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Abstract
Nitrogen ions pumped by intense femtosecond laser pulses give rise to optical amplification in the ultraviolet range. Here, we demonstrated that a seed light pulse carrying orbital angular momentum (OAM) can be significantly amplified in nitrogen plasma excited by a Gaussian femtosecond laser pulse. With the topological charge of ℓ = ±1, we observed an energy amplification of the seed light pulse by two orders of magnitude, while the amplified pulse carries the same OAM as the incident seed pulse. Moreover, we show that a spatial misalignment of the plasma amplifier with the OAM seed beam leads to an amplified emission of Gaussian mode without OAM, due to the special spatial profile of the OAM seed pulse that presents a donut-shaped intensity distribution. Utilizing this misalignment, we can implement an optical switch that toggles the output signal between Gaussian mode and OAM mode. This work not only certifies the phase transfer from the seed light to the amplified signal, but also highlights the important role of spatial overlap of the donut-shaped seed beam with the gain region of the nitrogen plasma for the achievement of OAM beam amplification.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Cavity-free lasing of air molecules or their derivative under excitation of intense ultrafast laser pulses are fascinating phenomena and has attracted many attentions in recent 10 years [1–11]. With properly chosen wavelengths of the pump laser, it has been demonstrated that many species of the air plasma, including N2+, N2, O atom, CO2+, even water vapor, can serve as gain media and produce coherent optical emission in the forward and/or the backward directions [6–9,12–15]. Air lasing is interesting from the perspective of fundamental research due to the rich high-field effects involved. In the mean time, it holds unique potential for optical remote sensing since it can provide a coherent optical beam from the sky to the ground observer. Among the different kinds of air lasing effects, the lasing of $N_2^ + $ has obtained most of the attentions [16–19]. This is not only due to the abundance of N2 in air, but also to the fact that these lasing effects can be activated by the intense 800 nm femtosecond pulses delivered by Ti: Sapphire laser system [3,20–23], which is the most widely available laser in the ultrafast optics labs. Under the excitation of 800 nm femtosecond laser pulses, nitrogen ions emit coherent 391.4 and 427.8 nm emission in the forward direction. With the injection of external seed pulse around these two wavelengths, it has been widely observed that significant optical amplification by 2-3 orders of magnitude can be obtained [24]. These two wavelengths correspond to the optical transitions of the second excited states of nitrogen ions ${\textrm{B}^2}\mathrm{\Sigma }_\textrm{u}^ + ({\nu^{\prime} = 0} )$ to the ground state ${\textrm{X}^2}\mathrm{\Sigma }_\textrm{g}^ + ({\nu = 0,\; 1} )$, where ν’ and ν denote the vibrational quantum number of the corresponding states. Although the mechanism for the optical amplification for $N_2^ + $ lasing is still under debated, its characteristics have been found to be in consistent with superfluorescence in many measurements [25–27]. While in most of the previous studies linearly polarized 800 nm femtosecond pulses were employed, several other forms of pump laser fields, including two color counter-rotating fields [28], polarization screwed optical pulse [29], have been used to clarify the physical mechanism or to improve the conversion efficiency. Recently, structured light has attracted great interest [30–32]. In 2023, the concept of orbital angular momentum (OAM) was also introduced to the study of $N_2^ + $ lasing [33,34].
Some of the current authors have demonstrated, for the first time, that a vector or vortex pump pulse can generate an amplified 391.4 nm emission with vector or vortex properties [33]. In particular, it was shown that a femtosecond vortex pump pulse with a topological charge of ℓ = 1 can directly generate a vortex beam at 391.4 nm carrying OAM with ℓ = 1, and can also amplify an external conventional Gaussian seed beam into an vortex beam with ℓ = 1. This opens a new degree of freedom for the study of $N_2^ + $ air lasing and holds unique potential for the remote generation and amplification of OAM beams in ambient air. Soon later, Y. Hu et al. also employed a vortex pump or seed pulse to produce $N_2^ + $ lasing effect [34]. They claimed that an OAM seed pulse with ℓ = 2 was amplified into a conventional Gaussian beam when the nitrogen gas was pumped by a Gaussian beam, and then drew a conclusion that the topological charges of N2+ lasing is not influenced by that of the seed beam. This is surprising since one would expect that the spatial spiral phase information of the seeding pulse will be encoded in the amplification process and an amplified emission with OAM should be expected.
