Fluorescence and lasing of neutral nitrogen molecules inside femtosecond laser filaments in air: mechanism and applications

Abstract

High power femtosecond laser pulses launched in air undergo nonlinear filamentary propagation, featuring a bright and thin plasma channel in air with its length much longer than the Rayleigh length of the laser beam. During this nonlinear propagation process, the laser pulses experience rich and complex spatial and temporal transformations. With its applications ranging from supercontinuum generation, laser pulse compression, remote sensing to triggering of lightning, the underlying physical mechanism of filamentation has been intensively studied. In this review, we will focus on the fluorescence and cavity-free lasing effect of the plasma filaments in air. The different mechanisms underlying the fluorescence of the excited neutral nitrogen molecules will be throughly examined and it is concluded that the electron collision excitation is the dominant channel for the formation of the excited nitrogen molecules. The recently discovered “air lasing” effect, a cavity-free bidirectional lasing emission emitted by the filaments, will be introduced and its main properties will be emphasized. The applications of the fluorescence and lasing effect of the neutral nitrogen molecules will be introduced, with two examples on spectroscopy and detection of electric field. Finally, we discuss the quenching effect of the lasing effect in atmosphere and the mechanisms responsible will be analyzed. An outlook for the achievement of backward lasing in air will be briefly presented.

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1. Introduction

Long range filamentary propagation of intense ultrafast laser pulses in air manifests itself as a spectacular nonlinear optical effect (as presented in Fig. 1). This phenomenon was first reported by G. Mourou and co-workers in 1995,¹ with powerful 200 fs laser of maximum energy 50 mJ in Michigan University. In their first experiment, it was found that the transverse diameter of a collimated (d = 4 mm) intense femtosecond laser spontaneously shrinked to below 100 μm after 10 m propagation in atmosphere. At the same time, the spectrum of the laser pulse was strongly modulated and broadened after this nonlinear propagation. This pioneering report attracted the attention of many research groups in the recent 3 decades, and the study of filamentation physics has spreaded in many different aspects and found applications in various fields.

Fig. 1 Filamentation of an intense femtosecond laser pulse in air and supercontinuum generation. The femtosecond laser pulse (35 fs, 18 mJ, 800 nm) were focused by a 1 m focal lens in atmosphere and a bright plasma channel of ∼20 cm long (the fluorescent blue section) was produced.

The filamentation process has several unique features. On the one hand, the intense laser pulses are confined in a narrow transverse size, typically on the order of 100 μm, over a distance much longer than the Rayleigh length of the beam. With powerful terawatts lasers, the length of the filaments ranges from tens of meters, to even kilometers.^2–4 The laser intensity inside the filaments, between 10¹³ –10¹⁴ W cm⁻², is sufficient for photoionization of oxygen and nitrogen molecules in air.⁵ Consequently, a thin and long plasma channel is created in air, manifesting itself as a bright channel or a set of several channels emitting blue fluorescence. In Fig. 1, a typical filamentation process of femtosecond laser pulses in air is presented. In this demonstration, the 40 fs laser pulses from a commercial laser system have a pulse energy of 18 mJ, central wavelength of 800 nm. The pulses are focused by a convex lens of f = 1000 mm in ambient air. A visible thin plasma channel of 20 cm (light blue section in Fig. 1) is produced, accompanied by a strong supercontinuum whitelight emission in the forward direction, shown as the very bright spot on the black screen in the figure. The optical beam path between the filaments and the screen is also visualized due to the scattering of the filament-generated supercontinuum by the atmosphere.

Soon after the observation of filamentation in air, study of nonlinear pulse propagation and filamentation in other transparent condense media also bloomed.^6–10 Fused silica and water were widely used for filamentation study in solids and liquids.^6,9 Due to their much lower critical power for self-focusing compared to gases, the filaments in condensed matter featured a smaller transverse size of 10–50 μm and shorter channel length on the order of millimetre to centimeters.⁸ A more detailed description of the filamentation in condensed matter is beyond the scope of this paper and can be found in ref. 5.

