Population dynamics of molecular nitrogen initiated by intense ...

PHYSICAL REVIEW A 92, 063412 (2015)

Population dynamics of molecular nitrogen initiated by intense femtosecond laser pulses Peng Wang,1 Chengyin Wu,1,2,3,* Mingwei Lei,1 Bo Dai,1 Hong Yang,1,3 Hongbing Jiang,1,3 and Qihuang Gong1,2,3 1

Department of Physics, State Key Laboratory for Mesoscopic Physics, Peking University, Beijing 100871, People’s Republic of China 2 Collaborative Innovation Center of Quantum Matter, Beijing 100871, People’s Republic of China 3 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, People’s Republic of China (Received 8 July 2015; published 15 December 2015) Tunneling ionization is one of the fundamental processes for molecules in intense laser fields, and the tunnelionized molecules are in various electronic states. Here, we report an experimental study of the population dynamics of N2 + (B 2 u + ) and N2 + (X 2 g + ) generated in intense femtosecond laser fields by simultaneously measuring the fluorescence emission spectra and the transmission spectra. The results reveal that the population inversion exists between N2 + (B 2 u + ) and N2 + (X 2 g + ). But the population difference is much smaller than the absolute population of N2 + (B 2 u + ). The present study provides insight into understanding the observation of the generation of an air laser from the tunnel-ionized nitrogen molecules, which has been attributed to the population inversion between N2 + (B 2 u + ) and N2 + (X 2 g + ) in intense femtosecond laser fields at 800-nm wavelengths. DOI: 10.1103/PhysRevA.92.063412

PACS number(s): 33.80.Rv, 42.50.Hz, 33.20.Xx

I. INTRODUCTION

Because of the potential applications for remote detection, air lasing driven by an intense ultrashort laser pulse has attracted much attention in recent years [1–14]. A forward narrow-bandwidth emission was first observed in air driven by intense midinfrared femtosecond laser pulses [15]. The emission lines at 391 and 428 nm were assigned to the transitions of N2 + (B 2 u + ,v = 0) → N2 + (X 2 g + ,v = 0) and N2 + (B 2 u + ,v = 0) → N2 + (X 2 g + ,v = 1), respectively. Because the third or fifth harmonic of the driver laser generated in air covers the emission lines, the authors proposed that the strong narrow-bandwidth emission lines come from the amplification of the harmonic seed in the presence of population inversion between N2 + (B 2 u + ) and N2 + (X 2 g + ). Later, these authors separated the harmonic seed and the driver laser pulse in order to study the population dynamics of N2 + (B 2 u + ) [16–18]. An intense femtosecond laser pulse at an 800-nm wavelength is utilized as the driver laser. A weak second-harmonic pulse is generated by a nonlinear crystal as the seed, which covers the emission lines at 391 and 428 nm. The intensities of the emission lines at 391 and 428 nm were measured as a function of the time delay between the driver laser and the seed as well as the spectrum of the seed. The results show that the enhancement of the emission lines at 391 and 428 nm critically depends not only on the delay between the driver laser and the seed, but also on the spectrum of the seed [16–18]. The population inversion between N2 + (B 2 u + ) and N2 + (X 2 g + ) is thus confirmed when nitrogen molecules are subject to intense femtosecond laser pulses at an 800-nm wavelength. By measuring the temporal profiles, the origin of the strong narrow-bandwidth emission lines is further attributed to the superradiance triggered by the seed [19]. However, the mechanism responsible for the population inversion is still under hot debate. Spectroscopic measurement has been demonstrated to be an effective method to identify the electronic states of

*

[email protected]

