Spatiotemporally confined interaction of intense femtosecond lasers and pure nitrogen or air molecules can result in laser-like emissions from N2+^[1–15], which has been one of the hottest research topics in the community of strong fields in the past decade. The two main operating wavelengths of N2+ lasing are at 391.4 and 427.8 nm, respectively. The visible property of these lasing lines makes them suitable for achieving remote atmospheric sensing, as demonstrated by many recent air-lasing-assisted experiments, which combine the advantages of the broadband femtosecond pump and the narrow band N2+ lasing^[16–19]. The femtosecond pump is beneficial for preparing rovibrational coherence of the target molecules, and the follow-up N2+ lasing is utilized to interrogate the coherence, which in principle is the same as the so-called hybrid fs/ps coherent Raman scattering^[20,21]. In spite of these significant applications, the physical mechanism regarding N2+ lasing creation is still under hot debate.

Strong-field ionization (SFI) is the first step for producing N2+ lasing. The electronic configuration of neutral N2 is (1σg)2(1σu)2(2σg)2(2σu)2(1πu)4(3σg)2^[22]. The ground state X2Σg+, the excited state A2Πu, and B2Σu+ of N2+, respectively, correspond to the removal of an electron from the orbitals of 3σg, 1πu, and 2σu. So, in a linearly polarized laser field, the yields of the population on the X2Σg+ and B2Σu+ states due to ionization are maximized when the driving laser polarization direction is along the molecular axis. A coincidence was spotted afterward that showed the transition energy between the X2Σg+ and A2Πu states of N2+ is nearly equivalent to the photon energy of the 800-nm pump, which facilitates the population transfer from the X2Σg+ to A2Πu states through Rabi oscillations^[23–25]. The resonant electronic coupling (REC) within the pump laser fields open the possibility for achieving the population inversion between the B2Σu+ and X2Σg+ states by optimizing the area of the pump pulse^[26]. The gain contribution of N2+ lasing caused by the ionization and coupling processes was analyzed from the perspective of population inversion and quantum coherence^{[10,25,27–29]}. Subsequently, this analysis was experimentally validated through typical intensity measurements. However, another essential effect brought by SFI and REC is the permanent alignment of N2+. Very recently, Gao et al. first proposed that the linear polarization of N2+ lasing can be explained based on the permanent alignment^[30]. Nevertheless, the cooperative effect of the permanent alignment and the molecular alignment on the polarization of N2+ lasing has not been fully understood in previous experiments. The main reason thereof is that the permanent alignment effect is usually deemed to be very small and cannot be decoupled from the usual intensity measurements.

In this work, we attempt to uncover and verify the pivotal permanent alignment effect in N2+ lasing by exploiting a polarization perpendicular configuration with a pump-seed scheme. The polarization arrangement circumvents the direct polarizability along the pump polarization direction induced by the seed pulse. By scrutinizing the output laser polarization, our results show that the permanent alignment effect is more pronounced when the seed intensity is extremely weak and gives rise to an unexpected lasing polarization. Meanwhile, the combined effect of the permanent alignment and the field-free molecular alignment caused by the coherent rotational wave packets on the N2+ lasing polarization is also revealed, which can result in the elliptical polarization. Our analysis indicates that the permanent alignment is due to the nonuniform distribution of magnetic quantum number M. The findings shed light on the physics of N2+ lasing and open new routes to control ionic emissions.