The physical mechanism underlying this nonlinear pulse propagation has been studied intensively and several scenarios have been proposed. In the first report, it was proposed that self-channelling due to a balance of self-focusing and diffraction was responsible.¹ Soon after, the moving-focus model was suggested.¹¹ Based on numerical simulation of nonlinear pulse propagation, M. Mlejnek et al.¹² put forward the dynamic spatial replenishment model, which emphasized the dynamic replenishment of a leading-edge pulse and the tail of the pulse in the spatial domain. The theoretical study of filamentation physics is mainly based on the coupled nonlinear Schrödinger equations with the photoionization of materials taken into account by models for strong-field ionization.⁵ Thanks to many efforts of different research groups, the underlying physical mechanism of long-range filamentation has been identified to the conspiration of many nonlinear and linear optical effects including diffraction, Kerr self-focusing, dispersion, plasma formation by photoionization, plasma defocusing, molecules quantum alignment, wherein Kerr self-focusing and plasma defocusing act as the primary players.^5,13

Since the laser pulses experience rich spatiotemporal transformation during this highly nonlinear propagation process, filamentation has been widely employed for generation of whitelight continuum spanning from ultraviolet to mid-infrared range,¹⁴ spatial cleaning of laser beams,¹⁵ and pulse compression to the few-cycle regime.^16,17 The air plasma associated with the filamentation process brought about many applications in different domains. Due to the presence of free electrons and transient current inside the plasma on the time scale of picoseconds to sub-nanosecond, the filaments can act as an efficient source for microwave and extreme broadband terahertz radiations.^18–22 The filamentation process is accompanied with the rapid deposition of laser energy in a confined volume of air. Therefore, on the microsecond to millisecond time scale, the filaments can evolve into a long channel of gas density modulation, with a density “hole” in the centre. Taking advantage of this unique feature, the concept of laser lightning rod has been investigated and it has been demonstrated that the filaments can lead to triggering and guiding of electric discharge over several meters.^23–25 In 2023, it was demonstrated that the filaments produced by Joule level ultrafast lasers guided a ∼70 m long lightning in real atmosphere,²⁶ fulfilment of the long-term scientific dream of laser lightning rod. In the meantime, filamentation of intense femtosecond laser pulses have found diverse applications in other domains such as artificial rain and snow formation,^27,28 remote detection of terahertz or DC field,²⁹ micro-machining inside solids,³⁰ and waveguiding of microwaves in air,³¹ to name just a few.

In this review, we discuss the phenomenon, properties, and applications of fluorescence and cavity-free lasing effect of neutral nitrogen molecules inside femtosecond laser plasma filaments in air. In Section 2, we begin by introducing the discovery of the clean fluorescence of femtosecond laser filaments in air and examining the physical mechanisms underlying the formation of fluorescent excited states of nitrogen molecules following the excitation by an intense laser field. In Section 3, we summarize the recent research progress and properties of the bidirectional cavity-free lasing radiation of neutral nitrogen molecules. Particularly, the temporal dynamics of the gain formation and lasing emission will be emphasized. In Section 4, applications of neutral nitrogen lasing in remote spectroscopy of trace molecules and detection of electric field will be discussed. Finally, the quenching effect of oxygen molecules on the nitrogen molecules lasing will be discussed. A brief summary and outlook on the scientific opportunities and challenges faced by nitrogen molecule air lasing will be presented at the end.