In this work, we employed a Gaussian femtosecond laser pulse to excite a nitrogen gas plasma and injected a seed pulse with OAM of ℓ = ± 1. It was observed that the seed pulse can be significantly amplified by about 1000 times, and the amplified emission inherits the topological charge of the incident seed pulse, in contrast with the recent report by Y. Hu et al where they claimed that the OAM seed pulse was amplified with the OAM property lost. We further show that the spatial alignment of the pump laser-induced plasma with the seed beam plays an important role, i.e., a misalignment leads to degeneracy of the amplified OAM beam to a Gaussian beam. This work opens the avenue of OAM beam amplification in $N_2^ + $ air lasing.
2. Experimental setup
The schematic of the experiment is depicted in Fig. 1. A commercial Ti: Sapphire femtosecond laser system (Legend-Elite-Duo HE+, Coherent Ltd) was employed in the experiments. The laser system produces 35 fs pulses at a central wavelength of 796 nm, at a repetition rate of 1 kHz. The output femtosecond laser pulses were split into two replica, one pulse serves as the pump pulse with a pulse energy of ∼3 mJ, and the other pass through a BBO crystal to generate its second harmonic around 398 nm. A spiral phase plate (SPP) was installed on the seed beam path to obtain an OAM seed pulse with the topological charge of ℓ = ± 1. As shown in the inset of Fig. 1, the beam profiles of the pump and seed pulses are Gaussian and donut-shaped, respectively, which are recorded by a charge-coupled device (CCD). The Gaussian pump pulse and the OAM seed pulse are collinearly combined by a dichroic mirror (DM) with high reflectivity around 400 nm and high transmission around 800 nm. They are then focused by a lens (L1) with a focal length of 30 cm into the gas chamber filled with 20 mbar nitrogen gas. After the chamber, the lasing emission from the nitrogen gas plasma is collimated by a lens (L2), spectrally filtered by a shortpass filter at 650 nm and two narrow bandpass filters at 390 ± 5 nm. The emission signal is recorded by a fiber spectroscopy or a CCD.
Fig. 1. Schematic diagram of the experimental setup. The seed pulse around 400 nm with the topological charge of ℓ = 1 was generated by a spiral phase plate (SPP). Inset: The spatial profile of the pump and seed beams.
3. Results and discussion
First, the vortex seed beam with the topological charge of ℓ = 1 is employed. The spectra of the emissions are shown in Fig. 2. The signal at 391 nm is associated with the transition of ${\textrm{B}^2}\mathrm{\Sigma }_\textrm{u}^ + ({\nu^{\prime} = 0} )\to {\textrm{X}^2}\mathrm{\Sigma }_\textrm{g}^ + ({\nu = 0} )$. When nitrogen gas is pumped by only the pump pulse, there is a very weak self-seeded signal [4]. With the injection of the OAM seed pulse at an optimal delay (∼ 200 fs), the intensity of the amplified signal is around 900 times as that of the seed beam. The corresponding spatial beam profiles of the seed and the amplified signal are shown in Fig. 3(a) and (c) . The beam profile of the seed pulse with an intensity singularity is the typical shape generated by the SPP, and we can notice the boundaries between the neighboring areas because the thickness of the SPP is not continuously varied. One notes that the amplified signal is donut-shaped and also have an intensity singularity, indicating that it may be an OAM beam. The emission intensity changes with the time delay between the pump and seed pulses, keeping the donut-shape unaltered. To measure the topological charge of the amplified pulses, we focus it by a cylindrical lens. The image at the focus is shown in Fig. 3(d). It is evident that the topological charge of the amplified signal is 1, identical to that of the seed beam whose focal image is shown in Fig. 3(b). Then we set the topological charge of the seed to be −1 by turning the back surfaces of the SPP to the front, presented in Fig. 3(f). The corresponding spatial beam profiles of the seed and the amplified signal are shown in Fig. 3(e) and (g). Their cylindrically focused images show that the topological charge of the amplified signal becomes ℓ = −1, as shown in Fig. 3(h).
Fig. 2. The spectra of the amplified OAM pulse (red line), the seed pulse (black line), and the self-seeded 391.4 nm emission produced by only the pump pulse (blue line). An amplification of the seed intensity by 900 times is evident.
Fig. 3. Beam profile and corresponding cylindrically focused images of the seed and the amplified signal. (a)-(b), seed beam with ℓ = 1 and the image of its focus. (c)-(d), the corresponding amplified signal and the image of the focus. In (e)-(f) and (g)-(h), the topological charge is ℓ = - 1.
The above experimental results suggest that the spatial helical phase structure of the seed beam is recorded in the amplified emission signal. This observation is in accordance with a recent study, which demonstrated the conservation of high-order OAM during amplification in the Ni-like krypton plasmas generated from gas targets [35]. In addition, the study also presented that the plasma inhomogeneities, density gradients, asymmetries, etc could modify or even destroy the OAM carried by the seed [35]. In our experiment, the OAM carried by the seed is well conserved in the amplification process.