1050-2947/2015/92(6)/063412(5)

molecules irradiated by intense femtosecond laser fields and explore their population dynamics [20–24]. For example, the tunnel-ionized nitrogen molecules as shown in Fig. 1 and the nitrogen molecular ions in the excited electronic state will decay to the ground electronic state, and their populations in the excited state therefore can be measured by fluorescence measurement. Whereas for the nitrogen molecular ions in the ground electronic state, their populations can be measured by laser-induced fluorescence in which a nanosecond laser is applied to populate the molecular ion from the ground electronic state to the excited electronic state, and then the fluorescence emission from the excited electronic state to the ground electronic state is detected. The transmission spectra can measure the population difference between the excited and the ground electronic states. When the population in the excited electronic state is larger than that in the ground electronic state, the incident light will be amplified, and a net emission will be observed. Otherwise, the incident light will be attenuated, and a net absorption will be observed. Very recently, the populations of N2 + (B 2 u + ) and N2 + (X 2 g + ) have been explored by measuring the fluorescence spectra and the laser-induced fluorescence spectra, respectively [25]. The results demonstrated that the collision will redistribute the population of N2 + (B 2 u + ) and N2 + (X 2 g + ). It is therefore suggested that collision-induced redistribution should be taken into account when exploring the population inversion dynamics between N2 + (B 2 u + ) and N2 + (X 2 g + ) observed in the interaction of nitrogen molecules and intense laser fields. In this article, we combine the fluorescence spectra and the transmission spectra to experimentally explore the population dynamics of N2 + (B 2 u + ) and N2 + (X 2 g + ) in intense femtosecond laser fields. We found that the probe laser at 391 and 428 nm was greatly enhanced when it passed through the tunnel-ionized nitrogen molecules by the 800-nm pump laser. However, the side fluorescence generated by the 800-nm pump laser has no obvious change in the presence or absence of the probe laser. These observations indicate that the population inversion exists between N2 + (B 2 u + ) and N2 + (X 2 g + ) in intense laser fields. But the population difference between

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FIG. 1. (Color online) Principal diagram for monitoring the population of tunnel-ionized nitrogen molecules by intense femtosecond laser pulses. (a) Laser-induced fluorescence spectra for exploring the population in the ground electronic state, (b) fluoresce spectra for exploring the population in the excited electronic state, (c) transmission spectra with the population in the excited electronic state being lower than that in the ground electronic state, and (d) transmission spectra with the population in the excited electronic state being larger than that in the ground electronic state.

N2 + (B 2 u + ) and N2 + (X 2 g + ) is much smaller than the absolute population of N2 + (B 2 u + ). II. EXPERIMENTAL SETUP

Figure 2 shows the schematic of the experimental setup. A linearly polarized femtosecond laser pulse (∼800 nm, 35 fs, 1 kHz) from a Ti:sapphire laser system was split into two beams by a 30:70 beam splitter. The stronger beam with a pulse energy of about 2 mJ was used as the pump laser to ionize the nitrogen molecules and generate N+ 2 in various electronic states. The other beam, which was frequency doubled with a β-barium borate crystal, was used as the probe to study the population dynamics of N2 + (B 2 u + ) and N2 + (X 2 g + ). The pump and probe beams were recombined collinearly using a dichroic mirror with high reflectivity at 400 nm and high transmission at 800 nm. They were then focused by an f = 30-cm silica lens into a gas chamber filled with pure nitrogen molecules. The forward transmission spectra and the side fluorescence spectra were simultaneously measured. The pump and probe pulses passing through the

chamber were collimated by an f = 30-cm lens and then separated by a filter. The forward transmission spectra were recorded by a grating spectrometer (AvaSpec-2048-SPU) with a resolution of 0.2 nm. The side fluorescence was focused by an f = 10-cm lens and recorded by a second grating spectrometer (AvaSpec-2048 × 14-2-USB2) with a resolution of 1.4 nm. In addition, a combination of one spherical mirror and one convex lens was applied to improve the fluorescence collection efficiency. III. RESULTS AND DISCUSSION

Figure 3(a) shows a typical forward emission spectrum of tunnel-ionized nitrogen molecules in intense 800-nm laser fields with a gas pressure of 10 mbars. In the absence of the probe laser, a narrow-bandwidth emission is observed at a wavelength of 391 nm, although the intensity is weak. In the absence of the pump laser, the spectral profile of the probe is broad extending from 390 to 430 nm. The intensities are very small around 391 and 428 nm. In contrast, when both the pump and the probe are present and the pump is ahead of the probe,

FIG. 2. (Color online) Schematic of the experimental setup. The forward emission and the side fluorescence emission were simultaneously measured by two grating spectrometers. 063412-2