The experimental setup resembles the conventional pump-probe configuration, as illustrated in Fig. 1(a). Briefly, a commercial Ti:Sapphire laser system (35 fs, 4 mJ, 795 nm, 1 kHz) was used, with the output laser split into two femtosecond pulses of different intensities by a 7:3 beam splitter. The stronger beam with an energy of 1.85 mJ was employed as the pump pulse. The weaker beam with an energy of 0.5 mJ passing through a 0.2 mm thick BBO crystal was utilized to generate a frequency-doubling signal around 400 nm, which was referred to as the seed pulse. A Glan–Taylor prism was inserted after the BBO crystal to ensure the strict linear polarization of the seed pulse. A half-wave plate optimized for 800 nm was used to adjust the pump pulse polarization direction, making it perpendicular to that of the seed pulse. The time interval between the pump and seed pulses was controlled by an electric mechanical translation stage with a 0.001 mm resolution. A dichroic mirror (high reflection at 800 nm and high transmission at 400 nm) then combined the two beams, and a lens with a 30-cm focal length was used to focus them collinearly into a gas chamber filled with pure nitrogen. The forward-propagating N2+ laser signal was collimated by another 30-cm focal length lens and was recorded using an integrating sphere and a grating spectrometer (Kymera-328I, Andor) after suitable filters. The width of the entrance slit was fixed at 250 µm for all measurements.

Since the seed intensity is a key parameter in our experiments and it is difficult to directly measure, here we give a rough theoretical estimation by assuming a linear propagation of the seed pulse. In our experiments, the adopted maximum seed pulse energy is about 2 nJ, and the pulse duration is 60 fs. The incident spot size of the seed beam is measured to be 5 mm. Considering the current focusing condition, the focusing spot size of the seed pulse is about 15 µm, and the peak intensity at the focus is 9×109W/cm2. Then, other seed intensities can be calculated by spectral intensity comparisons with a grating spectrometer.

Figure 1(b) shows N2+ lasing intensities at 391.4 nm [which can be assigned to B2Σu+(ν=0)→X2Σg+(ν=0)] as a function of the pump-seed delay. The polarization of the pump and seed pulses in this scanning is kept the same, by which the overall alignment and the anti-alignment of N2+ marked by t1 and t2 can be readily described. These two moments, together with the non-alignment delay of t3, were chosen for polarization measurements in the following analysis. The signal modulations near the delays of 2, 4, 6, and 8 ps arise from the coherent rotational wave packets of N2+ via Raman-like excitation processes.

Figure 2(a) shows the comparative output polarization of N2+ lasing under the triggering of three different seed intensities at the non-alignment delay t3 by rotating the angle ϕ of a polarization analyzer installed in front of the spectrometer. Three seed intensities of 9×109, 2.1×108, and 3.7×107W/cm2 are employed in the experiments, which are marked by Seed 1, Seed 2, and Seed 3, respectively. The pump and seed polarization directions are mutually perpendicular and separately denoted by the red and blue arrows, i.e., ϕ=90° and ϕ=0°. It can be seen that at a relatively high intensity of the seed pulses (i.e., Seed 1), the N2+ lasing is linearly polarized and follows basically the polarization direction of the seed pulse. The measured result is consistent with the previous measurements^[29–31]. Interestingly, as the seed intensity decreases, the polarization direction of the N2+ lasing gradually deflects from that of the seed pulse. The deflection angles for the cases of Seed 2 and Seed 3 are around 30° and 43°, respectively. We will analyze the origins thereof later. Figure 2(b) shows the signal intensity ratio when the polarizer angle ϕ=90° and ϕ=0° at the three different seed intensities. The lasing component along the pump polarization apparently decreases with the increasing seed intensity. Since the seed pulse energy is too low to measure, we recorded their spectra, as shown in the inset of Fig. 2(b). The intensities of Seed 2 and Seed 3 are magnified by a factor of 10 for comparisons.

