1. INTRODUCTION

Structured light is significant for its multidisciplinary applications [1,2]; e.g., the doughnut-shaped depletion beam is the key for the stimulated emission depletion (STED) microscopy to achieve unprecedented spatial resolution [3]. In fact, from structured light emerges a myriad of applications that range from optical tweezer trapping [4] and sensing [5], to optical communications [6] and laser material processing [7]. Although the control over other degrees of freedom is gradually gaining attraction, orbital angular momentum (OAM) is one of the most topical dimensions of structured light. OAM is related to the helical phase front and doughnut transversal profile of light [8]. Accordingly, a light beam carrying OAM is often referred to as a vortex beam. A Laguerre–Gaussian (LG) beam with circular symmetry is a type of vortex beam carrying OAM [8]. Every photon of an LG beam carries $| \ell |\hbar$ OAM, where $\ell$ is the topological charge (TC) and equals the number of twists in a wavefront per unit of wavelength. Research on various types of vortex beam generation is already in full swing [9,10].

Atmosphere can be a gain medium for remote cavity-free lasing action when it is pumped by intense ultrafast laser pulses. In fact, it emits laser-like coherent radiation in the UV-visible spectral range during the pump laser filamentation that is called “air lasing.” All three essential components of air (${{\rm N}_2}$, ${{\rm O}_2}$, and Ar) have been shown to generate air lasing [11–15]. Because of the long propagation distance of the plasma filament [16,17], air lasing shows great potential for remote sensing applications [18], diagnosis of molecular dynamics [19,20] and Raman spectroscopy [21,22], and is becoming a promising spectroscopic tool in various fields. Particularly, nitrogen molecular ion ${{\rm N}_{2}}{^{{{+}}}}$ lasing [14,23–25] has attracted much attention because of the abundance of ${{\rm N}_2}$ in the air and its switchable multiwavelength [12]. ${{\rm N}_{2}}{^{{{+}}}}$ lasing is a two-step process: The molecules undergo a single ionization from ${{\rm N}_2}$ to ${{\rm N}_{2}}{^{{{+}}}}$ to populate the ground (${X^2}{\Sigma}_g^ +$) and are in excited (${B^2}{\Sigma}_u^ +$) states in ${{\rm N}_{2}}{^{{{+}}}}$ [26–30]; afterward the ${B^2}{\Sigma}_u^ + - {X^2}{\Sigma}_g^ +$ transition leads to the coherence emission of the ${{\rm N}_{2}}{^{{{+}}}}$ lasing.

To date, to the best of our knowledge, there are still no reports for OAM ${{\rm N}_{2}}{^{{{+}}}}$ lasing, although distantly inducing and tailoring lasing in the open air is an intriguing challenge. Harnessing the spatial structure of the ${{\rm N}_{2}}{^{{{+}}}}$ lasing facilitates further exploration of remote structured light field control. The lasing carrying OAM promises access to the remote sensing of an object’s rotational orientation [5], Raman spectroscopy on complex chiral molecules [31], and wavefront self-healing beams for communications [6,32]. In addition, pump-to-signal OAM transfers have been demonstrated in numerous nonlinear optical processes, including four-wave mixing [33], stimulated Raman scattering [34], and high harmonic generation[35].

Here, we experimentally generated a vortex ${{\rm N}_{2}}{^{{{+}}}}$ lasing by using a near-IR pump beam with OAM. By measuring the TC of the ${{\rm N}_{2}}{^{{{+}}}}$ emission at 391 nm/428 nm, we observed that the TCs of the light emissions are twice that of the pump. Interestingly, as the pumping energy increases, the ${{\rm N}_{2}}{^{{{+}}}}$ lasing efficiency is higher for the vortex pump compared to the plane wavefront one. It is attributed to the increased clamping intensity of the vortex pump where the structured transversal profile of the filament reduced the on-axis plasma density to defocus the incident laser beam.