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FIG. 3. (Color online) (a) The forward emission and (b) the side fluorescence emission of N2 + (B 2 u + ,v = 0) → N2 + (X g + ,v = 0,1) in the presence and absence of the probe laser. The forward emissions at 391 and 428 nm are greatly enhanced in the presence of the probe laser. The side fluorescence emissions have no obvious change in the presence or absence of the probe laser.

the narrow-bandwidth emissions at 391 and 428 nm are greatly enhanced. The emission intensity at 428 nm is much smaller than that at 391 nm, which is magnified and displayed in the inset. The emission lines at 391 and 428 nm can be assigned to the transitions of N2 + (B 2 u + ,v = 0) → N2 + (X 2 g + ,v = 0) and N2 + (B 2 u + ,v = 0) → N2 + (X 2 g + ,v = 1), respectively. The enhancement of the emissions at 391 and 428 nm in the presence of the probe laser can be attributed to the superradiance triggered by the probe [19]. It should be mentioned that we have measured the intensities of the emission lines at 391 and 428 nm as a function of the time delay between the pump and the probe pulses. The results demonstrate that the enhancement of the emissions can occur for several picoseconds depending on the gas pressure. These observations indicate that n = (nB − nX ) > 0 with nB and nX being the population of N2 + (B 2 u + ) and N2 + (X 2 g + ), respectively. In other words, population inversion between N2 + (B 2 u + ,v = 0) and N2 + (X 2 g + ,v = 0,1) is generated by the pump laser. Figure 3(b) shows a typical side fluorescence spectrum in the presence and absence of the probe laser. The emissions are also assigned to the transition of N2 + (B 2 u + ,v = 0) → N2 + (X 2 g + ,v = 0) and N2 + (B 2 u + ,v = 0) → N2 + (X 2 g + ,v = 1), respectively. Different from the forward emission spectra, the side fluorescence intensity is almost unchanged with and without the probe laser. As discussed in the following, these observations imply that n nB , i.e., the population inversion

FIG. 4. (Color online) (a) The forward emission intensity in the presence of the probe laser and (b) the side fluorescence emission intensity of N2 + (B 2 u + ,v = 0) → N2 + (X g + ,v = 0,1) as a function of gas pressure. The side fluorescence intensity has no obvious change with and without the probe laser.

between N2 + (B 2 u + ) and N2 + (X 2 g + ) is much smaller than the absolute population of N2 + (B 2 u + ). In addition, the fluorescence intensity at 391 nm is about twice that at 428 nm. The ratio of the emission intensities at 391 and 428 nm is close to the ratio of the Franck-Condon factors of N2 + (B 2 u + ,v = 0) → N2 + (X 2 g + ,v = 0) and N2 + (B 2 u + ,v = 0) → N2 + (X 2 g + ,v = 1), which are 0.663 and 0.253 [26], respectively. In our previous report [25], we demonstrated that the collision-induced population redistribution should be taken into account when exploring the population inversion between N2 + (B 2 u + ) and N2 + (X 2 g + ). As we know, the frequency of collision is proportional to the gas pressure. Therefore, we study the population dynamics of N2 + (B 2 u + ) and N2 + (X 2 g + ) in intense laser fields by measuring the forward emission and the side fluorescence emission as a function of gas pressure. Figure 4(a) displays the intensities of the forward emission lines at 391 and 428 nm in the presence of the probe laser as a function of gas pressure. The intensity at 428 nm was multiplied by 10 for visibility. It should be emphasized that the forward emission generated by the pump laser alone is not included. When the gas pressure is larger than 4 mbars, the narrow-bandwidth emission lines at 391 and 428 nm begin to appear. With increasing the gas pressure, the intensities of these emission lines first increase and then decrease and disappear when the pressure is higher than 100 mbars. The enhancement of the forward emission lines at 391 and 428 nm can be realized in the pressure scope of 5–100 mbars. Because the enhancement of the emission lines requires the population inversion between N2 + (B 2 u + ) and N2 + (X 2 g + ), it is