Another critical factor that can influence the polarization characteristics of N2+ lasing is molecular alignment induced by the coherent rotational wave packet of N2+. To verify this, we performed similar polarization measurements at the alignment delay t1 and anti-alignment delay t2. The results for the cases of strong and weak seed pulses are presented in Figs. 3(a) and 3(b), respectively. Note that the seed intensity in these cases is a bit different from those in Fig. 2. The strong and weak seed intensities are 6.3×108 and 4.2×107W/cm2, respectively. The left panel shows that N2+ lasing is linearly polarized and follows the seed polarization direction at the delay of t2, whereas at the delay t1, a slight deflection angle of 10° is observed relative to the seed polarization direction. Additionally, for the case of weak seed pulse triggering, the polarization direction of the N2+ lasing is deflected by approximately 25° from the seed pulse polarization at the delay of t2. Surprisingly, at the alignment delay t1, N2+ lasing becomes elliptically polarized with its main axis along the seed polarization. The ellipticity of N2+ lasing reaches as high as 0.86. For a direct comparison, we also measured the polarization state of N2+ lasing induced by the pump laser alone by blocking the seed laser pulse, as shown by the gray curves in Figs. 3(a) and 3(b). In this case, the N2+ lasing strictly follows the pump laser polarization since the self-seeding pulse polarization is always the same as that of the pump laser.

The comparison of typical spectra of the lasing component along the seed polarization (i.e., ϕ=0°) and that along the pump polarization (i.e., ϕ=90°) at the delays of t1 and t2 by the strong and weak seed pulses is plotted in Fig. 3(c). The lasing component along the seed polarization is significantly stronger than the lasing component along the pump polarization for the case of the strong seed pulse. However, for the case of excitation by the weak seed pulse, the lasing component along the pump polarization becomes comparable to the lasing component along the seed polarization despite the perpendicular polarization arrangement, resulting in the peculiar polarization observed in Fig. 3(b).

To further study the observed elliptical polarization phenomenon, we conducted similar polarization measurements for different seed intensities while the pump-seed delay was fixed at t1. The results are presented in Fig. 4. It can be seen that when the seed intensity is above 4.3×109W/cm2, the output polarization of N2+ lasing follows that of the seed polarization. When the seed intensity is decreased to 1.6×108W/cm2, the output lasing maintains linear polarization but deviates from the seed polarization with a deflection angle of nearly 30°. Moreover, at the lowest seed intensity of 7.6×107W/cm2, the output N2+ lasing becomes elliptically polarized, which is close to 0.5.

The complicated polarization of N2+ lasing is related to its gain and amplification mechanisms, which has been in hot debate over the last several years. Specifically, the output polarization depends on the spatial distribution of N2+ upon the arrival of the seed pulse. To describe the spatial anisotropy of N2+, the value of ⟨cos2θ⟩ summing over all the rotational states J and magnetic quantum number M can be calculated^[32–34]. θ denotes the angle between the molecular axis and the pump laser polarization direction. This is to say, the distributions of quantum numbers J and M play a pivotal role in molecular spatial arrangements, which can be influenced by several processes.

First, the non-resonant Raman-like rotational excitation of neutral N2 before ionization could result in a coherent rotational wave packet composed of many higher rotational states relative to the initial rotational distribution at the thermal equilibrium state^[33,34]. In the process, the quantum number M is preserved. The revival of the coherent rotational wave packet after the pump interaction, i.e., the phase revival of the rotational state J, causes the well-known field-free molecular alignment^[33,34]. Additionally, the higher rotational population distribution can cause a small permanent alignment, which is usually reflected by a baseline improvement in the calculated curve of ⟨⟨cos2θ⟩⟩. The alignment degrees due to the phase revival and population would decay in the presence of inelastic collisions^[35].