Our experiment results also meet the theoretical expectations of stimulated emission radiations and superfluorescence [36–38]. That is, the spatial phase of the amplified signal originates from the seed beam in a point-to-point manner in space, which means that the helical phase relationship between different spatial points in the seed beam is maintained in the amplified signal. To be specific, with the injection of the vortex seed pulse, the slowly varying part of the induced dipole moment of a nitrogen ion is given by [36,37]
where $\hbar $ is the reduced Planck constant, $\gamma $ is the decay rate from the B to the X state, ${d_{BX}}$ is the transition dipole moment between the B and X states of N2+, $E({x,y,z} )$ is the electric field of the seed pulse in the gain medium. Because the pump and seed light fields are both x-polarized, all equations are expressed in the scalar form. We assume the injected seed light field is $E({x,y,z = 0} )= {E_0}{e^{i\ell \phi }}$, where ${e^{i\ell \phi }}$ is Hilbert factor possessing the spiral helical phase structure. The gain medium is a large number of ionized nitrogen molecules. The slowly varying amplitude of the macroscopic polarization of the gain medium is expressed as where $N({x,y} )$ represents the average inversion number of nitrogen ions per unit volume, which is determined by the cross section of the pump beam. If the pump beam profile is donut-shaped, $N({x,y} )$ will be donut-shaped too. To make the physical relationship clear, here we only consider the propagation term and neglect the diffraction effect. Thus, the wave equation (under the condition of a slowly varying approximation) is expressed as where k is the wavenumber, $\mu $ is the permeability, $\omega $ is the angular frequency. The Eq. (3) has an analytic solution, namely, where A represents the amplification coefficient and is expressed as $N({x,y} )\mu {\omega ^2}d_{BX}^2/2k\hbar \gamma \; $. As the Eq. (1)–(4) present, the spatial helical phase term, ${e^{i\ell \phi }}$, naturally transfers from the seed beam $E({x,y,z = 0} )$ to the dipole moment $p({x,y,z} )$.The macroscopic polarization $P({x,y,z} )$ takes this spatial phase information and finally it is transferred to the output signal $E({x,y,z = L} ), $ in the amplification process.In contrast, surprisingly, Y. Hu et al. claimed that a vortex seed beam with ℓ = 2 was amplified into a Gaussian beam when pumped by an 800 nm Gaussian light [34], leading to the conclusion that the topological charges of N2+ lasing are not influenced by that of the seed beam, namely, the spatial helical phase structure of the vortex seed beam was wiped off in the amplification process in $N_2^ + $ lasing. Our experimental observations are in sharp contrast with the results by Y. Hu et al. We found that the spatial alignment of the pump and the seed pulses is crucial for the spatial mode of the output signal. The Gaussian pump pulse produces a thin plasma channel in nitrogen gas that serves as an optical amplifier with maximum gain at the transverse center. In contrast, the seed beam exhibits a donut-shaped profile, where the intensity is null at the center. Therefore, to achieve a uniform optical amplification of the vortex seed beam, the spatial overlap of the donut-shaped seed pulse with the thin plasma gain medium turns out to be important.
In the experiments, we intentionally tilted the DM in the left, right, up and down directions to introduce misalignment of the pump and seed pulses. As shown in Fig. 4, the output modes become to be Gaussian mode with topological charge of ℓ = 0, instead of the OAM mode shown in Fig. 3. The schematic diagrams of the spatial overlap between the seed and pump beams is showed at the upper right corner of each panel, in which the red circles and the blue rings respectively represent the pump and the seed beam. We also noticed that the amplification ratio here is larger than that in Fig. 3. This is because a certain portion of the donut-shaped seed beam with higher intensity overlaps with the center of gain region.
Fig. 4. Effect of misalignment of the focus of the OAM seed pulse with respect to the thin plasma amplifier created by the pump laser. In (a)-(d), the seed pulse was intentionally misaligned in the up, down, left, right directions, as illustrated by the insets.
To intuitively demonstrate the impact of spatial overlap on the results, we have recorded a video that dynamically captures how the tilting of the DM changes the spatial mode of the amplified signal. As shown in Fig. 5, we picked two frames of the video before and after adjusting the y-direction screw of DM. We strongly recommend the readers to watch the full video in Supplementary Material, as it visually demonstrates this process.
Fig. 5. Frames of the supplementary video correspond to (a) before and (b) after adjusting the y-direction screw of DM. See the full video in Visualization 1 of Supplementary Material. The bottom left illustration shows the images captured by the CCD and synchronized with the computer screen.