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necessary to take the population of both the upper and the lower electronic states into account when analyzing the pressure-dependent forward emission lines. According to the present observation and the previous reports [16–19], n = (nB − nX ) > 0 is formed when nitrogen molecules are subject to intense femtosecond laser pulses at an 800-nm wavelength [16–19]. It is known that the absolute value of n will increase linearly with increasing the gas pressure when the collision-induced depopulation of N2 + (B 2 u + ) and N2 + (X 2 g + ) can be neglected under low gas pressure. That explains our observations that the enhancement degree of emission lines at 391 and 428 nm was increased with increasing the gas pressure and reached a maximum at ∼10 mbars for 391 nm and ∼20 mbars for 428 nm. When the gas pressure was further increased, the forward emission lines at 391 and 428 nm become weaker and disappear finally. It should be noted that the forward emission line at 391 nm disappears when the gas pressure is higher than 20 mbars. However, the forward emission line at 428 nm disappears until the gas pressure is higher than 100 mbars. These observations should come from the collision-induced population redistribution. For the forward emissions of 391 and 428 nm, they have the same upper level N2 + (B 2 u + ,v = 0) but different lower levels, which are N2 + (X 2 g + ,v = 0) and N2 + (X 2 g + ,v = 1), respectively. The different pressure-dependent behaviors of 391 and 428 nm indicate that the populations exhibit different pressure dependences for N2 + (X 2 g + ,v = 0) and N2 + (X 2 g + ,v = 1). The increase in the population of N2 + (X 2 g + ,v = 0) is faster than that of N2 + (X 2 g + ,v = 1) as a function of gas pressure. The increase might come from the collision-induced population redistribution. State-resolved fluorescence spectra revealed that N+ 2 generated in intense laser fields has broad rotational and vibrational population distributions [27]. It has been demonstrated that collision-induced population redistribution occurs when the gas pressure is high [25]. Because collision is efficient for energy transfer, the vibrational population will relax to N2 + (X 2 g + ,v = 0) through collision. In addition, the other excited electronic state of N2 + , such as N2 + (A 2 u ), will also relax to the ground electronic state through collisions. All these collision-induced nonradiative processes will increase the population of N2 + (X 2 g + ,v = 0,1). At the same time, N2 + (B 2 u + ,v = 0) will relax to the ground electronic state through the collision-induced nonradiative processes. As a result, the population inversion between N2 + (B 2 u + ) and N2 + (X 2 g + ) generated by the pump laser will be destroyed, and the enhancement of the emission line at 391 nm cannot be fulfilled. The phenomena that the enhancement of the emission line at 428 nm can exist in higher gas pressures than that of 391 nm might be attributed to the fact that the population of N2 + (X 2 g + ,v = 0) increases faster than that of N2 + (X 2 g + ,v = 1) by collision. Therefore the population inversion generating 391-nm emission will be first destroyed as the pressure gets increased. Under this pressure, the population of N2 + (X 2 g + ,v = 1) has not been accumulated enough to destroy the population inversion between N2 + (B 2 u + ,v = 0) and N2 + (X 2 g + ,v = 1). However, when the pressure was further increased and exceeded 100 mbars, the faster collision leads to the increase in the population of N2 + (X 2 g + ,v = 1) and the decrease in the population of N2 + (B 2 u + ,v = 0). Thus the population inversion

