slope when changing the TC. Furthermore, it is found that the dependence of the 337-nm emission intensity on gas pressure shows a universal plateau. In contrast, the dependence of the 391-nm emission intensity on gas pressure shows an apparent hump when the TC is zero, while it disappears for a non-zero TC, which is due to that the lasing action at 391 nm is suppressed by the OV field. These experimental findings are actual new which will inspire further theoretical investigations, and our study highlights that the versatile OV can be used as a unique tool to manipulate the transitions between different electronic-vibrational states and thus nitrogen fluorescence emissions.

Data availability statement
The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

Author contributions
YC: Measurements, pictures production, data analysis, preparation of the first draft. XM: Measurements, data analysis. BL: Data analysis. ZL: Conception and design of study, funding, interpretation of results, editing manuscript draft. All authors contributed to the article and approved the submitted version.
Funding ZL acknowledges funding support by the National Natural Science Foundation of China (11504116) and the Scientific Research Startup Foundation of Huaqiao University (13BS406 and 605-50Y21003).