1. Introduction

Cavity-free lasing of ambient air (nitrogen, oxygen) pumped by ultrafast laser pulses has opened the perspective to perform optical remote sensing with a directional coherent laser beam emitted from the sky to the ground observer [1–12]. This is in strong contrast with the traditional Light Detection and Ranging (LIDAR), where the incoherent scattered photons or the fluorescence of the target molecules in the atmosphere excited by a forward-propagating laser was collected by a telescope on the ground. The directionality and coherent nature of the backward propagating air laser beam promises significant improvement of the sensitivity of remote sensing [1–4,13]. Up to now, both oxygen and nitrogen have been shown to be able to emit lasing radiation under proper pump conditions. The bidirectional near-infrared emission at 845 nm of oxygen atoms has been identified due to population inversion promoted by two-photon dissociation followed by a resonant two photon absorption of the oxygen molecules [1,2,6,14]. In the meantime, the lasing emission of singly ionized nitrogen molecules has been intensely debated concerning its nature and mechanism [3,7–9,15–20]. This is partially due to the complexity of this emission process, where the electronic, vibrational, and rotational freedom of the nitrogen molecules are all coupled by the strong laser field [3,15,16,19]. Moreover, it is found that the pump laser wavelength also plays a critical role and different mechanisms can be involved for 800 nm or mid-infrared pump pulses [16,18].

A remarkable observation of the nitrogen ion lasing is that a delayed seeding pulse around 391.4 nm can be significantly amplified, up to a few hundred times, as to its energy [5,15–17]. Several interpretations have been proposed for this optical amplification, such as population inversion mediated by the intermediate $A^2{\Pi }_u$ state [8,16], transient inversion due to molecular rotational wavepackets [21,22], inversion of partial rotational quantum levels without entire inversion of the $B^2{\Sigma }_u^{+}$ and $X^2{\Sigma }_g^{+}$ electronic levels [19]. Recently, it was revealed with time-resolved technique that the amplified 391.4 nm radiation actually largely lags behind the injected seeding pulse [5,17,23]. More specially, the amplified pulse shows a pressure dependent temporal profile. With increasing nitrogen gas pressure p, both the built-up time τ_d and the pulse width τ_w decrease as p⁻¹, while the emission peak intensity scales up as p², which are characteristic for superradiance [17,23–25]. Superradiance refers to a cooperative emission process of an ensemble of emitters where a large macroscopic coherence built up, which is normally initialized by spontaneous photons or externally seeding pulse [24,25]. After the initialization, macroscopic coherence between the two involved energy levels increases with time, and when it is large enough, huge superradiance pulse is released. This process is revealed by theory, however the increase of the polarization in the process is rarely observed directly although the superradiant pulse implies it.

In this paper, we examined the buildup and the increase of the macroscopic coherence in the nitrogen ions lasing system by injecting two seeding pulses at the resonance wavelength (391.4 nm) after the 800 nm pump pulse. In the experiment, it was found that the amplified 391.4 nm emission experiences strong intensity modulation with a period of 1.3 fs as the delay between the two seeding pulses were finely tuned. This period corresponds to the transition frequency between the $B^2{\Sigma }_u^{+}$ and $X^2{\Sigma }_g^{+}$ electronic levels. The variation of the coherent modulation contrast on the delay time between the two probe pulses was studied for different intensity ratio of the two seeding pulses, where different behavior of the modulation contrast revealed the buildup of the macroscopic coherence. We theoretically considered the nitrogen ions as a two-level system, interacting resonantly with the two seeding pulses. It is shown that the relative phase (delay) of the two seeding pulse causes a dynamic modulation on the coherence, which leads to the intensity variation during the superradiant emission process.