between N2 + (B 2 u + ,v = 0) and N2 + (X 2 g + ,v = 1) is destroyed and the enhancement of the emission line at 428 nm cannot be achieved. The process for the side fluorescence emission is quite simple in comparison with the forward emission which is related with several complicated processes. Fluorescence emission is only related with the upper level. The intensity is proportional to the population of the upper level and is not related with the lower level. Figure 4(b) shows the fluorescence intensities at 391 and 428 nm as a function of gas pressure. It can be seen that the fluorescence can be observed in a wide range of gas pressures from 0.03 to 1000 mbars. It should be noted that 0.03 mbar is the ultimate pressure in the present measurement. In our previous report [28], the fluorescence can be observed in the pressure lower than 10−5 mbars. In addition, the fluorescence emissions at 391 and 428 nm have the same pressure dependence. This observation is consistent with the fact that fluorescence emission is only related with the upper level and has no relation with the lower level. According to the measurement, the fluorescence intensities first increase and then decrease with increasing the gas pressure. It is known that the density of nitrogen molecules is increased linearly as the gas pressure is increased. Thus the density of molecular ions is increased after the laser irradiation. However, the depopulation of the excited electronic state can occur through the radiative and nonradiative processes. In the case of the radiative process, the excited state relaxes to the ground state through emitting a photon, i.e., fluorescence emission. In the case of the nonradiative process, the excited state relaxes to the ground state through collision. The fluorescence intensity is proportional to the population in the excited electronic state. When the radiative lifetime is comparable to or shorter than the nonradiative lifetime, the effect of the collision-induced nonradiative processes cannot be neglected for depopulating the excited state. The radiative lifetime is around 60 ns for N2 + (B 2 u + → X 2 g + ) [28]. The nonradiative lifetime caused by the collision is inversely proportional to the gas pressure and about 160 ns at the gas pressure of 1.0 mbar. When the gas pressure is lower than 0.1 mbar, the depopulation of the excited electronic state occurs mainly through the radiative process, and the fluorescence intensity was increased linearly with increasing gas pressure. However, when the gas pressure gets higher, two more processes become efficient. One is collision-induced quenching, which leads to the reduction of N2 + (B 2 u + ). The other is plasma-induced defocusing, which results in the decrease in laser intensity at the focus as well as the ionization and excitation probabilities. The change in the fluorescence intensity may reflect the balance between these processes. It should specially be noted that the forward emission and the side fluorescence emission exhibited different behaviors in the presence and absence of the probe laser. In the case of the forward emission as shown in Fig. 3(a), the narrow-bandwidth emissions at 391 and 428 nm were greatly enhanced in the presence of the probe laser. The enhancement originates from the superradiance triggered by the probe laser and can be attributed to the population inversion between N2 + (B 2 u + ) and N2 + (X 2 g + ). After being trigged by the probe laser, the molecular ions in the excited states will

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relax to the ground state. As a result, the population of N2 + (B 2 u + ) should be decreased, and the side fluorescence intensity of N2 + (B 2 u + → X 2 g + ) should be reduced as well. However, as a big surprise, we find that the fluorescence intensity is almost unchanged in the presence and absence of the probe laser. As has been mentioned, fluorescence intensity is proportional to the population of the ions in the excited electronic state. The almost unchanged fluorescence intensity indicates that the population has no obvious change with and without the probe laser. But at the same time we observed the enhancement of the probe laser at 391 and 428 nm in the presence of the probe laser. Combining these observations, we concluded that the population inversion between N2 + (B 2 u + ) and N2 + (X 2 g + ) is much smaller than the absolute population of N2 + (B 2 u + ), i.e., n nB . This conclusion is verified by recent theoretical simulations [29].

428 nm are greatly enhanced in the presence of the probe laser, which can be attributed to the superradiance triggered by the probe laser. In contrast with the enhancement of the emission lines in the transmission spectra, the side fluorescence intensity has no obvious change in the presence or absence of the probe laser. The enhancement of the emission lines indicates the population inversion between N2 + (B 2 u + ,v = 0) and N2 + (X 2 g + ,v = 0,1). These observations demonstrated that the population inversion between N2 + (B 2 u + ) and N2 + (X 2 g + ) is generated by intense femtosecond laser fields at an 800-nm wavelength, but the population difference is much smaller than the absolute population of N2 + (B 2 u + ). The present study provides insight into understanding the mechanism responsible for the population inversion observed in tunnel-ionized nitrogen molecules by intense femtosecond laser fields with an 800-nm wavelength.

IV. CONCLUSION ACKNOWLEDGMENTS

To summarize, we present an experimental study of the population dynamics of N2 + (B 2 u + ) and N2 + (X 2 g + ) in intense femtosecond laser fields by measuring the fluorescence spectra and the transmission spectra. In the case of transmission spectra, the narrow-bandwidth emissions at 391 and

This work was supported by the National Basic Research Program of China under Grant No. 2013CB922403 and by the National Natural Science Foundation of China under Grants No. 61178019, No. 11474009, and No. 11434002.

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