Instead of introducing misalignment of the pump and seed beam, we have also displaced the SPP, to spatially shift the position of the singular point of the seed beam while the alignment of the pump and seed beams remains untouched. The corresponding results are also presented in the video (see Visualization 1 of Supplementary Material). When the SPP is moved to any directions, there is one position that the amplified signal exhibits Gaussian mode. We also show these results in Fig. 6. Therefore, it becomes clear that the spatial alignment of the pump and OAM seed pulses (Fig. 4) and a spatially well positioned phase singularity of the seed beam (Fig. 6) are both crucial for the achievement of an amplified vortex emission. From a technical perspective, we can easily switch back and forth between Gaussian mode and vortex mode in such a cavity-free amplifier, which can be employed as an optical switch of OAM.
Fig. 6. Profiles of the seed pulse (a-d) and amplified emission (e-h) when the SPP is shifted to up, down, left and right sides. Insets are the illustrations of spatial overlap where red circle represents pump beam and the blue donut shape represent the seed beam.
To get insight into the effect of the misalignment of the Gaussian pump and vortex seed beams, we have employed numerical simulations to study the evolution of both the intensity and phase distribution of the OAM seed beam during amplification along propagation. Because the evolution of the spatial mode is concerned, the diffraction effect presented by the Laplacian term should now be considered in the wave equation and the time dependence of the quantities are neglected. Thus, Eq. (3) becomes
Fig. 7. Numerical simulation results of the OAM seed beam along propagation in plasma gain media of 10 mm. In (a) the seed beam is well aligned with the pump, while in (b) the two beams are misaligned in the horizontal direction. In both (a) and (b), the upper row show the intensity distribution and the lower row corresponds to the spatial phase distribution. The amplification ratio at z = 0 mm, 2.5 mm, 5 mm, 7.5 mm and 10 mm is about (a) 1, 6, 34, 170 and 689, respectively; (b) 1, 6, 48, 414 and 3812, respectively.
As a final remark, we would like to point out that the intensity of the vortex seed pulse is not so crucial for the observation of an amplified OAM beam. In our experiments, we have reduced the intensity of the vortex seed light to the detection limit of the spectrometer while we increased the integration time of the spectrometer by 2000 times in comparison to that of the 391 nm lasing. We found the output signal is also an amplified vortex beam, whose intensity is ∼12000 times as that of the attenuated seed light (see the video in Visualization 1 of Supplementary Material), and the intensity is still much higher than that of the self-seeded signal. This means that the helical phase structure of the seed beam is always maintained in the output signal, even though its input intensity is too weak to be measured. These observations support the statement in our recent work [33]: the fully extinguishing of the parasitic second harmonic of the pump light generated by the waveplates is very necessary when the 800 nm pump light is a vortex beam with ℓ = 1. Otherwise, when pumped by 800 nm pulse alone, the parasitic second harmonic at 400 nm will play the role of an external seed pulse carrying 2 units of OAM, resulting in the output of a vortex amplified signal that also carries 2 units of OAM. In particularly, the amplified signal of N2+ lasing seeded by the parasitic second harmonic can be easily misidentified as a self-seeded signal. This could complicate the observation and interpretation of experimental results, even if the intensity of the parasitic second harmonic is very weak.
4. Conclusion
In conclusion, we have shown that a weak 400 nm seed pulse carrying OAM of ℓ = ±1 can be substantially amplified in the nitrogen gas plasma excited by an intense 800 nm femtosecond Gaussian pulse, with the OAM property well maintained. This is different from a recent report that an OAM seed pulse was amplified into a conventional Gaussian beam in the amplification process. We found that the misalignment of the pump and seed pulse at the common focus can lead to the degeneracy of the amplified OAM beam (ℓ = ±1) into a conventional Gaussian beam (ℓ = 0). This sensitive dependence of the OAM amplification should be due to the particular spatial intensity and phase distribution of the seed pulse at the focus, where it manifests as a donut-shaped profile with an inner singular spot. Consequently, a misalignment of the donut-shaped seed pulse with the pump-induced plasma can break the cylindrical symmetry and leads to amplification into a Gaussian beam. From a technical perspective, we can easily switch the output signal back and forth between Gaussian mode and vortex mode in such a lasing system by simply shifting the SPP. These results complement the previous study in which we found that the phase information of the pump pulse is transferred to the final lasing radiation [34]. This study unambiguously shows that seed pulse with OAM can be amplified in the nitrogen gas plasma via a cavity-free process and opens the avenue of OAM beam amplification in remote atmosphere, which can be interesting for free-space optical communication, remote sensing, as well as quantum information relay.
Funding
National Natural Science Foundation of China (12034013, 12174011); National Key Research and Development Program of China (2018YFB2200401).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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