2. METHODS

A schematic of the experimental setup is depicted in Fig. 1(a). The experiments were implemented with a femtosecond Ti:sapphire laser system, which produces 35 fs, 800 nm (near-IR), 1 kHz, linear polarized, Gaussian-mode laser pulses as the pump. After passing a spiral phase plate (SPP), the pump beam in Gaussian mode ($\ell = 0$) is turned into the Laguerre–Gaussian mode ($\ell = 1$), as illustrated in Fig. 1(a), which was focused by a convex lens (${\rm f}\; = {20}\;{\rm cm}$) into a gas chamber to ionize the ${{\rm N}_2}$ molecules. The intense femtosecond laser pulses in the pump beam induced a laser plasma filament and gave rise to the coherent emission in the forward direction, i.e., ${{\rm N}_{2}}{^{{{+}}}}$ lasing. In the external seed experiment, the UV seed pulses were produced by the second-harmonic (SH) pulses of 800 nm (using a ${\beta}$-BBO crystal). Before, the chamber was initially evacuated to a pressure of about ${{10}^{- 2}}\; {\rm mbar}$ and then filled with pure ${{\rm N}_2}$ gas at various pressures. A laser plasma filament of about 10 mm in length along the propagation direction arose from the ${{\rm N}_2}$, and its length changes with the pump pulse energy and gas pressure. The multicomponent pulses emerging after the filament were collimated by another convex lens (${\rm f}\; = {15}\;{\rm cm}$) after the gas chamber and then filtered by a short-pass filter. Thus, the spectral components shorter than 600 nm were transmitted but the pump pulses and the accompanying supercontinuum was mostly blocked. The transmitted lasing emissions were then focused into a CMOS industrial digital camera to a record its transversal spatial profile or a fiber spectrometer (HR 4000, Ocean Optics) to measure the spectrum. A beam splitter was used here to ensure that the spectrum and the spatial profile were captured simultaneously. In addition, the intensity distributions of the filament plasma formed by the pump pulse along its propagation direction inside the chamber were imaged through a side-view window by a CMOS camera.

 

Fig. 1. Schematic of the experiment. (a) Schematic diagram of the vortex ${{\rm N}_{2}}{^{{{+}}}}$ lasing generation and measurement setup. See details in Section 2 (Methods). The typical ${{\rm N}_{2}}{^{{{+}}}}$ lasing spectra at (b) 391 nm (at 25 mbar) and (c) 428 nm (at 100 mbar). The solid and dashed curves represent the lasing pumped by Gaussian and vortex beams, respectively. The pumping pulse energy is fixed at 3.0 mJ. (d) Schematic diagram of relevant energy levels of nitrogen molecules and its ions. (e) Broad radiation around 400 nm (second-harmonic generation of near-IR pump beam). Each spectrum present here is averaged over $3.0 \times {10^4}$ laser shots. Note that a.u. stands for arbitrary units in Figs. 1, 3, and 4.

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3. RESULTS

Figures 1(b) and 1(c) show that the emission occurred at about 391 nm (at 25 mbar) and 428 nm (at 100 mbar), which represents the transition between the ${B^2}{\Sigma}_u^ +$ ($\nu ^\prime = {0}$) and $\;{X^2}{\Sigma}_g^ +$ ($\nu = {0},{1}$) states of ${{\rm N}_{2}}{^{{{+}}}}$. The potential energy curves of the involved electronic states are illustrated in Fig. 1(d). The solid and dashed curves describe the lasing pumped by the Gaussian and vortex beams, respectively. The pumping pulse energy was fixed at 3.0 mJ.