2. Experimental setups

The laser pulses are delivered by a Ti: Sapphire amplification system at 800 nm wavelength with pulse energy of 3.6 mJ, pulse duration of 40 fs and repetition rate of 1 kHz. The output laser beam is split into two parts with a beam splitter. The main pulse of 2 mJ energy is used as the pump pulse to ionize nitrogen gas. Another beam passed through a 0.1 mm thick Beta barium borate (BBO) crystal to generate second harmonic pulse around 391 nm. The second harmonic pulse is further split into two beams. Each UV beam pass through a high precision mechanic delay line with a resolution of 10 nm, corresponding to a temporal resolution of 33 attoseconds. Then the two UV beams were combined together by another beam splitter. The pump pulse at 800 nm and the seeding pulse sequence were combined with a dichromatic mirror, presented in Fig. 1. The relative time delay between the three pulses can be changed with the two mechanic delay lines. The three pulses were focused together with an f = 200 mm lens into a gas chamber filled with nitrogen gas at different pressures. A visible plasma was formed due to photoionization by the intense laser field. After the nonlinear interaction inside the gas chamber, the radiation around 391.4 nm was analyzed with a spectrometer. Since we concentrated on UV emission from the nitrogen ions, the strong pump pulse around 800 nm and the accompanying white light were suppressed with proper glass filters before detection.

 

Fig. 1 Experimental setup for coherent modulation of the nitrogen ions superradiance. The pump pulse at 800 nm and the seeding pulses pair around 391 nm were combined together by a dichromatic mirror (DM). They were focused by an achromatic lens of f = 200 mm in a gas cell filled with nitrogen gas. The forward radiation was spectrally filtered and further measured with a spectrometer. The relative delay between the pump and the first seeding pulse τ_ps and the delay between the two seeding pulse τ_ss can be separately controlled with two mechanic delay lines.

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3. Experimental results

We first characterized the optical amplification and superradiance behavior of the 391.4 nm emission by injection of one seeding pulse. The gas pressure is 7.2 mbar and the delay time of the seeding pulse to the pump pulse τ_ps is set fixed about 0.75 ps. The results are presented in Fig. 2.

 

Fig. 2 (a) Amplification of the seeding pulse. The intensity of the seeding pulse was multiplied by a factor of 20 for easy comparison. Inset, comparison of seeding pulse and the amplified emission with zoomed vertical scale. (b) Time-resolved 391.4 nm signal measured by cross-correlation method with two different seeding intensity. The seeding pulse intensity was doubled from the pink curve to the black curve. The weak peak around 0.75 ps corresponds to the seeding pulse.

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In the presence of the seeding pulse, a strong amplified emission around 391.4 nm and 388.5 nm was obtained, which correspond to the P and R branch of the $B^2{\Sigma }_u^{+}$ to $X^2{\Sigma }_g^{+}$ transition in Fig. 2(a). Time-resolved measurement of this amplified 391.4 nm was performed with a crossed correlation method similar to ref [5,17], where the 391.4 nm pulse was frequency mixed with another weak 800 nm probe pulse in a sum-frequency BBO crystal and the sum-frequency generation signal at 263 nm was measured for varying delay between the 391.4 nm radiation and the weak 800 nm probe pulse. We presented the results in Fig. 2(b) for different intensities of the seeding pulse. We note that the amplified 391.4 nm emission lags largely behind the femtosecond seeding pulse, in agreement with the previous reports [17,23]. With increased intensity of the seeding pulse, it was observed that the emission built up more rapidly. This is expected since the seeding pulse serves as the initial trigger for the formation of the macroscopic coherence during the superradiance process [25,26]. The sharp emission peaks around 8.4, 12.6, and 16.8 ps were revealed in our measurement, which corresponds to the quantum alignment of the nitrogen molecular ions [21,27].

Then we injected a pair of seeding pulses with the same intensity inside the nitrogen gas plasma. The spectrum of the emission was recorded as a function of the time delay τ_ss between the two seeding pulses. In this experiment, the delay of the first seeding pulse with respect to the 800 nm pump was fixed to be around 0.3 ps. We present in Fig. 3 the experimental results. In Fig. 3(a), strong variation with modulation depth about 48% of both the P and R branch is observed when the delay was finely changed, with a delay τ_ss in the vicinity of 3 ps. The modulation period was determined to be 1.3 fs after a Fourier transformation of the data in Fig. 3(a) with larger temporal window, in consistent with the oscillation period of 391.4 nm polarization. We have performed such measurements at different delays and some results are shown in Figs. 3(b) and 3(c). Significant modulation with 1.3 fs period can be observed for longer delay τ_ss up to 13 ps in our experiments.

 

Fig. 3 (a) Spectrum of the forward UV emission around 391.4 nm as a function of the delay τ_ss between the two seeding pulses. The nitrogen gas pressure was 4 mbar. (b) and (c) Spectrum intensity at 391.4 nm versus fine tuning of τ_ss for different rough time delay τ_ss. In (a) and (b), τ_ss is about 3 ps while it is about 5 ps for (c).