Second, the transient ionization and resonant electronic couplings mediated by the alternating current (AC) Stark effect can result in a certain permanent alignment^[30,31], which is overlooked in the studies of N2+ lasing. Since M is the projection of J on the spatially fixed z-axis (the same direction as the pump laser polarization), for parallel transitions, the rotational state M=0 is more likely to be excited than the rotational state M=J^[36]. For the M=0 state, the molecular axis is always in the plane containing the z-axis, whereas for the M=J state, the molecular axis is always in the plane perpendicular to the z-axis and results in ⟨cos2θ⟩=0. For the current N2+ system, the electronic states of X2Σg+ and B2Σu+ are prepared through tunneling ionization from the HOMO and HOMO-2 orbitals, respectively. According to the MO-ADK theory^[37], their ionization possibility, depending on the value of the quantum number M, is maximized when the molecular axis is parallel to the pump laser polarization. Hence, the average alignment of the generated N2+ on both the B2Σu+ and X2Σg+ states is along the z-axis, which means that M is close to 0, and permanent alignment is naturally created. In addition, the electronic coupling immediately after ionization between ionic states can further change the M-state distribution since the coupling between the states of X2Σg+ and A2Πu belongs to the perpendicular transition, while the coupling between the states of B2Σu+ and X2Σg+ belongs to the parallel transitions^[23,24]. These two coupling transitions generally cause the enhancement of the permanent alignment of N2+ on the B2Σu+ and X2Σg+ states along the pump polarization direction. Note that the distribution of rotational state J because of ionization is regarded as invariably fundamental, and the permanent alignment of N2+ primarily originates from the nonuniform distribution of magnetic quantum number M.

Knowing that a certain permanent alignment along the pump laser polarization direction can be induced after the pump laser interaction, the elusive polarization results in Figs. 2(a) and 3 can be interpreted as follows. At the non-alignment delay t3, for a strong seed pulse, the polarizability along the seed polarization direction is the largest, and the amplification of N2+ lasing at 391 nm can be basically completed within the seed pulse duration according to our recent experimental results^[38], which leads to the same polarization of N2+ lasing with the seed pulse. However, when the seed pulse intensity is quite weak, the retarded time required for establishing macroscopic quantum coherence becomes longer^[7]. At this time, the polarization intensity along the pump laser polarization due to the existence of the permanent alignment can be comparable with that along the seed polarization direction, which causes a small deflection angle in the measured polarization for the cases of Seed 2 and Seed 3 in Fig. 2(a). Moreover, the deflection angle increases with the decreasing seed intensity due to the increasing polarization ratio of I(ϕ=90°)/I(ϕ=0°). It deserves mentioning that there is no significant phase delay between the polarization components along the pump laser polarization and that parallel to the seed polarization in these cases, giving rise to a linear polarization of N2+ lasing.

Moreover, apart from the permanent alignment, the molecular alignment induced by coherent rotational wave packets can also change the spatial anisotropy of N2+^[31]. In Fig. 3(a), we note that a small deflection angle of 10° can be discerned in the measured N2+ lasing polarization with respect to the seed polarization at the alignment delay t1, under the triggering of a relatively intense seed intensity. This deflection is ascribed to the nonnegligible polarization along the pump polarization due to the combined contributions of molecular alignment and permanent alignment. As for the generated elliptical polarization in Fig. 3(b) at the alignment delay t1, we speculate that there are at least two different amplification mechanisms that compete mutually for the weak seed pulse triggering, and a certain phase delay exists between them. The output polarization of N2+ lasing in our cases is mainly determined by three factors, the permanent alignment, the molecular alignment, and the seed intensity. The first two factors determine the spatial arrangement of N2+ and the gain anisotropy. The magnitude of the seed intensity could show a critical impact on the spatially nonuniform amplification and the involved amplification mechanisms. A further time characterization of their time profiles is required, which will be performed in our future work.

We reveal and demonstrate the extremely significant contribution of permanent alignment to the polarization of N2+ lasing using a perpendicular polarization configuration in a pump-seed scheme. Our results show that the output polarization of N2+ lasing can deviate from that of the seed pulse and can even become elliptical polarization under the triggering of a weak seed pulse. The elusive polarization phenomenon is explained by molecular alignment and permanent alignment caused by the processes encapsulating Raman-like rotational excitation, strong-field ionization, and electronic couplings. Our further analysis indicates that the permanent alignment is in essence due to the anisotropic distribution of the quantum number M, which is responsible for elucidating N2+ lasing polarization. These findings offer new ingredients for ionic laser physics and open new routes for controlling N2+ air lasing intensity by manipulating either the coherent rotational wave packet or strong-field ionization and coupling procedures.