Figures 2(a)–2(c) show the transverse intensity profiles of the pump beam, the 391 nm emission (at 25 mbar), and the 428 nm emission (at 100 mbar), respectively. A dark core at the transversal profile appears in all three images, which suggests a spatial phase singularity. Notwithstanding, this doughnut-like intensity profile is a necessary, but not sufficient, condition to distinguish a vortex beam because the transverse intensity distribution of the conical emission, which also emerges in Gaussian-pumped lasing at high gas pressures [13], can be indistinguishable from the doughnut-like intensity profiles of vortex emission. Both Gaussian (at low pressure) and conical emission (at high pressure) pumped by Gaussian beam present a plane wavefront [13,36]. To verify the vortex characteristic of the ${{\rm N}_{2}}{^{{{+}}}}$ emission, we used a straightforward method of OAM (topological charge) measurement: the cylinder lens method [37,38]. This method is based on the fact that a cylinder lens can transform incident photon momentum to position at the focal plane; thus, the vortex beam with an average topological charge $\;\ell$ performs a $| \ell |$ inclined dark stripes pattern in its image at the focal plane [37]. As illustrated in Figs. 2(d)–2(f), the number of high-contrast dark stripes across the images shows the average topological charge carrying by each beam: The pump beam carries $\ell = 1$, and the lasing emission (391 nm/428 nm) carries $\ell = 2$. It is cross-checked by adjusting the topologic charge of the pump beam to $\ell = - 1$, resulting in an opposite inclination of the dark stripes compared to the previous scenario, as shown in Figs. 2(g)–2(i). To compare the power and spectral characteristics of the vortex (LG) pumped ($\ell = + 1$) and the Gaussian pumped ${{\rm N}_{2}}{^{{{+}}}}$ lasing, we focused the emissions to a fiber spectrometer to measure their spectra. Both the vortex and the Gaussian-pumped lasing are manifested as strong narrow-line radiation around 391 nm/428 nm.

 

Fig. 2. Transverse intensity profiles and focal images of pump beam and ${{\rm N}_{2}}{^{{{+}}}}$ lasing. (a)–(c) Transverse intensity profiles of vortex beams taken by CMOS. (800 nm pump beam, 391 nm, and 428 nm emission, similarly throughout this paper). (d)–(f) Cylinder-lens-passed intensity profiles of vortex beams near the focus when the pump 800 nm photon carries $\ell = + 1$. (g) and (h) is similar to the former but obtained after flipping the side of the spiral phase plate so that the pump 800 nm photon carries $\ell = - 1$.

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A pumping power dependencies comparison of the lasing emission with the vortex and the plane wavefront was implemented. Figures 3(a) and 3(b) show the lasing radiation intensity of two lasing lines as a function of the pumping laser pulse energy. The used nitrogen gas pressures are 25 mbar and 100 mbar for 391 nm and 428 nm, respectively, which are the optimal pressures to efficiently generate the ${{\rm N}_{2}}{^{{{+}}}}$ lasing at corresponding wavelengths. For the 391 nm case in Fig. 3(a), the Gaussian-beam-pumped ${{\rm N}_{2}}{^{{{+}}}}$ lasing increases as the pumping pulse energy increases from 1.6 mJ to 2.4 mJ and then decreases sharply up to 3.8 mJ. However, the vortex-beam-pumped 391 nm lasing increases progressively from 1.6 mJ, exceeds the Gaussian-beam-pumped lasing from 3.0 mJ on, and saturates at about 3.4 mJ.

 

Fig. 3. Pumping power dependences of ${{\rm N}_{2}}{^{{{+}}}}$ lasing pumped by a Gaussian or vortex beam. Pumping intensity dependence of (a) the 391 nm and (b) 428 nm lasing radiation on the incident laser pulse energy. The ${{\rm N}_2}$ pressures are (a) 25 mbar and (b) 100 mbar.

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As shown in Fig. 3(b), the 428 nm lasing maintains consistent results; i.e., the vortex lasing shows a higher generation efficiency compared to the Gaussian pump in a high incident energy condition. It is noteworthy that the evolution of 428 nm lasing is a little different compared to that of 391 nm lasing. Both the Gaussian- and vortex-pumped 428 nm lasing increased monotonically in our measurements.