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Considering of the narrow bandwidth of the 391.4 nm emission, interference of the seeding pulses can also lead to intensity modulation on time scale determined by the inverse frequency width of the spectral component, which can be largely longer than the duration of the femtosecond seeding pulse. Therefore, to get further insight into this signal modulation, we examined the variation trend of the modulation contrast on the delay τ_ss at different intensity ratio of the two seeding pulses. We defined the modulation contrast η as the absolute value of η = (I_max - I_min) / (I_max + I_min), where I_max and I_min are maximum and minimum 391.4 nm intensity. In Fig. 4, we presented the results for three different intensity of the second pulse while the intensity of the first pulse is fixed. For the case of I_s2 = I_s1, a monotonous decrease of the modulation contrast was observed. For larger intensity of the second seeding pulse of I_s2 = 2I_s1 and I_s2 = 4I_s1, we noticed that the contrast first increases and then decreases. And the maximum modulation occurred at longer delay time for larger intensity of the second pulse. This can only be understood by the coherent interaction of the dipole induced by the two pulses. With interference effect of the two seeding pulses, one can only expect a maximum modulation contrast when the two pulses overlap with each other at near zero time delay. This confirms what we observed is not induces by interference of the two seeding pulses. A full understanding of these results will only be possible in the framework of a complete Maxwell-Bloch equation describing the interaction of the resonant seeding fields with the two-level molecular system, as well as the formation process of the superradiance [25,26]. Here we would like to discuss qualitatively the main reasons underlying these observations.

 

Fig. 4 Experimental result of the superradiance modulation contrast as a function of the time delay τ_ss, for different ratio of intensity between the two seeding pulses. The points are experimental data, and the lines are for eye guide.

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4. Discussion

For the purpose of understanding the fundamental mechanism of this coherent modulation effect, here we consider a simple model of two-level system, where level 1 is the ground state $X^2{\Sigma }_g^{+}$ and level 2 is the excited state $B^2{\Sigma }_u^{+}$. The fine vibrational and rotational levels of the two levels are not considered here since we concentrate on the coherence of the electronic levels. We assume that the system has initial population distribution ρ₁₁(0) and ρ₂₂(0) as well as the initial coherence (dipole) ρ₁₂(0) = 0 at t = 0 after the first 800 nm pump field passes through the medium. There is no superfluorescence signal without the seed, so the initial coherence (dipole) ρ₁₂(0) could be ignored. We consider the process that the first seeding pulse $\frac{1}{2}{E}_1\left(t\right)e^{i\omega t}+c.c.$ interacts with this two-level system where E₁(t) is the envelope of the seeding pulse. For simplicity, we assume that the center frequency of the seeding field is resonant with the two-level transition, i.e., ω = ω₁₂. Therefore, one can write the evolution equation of the density matrix element under the rotating-wave approximation:

The seeding field is ultrashort with a temporal width Δ (from center to nearly zero). It locates at time τ₁ and the electric field is described as $\frac{1}{2}{E}_1\left(t-{\tau }_1\right)e^{i\omega \left(t-{\tau }_1\right)}+c.c.$ In the limit of $\wp E_1\Delta /\hslash \ll 1$, one can integrate Eq. (2) with the first-order approximation, and therefore obtain the expression of the coherence after the passage of the first seeding field passes (t = τ₁ + Δ):

Here ${\rho }_{12}^I$ gives the amplitude of the coherence built after the first seeding field leaves the medium. The amplitude of the coherence at the moment that the seeding passes is dependent on the population distribution of the medium, the seeding field intensity, and the seeding field profile. Once the coherence is prepared by the first seeding pulse, it starts to grow up due to the optical gain g(t) in the system, and the phase of the coherence is oscillating at the frequency ω, i.e. ${\rho }_{12}\left(t\right)=-i{\rho }_{12}^I{e}^{i\omega \left(t-{\tau }_1\right)}{e}^{{\displaystyle {\int }_{{\tau }_{{}_1}}^{t}dt\text{'}g\left(t\text{'}\right)}}$. Before the second seeding pulse comes at t = τ₂, we assume that its amplitude becomes ${\rho }_{12}^{II}$ ($\left|{\rho }_{12}^{II}\right|>\left|{\rho }_{12}^I\right|$ due to the optical gain of the nitrogen ion system). Next, we consider the second seeding field $\frac{1}{2}{E}_2\left(t-{\tau }_2\right)e^{i\omega \left(t-{\tau }_2\right)}+c.c.$ coming at t = τ₂ with the same pulse width Δ. The delay between two seed fields is much larger than the pulse width, i.e., τ₂ -τ₁ >>Δ. We again assume that $\wp E_2\Delta /\hslash \ll 1$, so one can integrate Eq. (2) and find the coherence after the passage of the second seeding field:

Here${\rho }_{12}^{III}$represents the net amplitude change of the coherence induced by the injection of the second seeding pulse. The emission from the coherence is collected by the detector and the signal is measured after integration. The signal, which integrates the intensity of the emission over time, is $I={\displaystyle {\int }_0^{\infty }|E_{emission}{|}^{2}dt}\propto {\displaystyle {\int }_0^{\infty }|{\rho }_{12}(t){|}^{2}dt}$. As for the illustration, we assume that the emission lasts much longer than the time scale of τ_1,2, so the signal is mainly contributed from the coherence built up after the second seeding pulse passes. Without loss of generality, we can write the signal from the coherence in Eq. (4)

With the above understanding in hand, we now return back to the experimental results in Fig. 4. We first concentrate on the case where the two seeding pulses had the same energy. After the injection of the first seeding pulse, a seed-induced initial polarization ${\rho }_{12}^I$ is excited in the nitrogen plasma. It grows with time before releasing the superradiance pulse [25,26]. At time τ₂, the second seeding was injected in the system. It interacts with the evolving two-level system and provokes an instantaneous polarization change ${\rho }_{12}^{III}$ inside the system, presented by the last term in Eq. (4). This net polarization change adds up coherently with the polarization under evolvement from τ₁ to τ₂, with their relative phase determined by ω(τ₁ - τ₂). Strong modulation contrast of the final superradiance intensity is expected when ${\rho }_{12}^{III}$ has a comparable amplitude with the instantaneous polarization before the injection of the second seeding pulse ${\rho }_{12}^{II}$. In the case of I_s2 = I_s1, we expect that ${\rho }_{12}^{III}$ is normally less than ${\rho }_{12}^{II}$ due to two reasons. First, the polarization after the first seeding pulse is increasing with time and we expect ${\rho }_{12}^{II}$ is much larger than the initial polarization ${\rho }_{12}^I$. At the same time, the second seeding pulse sees a decreased population difference ρ₁₁(τ₂)-ρ₂₂(τ₂) compared to that at time τ₁ and we expect ${\rho }_{12}^{III}$ is less than${\rho }_{12}^I$. As a result, the modulation contrast decreases when the time delay τ_ss is increased, as is presented in Fig. 4. For increased intensity of the second seeding pulse, the polarization change ${\rho }_{12}^{III}$ due to its injection can be larger. Therefore, the amplitude of ${\rho }_{12}^{III}$ can be comparable to the amplified polarization ${\rho }_{12}^{II}$ due to the gain at a proper time delay τ_ss, and hence a maximum modulation contrast can be expected. Obviously, for further increased intensity of the second seeding pulse I_s2 = 4I_s1, the maximum contrast occurs for longer time delay. Therefore, the increase of the polarization with time is encoded in the variation of the modulation contrast presented in Fig. 4, while a quantitative understanding will be possible with a complete modeling and numerical simulation.

5. Conclusion

In conclusion, we demonstrated coherent modulation of the nitrogen ions “air laser” with pairs of seeding pulses with different intensity ratios at the resonant wavelength of the $B^2{\Sigma }_u^{+}$ to $X^2{\Sigma }_g^{+}$ transition. The superradiant emission at 391.4 nm shows a strong intensity modulation with a period determined by the transition frequency when the relative delay (phase) between the two seeding pulses is varied, and the modulation contrast is increased at first and then decreased with the increasing of the delay time when the second pulse is stronger than the first one. With this method, the dipole interference is observed, and the buildup and evolution of the macroscopic coherence between two electronic levels have been experimentally revealed. This work provides a new level of control on the nitrogen ions “air laser”, which can be beneficial for its application in remote sensing.