To exclude the influence of the second harmonic and supercontinuum generation on the measured TC of the ${{\rm N}_{2}}{^{{{+}}}}$ lasing, we executed experiments under the same conditions in argon atoms because they have ionization potential like that of the ${{\rm N}_2}$ molecules. Without a 391 nm or 428 nm signal appearing, a broad radiation around 400 nm can be observed, as shown in Fig. 1(e). It rises at the low pressures from $p = {5}\;{\rm mbar}$ and reaches a maximum around 10 mbar and then decreases progressively up to 60 mbar. It can be attributed to the second harmonic of the near-IR pump beam. It could be observed clearly only when the pumping pulse energy is higher than 2.0 mJ. Under the electric dipole approximation, second-harmonic generation in centrosymmetric media (e.g., atomic gases) is strictly forbidden by parity conservation or symmetry. However, charge separation produced by ionization induces a spontaneous polarization field when there is an ultrashort laser pulse irradiating the atomic gases and yields a weak signal of the second harmonic [39]. In our experiments, the strength of the second harmonic or supercontinuum generation is about three orders weaker than the minimum of the 391 nm and 428 nm signal. When the gas pressure is higher than 20 mbar, a broad radiation around 440 nm [like that in Fig. 1(c)] emerges. We attributed this to the component of the supercontinuum: It is well separated from the 428 nm signal and has no possibility to be counted into the 428 nm signal intensity. Furthermore, a short-pass filter (430 nm) is used to weaken the influence of the supercontinuum on the spatial profile measurement.

4. DISCUSSION

Here is a brief description of the mechanism of the pump-to-signal OAM transfer in ${{\rm N}_{2}}{^{{{+}}}}$ lasing: Compared to the ground state (${X^2}{\Sigma}_g^ +$), the excited state (${B^2}{\Sigma}_u^ +$) is populated by absorbing two more 800 nm photons with OAM ($\ell = 1$) upon the photoionization of the ${{\rm N}_2}$. Because of the conservation of OAM, it is stored in the electron of the rovibrational levels of ${B^2}{\Sigma}_u^ +$. When the electron of the excited ${B^2}\Sigma _u^ +$ state with extra OAM transits back to the ground state (${X^2}{\Sigma}_g^ +$), the stored OAM transfers to the generated 391 nm/428 nm signals, and represents a topological charge of $\ell = 2$. Our results are compatible with all three mechanisms discussed in the literature: the population inversion followed by stimulated emission [14,27], the coherent coupling V-scheme without population inversion [29], and the rotational quantum beat lasing [30], all of which attribute the ${{\rm N}_{2}}{^{{{+}}}}$ lasing emission to the ${B^2}{\Sigma}_u^ + - {X^2}{\Sigma}_g^ +$ transition.

The basic idea to transfer the vortex from the pump to the signal is attributed to the variety of the wavefront phases across the transverse profile of the laser beam. It has been well observed in nonlinear processes; e.g., high-order harmonic generation driven by vortex pump[40]. In the cross section of the Gaussian beam, the spatially phase distribution is a constant, i.e., a plane wavefront. However, the LG beam has a spatially varying vortex phase state on its cross section. Each molecule (or ion) emits ${{\rm N}_{2}}{^{{{+}}}}$ lasing radiation when it interacts with the pump field and causes a phase delay along the rotation direction of the pump beam wavefront; therefore, the vortex wavefront of the new lasing. The difference of phase variation with the azimuthal angle (i.e., the topological charge of the pump beam and lasing) could be attributed to the involved nonlinear processes during the ${{\rm N}_{2}}{^{{{+}}}}$ lasing generation.

To understand the pumping pulse energy dependence of the ${{\rm N}_{2}}{^{{{+}}}}$ lasing, one should consider the nonlinear propagation effects of the intense femtosecond pump pulses. At a low pumping pulse energy (${\lt}{2.4}\;{\rm mJ}$), the laser peak intensity at the focus scales with the incident pulse energy and thus the generation of the ${{\rm N}_{2}}{^{{{+}}}}$ lasing. Meanwhile, the plasma density because of the molecular ionization increases, which has an on-axis maximum compared to the periphery of the laser beam. Due to the negative contribution of the plasma on the refractive index (i.e., ${\Delta}n = - {n_{\rm e}}/2{n_{\rm c}}$), where the ${n_{\rm e}}$ is free electron density and ${n_{\rm c}}$ is the critical density, the plasma lens created by the leading edge of the incident laser pulse diffracts the subsequent part of the pulse and thus limits the increase in the on-axis peak field intensity. This influences the efficiency of the ${{\rm N}_{2}}{^{{{+}}}}$ lasing and becomes more serious for higher incident pulse energy where most energy of the incident pulse is diffracted or formed multiple filaments. Meanwhile, the new ${{\rm N}_{2}}{^{{{+}}}}$ lasing will experience and may further be diffracted by the pump-photoionization-created plasma lens. As a result, the strength of the measured ${{\rm N}_{2}}{^{{{+}}}}$ lasing decreases as the pumping pulse energy increases to larger than 2.4 mJ.

This is, however, not the case for the vortex pumping pulse that is focused to have a doughnut-shaped beam and thus properly avoid the formation of the defocusing plasma lens. It allows more energy to be deposited into the filamentation as higher incident pulse energy. Meanwhile, the weakened defocusing plasma lens effect also causes a longer collapse distance for self-focusing, and the length of the filament plasma increases; thus, it is more efficient than the new ${{\rm N}_{2}}{^{{{+}}}}$ lasing. For instance, as displayed in Fig. 4, the filament formed by vortex pump beam is relatively longer and the energy is distributed more evenly than that produced by the Gaussian pump beam for high incident pulse energy (25 mbar, 3.25 mJ). As shown in Fig. 3(a), the measured strength of the vortex-pumped 391 nm lasing surpasses that of Gaussian-pumped one when the incident pulse energy is higher than 3.0 mJ. Note that a recent theorical work [41] shows that with an increase in the vortex TC number and the intensity parameter, the self-focusing strength of the LG beams decreases, which breaks the intrinsic equilibrium between the Kerr self-focusing and plasma defocusing. This result suggests that we could enhance the ${{\rm N}_{2}}{^{{{+}}}}$ lasing by reworking the filament process as we have demonstrated here.

 

Fig. 4. Captured images (on bottom of each curve) and corresponding signal intensity of the laser filaments for (a) Gaussian and (b) vortex pump beams when the pump pulse energy is set to 3.25 mJ. The gas pressure is 25 mbar.

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The lower 391 nm lasing generation efficiency with the vortex pump beam in a low incident pulse energy (${\lt}{2.4}\;{\rm mJ}$) case could be attributed to the relatively weak peak intensity of the pump pulse. More specifically, although we executed the same pulse energy for the vortex and the Gaussian pump beams, the peak intensity in the cross section of the vortex pump beam is conspicuously lower than that in the Gaussian one. The center with concentrated energy in the Gaussian mode turns into singularity with zero intensity in vortex mode, resulting in a more dispersive transverse energy distribution. Consequently, it is harder to meet the excitation threshold in the vortex condition; therefore, there is less efficient excitation of the ${{\rm N}_{2}}{^{{{+}}}}$ ions and a lower intensity in the 391 nm lasing.

 

Fig. 5. Transverse intensity profiles and focal images of the pump beam, external seed beam, and ${{\rm N}_{2}}{^{{{+}}}}$ lasing. (a)–(d) Transverse intensity profiles of beams taken by CMOS. (800 nm pump beam, 400 nm external seed beam, and 391 nm and 428 nm emission, similarly throughout this paper). (e)–(h) Cylinder-lens-passed intensity profiles of beams near the focus when the pump 800 nm and external seed 400 nm photon carries $\ell = 0$ and $\ell = 2$, respectively. (i)–(p) Similar to the left panels but obtained when the pump 800 nm photon carries $\ell = 1$ and the external seed 400 nm photon carries $\ell = 0$.

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The monotonic increase with the pumping energy for both the Gaussian and vortex lasing in Fig. 3(b) could be attributed to the appearance of the seed beam for 428 nm lasing at a higher pumping pulse energy: The 428 nm lasing is seeded by the supercontinuum generation, which is produced by a near-IR pump beam [13]. The wavelength distribution of the supercontinuum generation varies with the pump laser pulse energy; more specifically, a blue-broadening due to self-phase modulation in the plasma. The blue-broadening is proportional to the laser pulse energy at a given pulse duration[42,43]. At the low pulse energy (${\lt}{2.6}\;{\rm mJ}$), there is barely any components around 428 nm as a seed in the supercontinuum, which cannot lead to the generation of 428 nm lasing. This also explains why the 428 nm signal barely increases with the pumping pulse energy below a pumping threshold that is around 2.6 mJ in our measurements: The 428 nm is almost not generated in both Gaussian-pump and vortex-pump cases at the low pumping energy. When the pumping pulse energy exceeds the threshold (${\gt}{2.6}\;{\rm mJ}$), the supercontinuum generation continues to expand to the blue side, covering the band around 428 nm, and finally leading to the appearance of a 428 nm seed beam and an upsurge in the intensity of the 428 nm lasing. The positive contribution of the self-seeding offsets and outstrips the negative contribution of the plasma-induced diffraction when the incident pulse energy is higher than 2.6 mJ.

In addition to the experiment above to generate ${{\rm N}_{2}}{^{{{+}}}}$ lasing in a self-seeding scheme, in which the seed pulses [13] to trigger the ${{\rm N}_{2}}{^{{{+}}}}$ lasing are provided by the vortex pump pulses, we implemented the experiment in the external seed (400 nm) scheme (Fig. 5) to explore how the topological charges of the pump/seed pulse affect the generation of ${{\rm N}_{2}}{^{{{+}}}}$ lasing. The temporal delay between the pump and the external seed pulses was finely tuned to reach an optimal amplification. As shown in Figs. 5(a)–5(h), when the vortex ($\ell = 2$) external seed beam is amplified by a Gaussian ($\ell = 0$ ) pump beam, the new lasing emission (391 nm/428 nm) does not carry a vortex wavefront ($\ell = 0$). On the other hand, in Figs. 5(i)–5(p), the Gaussian ($\ell = 0$) external seed beam with a vortex ($\ell = 1$) pump beam leads to a lasing emission (391 nm/428 nm) that carries $\ell = 2$, which is identical to that in the preceding self-seeding experiment. The results indicate that the topological charges of ${{\rm N}_{2}}{^{{{+}}}}$ lasing are determined by that of the pump beam, not the seed beam.

5. CONCLUSION

In conclusion, we generated a vortex ${{\rm N}_{2}}{^{{{+}}}}$ lasing at 391 nm and 428 nm pumped by near-IR OAM pulses. The photon OAM of the pump beam was deposited into the light-excited rovibrational states of ${{\rm N}_{2}}{^{{{+}}}}$, which afterward transfers to the new photon of the ${{\rm N}_{2}}{^{{{+}}}}$ lasing. The TCs of the 391 nm/428 nm emission are determined to be twofold that of the pump beam. The vortex pumped lasing surpasses the Gaussian pumped one when the incident pulse energy exceeds a pumping threshold. The underlying process is simple: The vortex pump beam induces a “hollow” filament and reduces the on-axis plasma density to defocus the laser beam. It has a higher clamping intensity and benefits the ${{\rm N}_{2}}{^{{{+}}}}$ lasing generation. We believe that our findings herald a march toward structured ${{\rm N}_{2}}{^{{{+}}}}$ lasing. The transfer of phase structures and spatial modes in ${{\rm N}_{2}}{^{{{+}}}}$ lasing opens a new perspective to construct a far-field structured laser field.