2. Mechanism of excited state nitrogen molecules formation

2.1. Discovery of the “clean” fluorescence of femtosecond filaments

After the pioneering report of long range femtosecond laser filamentation by G. Mourou and co-workers in 1995,¹ several groups immediately devoted their attention to this topic.^{11–13,32,33} The forward conical emission, or the supercontinuum, was rapidly reported by different groups.^32,33 In 1999, A. Talebpour et al. observed for the first time the fluorescence emission of the femtosecond laser filaments in air.³⁴ Later, the same group led by Prof. S. L. Chin of Laval University has performed a systematic comparison of the plasma fluorescence induced by 200 ps and 40 fs pulses, as shown in Fig. 2.³⁵ Compared to the broadband emission from air plasma induced by 200 ps lasers (Fig. 2(a)), very clean fluorescence emission lines in the UV range were observed with femtosecond laser excitation, which was later coined as “clean” fluorescence of filaments.^35,36 It has been widely observed that the air plasma emission excited by long pulses of sub-nanosecond duration presents a broadband spectrum in the visible range, with atomic lines of nitrogen and oxygen superimposed on it. The underlying mechanism has been attributed to the recombination of hot electrons with ions, where the electrons are accelerated by an inverse Bremsstrahlung process by the long laser pulses.³⁵ In contrast, in the case of filamentation of femtosecond pulses, the fluorescence is “cleaned” from plasma continuum, as presented in Fig. 2(b). The origin of the remaining sharp fluorescence lines can be readily assigned. These lines correspond to transitions between excited triplet states C³Π_u (hereinafter referred to as “C”) and B³Π_g (hereinafter referred to as “B”) of neutral nitrogen molecules (2nd positive system of N₂) and between second excited state B²Σ⁺_u and ground state X²Σ⁺_g of nitrogen molecular ions (1st negative system of N₂⁺), as indicated in Fig. 2(b).

Fig. 2 Fluorescence spectra of air plasma induced by (a) 200 ps and (b) 40 fs laser pulses in ambient air. The energy per pulse was 5 mJ for both cases. The 40 fs and 200 ps laser pulses were focused into air respectively by lens with a focal length of f = 100 cm and f = 5 cm. Reproduced from ref. 35.

The fluorescence emission from the first negative band system (B²Σ⁺_u–X²Σ⁺_g transition) of N₂⁺ has been ascribed to intense laser-induced multiphoton or tunnel ionization of inner-valence electrons of neutral nitrogen molecules, leaving the molecular ion N₂⁺ in the excited state B state.³⁴ The electronic configuration of N₂ molecules in the ground state is KK (σ_g2s)²(σ_u2s)²(π_u2p)⁴(σ_g2p)². When any of the electrons in the inner orbital (σ_u2s) is ionized, the molecular ion is produced in the excited electronic B²Σ⁺_u state. In the recent 10 years, there has been a tremendous study on the lasing action of N₂⁺ pumped by femtosecond pulses and the underlying gain mechanism has been intensively discussed.^37–43 The readers are referred to the review papers on this special topic for more detailed information.^44–46

The most important fluorescence signal from the filaments in ambient air originates from the C → B transition of the neutral nitrogen molecules. How is the excited state C populated during the filamentation process? Direct high-field photonic excitation of the triplet state N₂(C) is a spin-forbidden process and therefore unlikely. Therefore, the population of the C state should be achieved through a non-photonic process. As will be seen in the following three sub-sections, several mechanisms have been proposed and discussed.

2.2. Dissociative recombination

In their first report on the fluorescence emission of femtosecond laser filaments in air, A. Talebpour and co-workers³⁵ have reflected on the mechanism for the formation of the C state. They speculated that N₂ molecules in the singlet ground state (X¹Σ_g) are excited to some highly excited singlet electronic state. Through collisions, the populations in such an excited singlet state might be transferred to the triplet electronic state, C³Π_u. Later, the same group proposed that this excited state is created through the formation of N₄⁺:⁴⁷

N₂⁺ + N₂ ⇒ N₄⁺ (2.1)

N₂⁺ + e ⇒ N₂(C³Π_u) + N₂. (2.2)

The authors also employed a weak, delayed 400 nm probe pulse to ionize the excited nitrogen molecules in the C state and monitored the decreased fluorescence signal as a function of the pump–probe time delay. The excited nitrogen was found to decay rapidly, with a lifetime of 85 ps determined by fitting the experimental data with an exponential decay. It should be noted however that study of the decay process of the C state does not provide valuable information on its formation process, as will be discussed in Section 2.4.

2.3. Intersystem crossing

In view of the importance of the nitrogen fluorescence for the understanding of the filamentation, B. Arnold et al.⁴⁸ examined the temporal dynamics of the fluorescence with a gated ICCD detector with a time resolution approaching 1 ns. This setup allowed them to capture the temporal evolution of the fluorescence on a nanosecond time scale. Experiments were conducted by examining the time-resolved 337.1 nm signal in a mixture of N₂ with He gas. Based on their experimental results, the authors proposed that the following collision-assisted intersystem crossing (ISC)can be an important reaction channel for the formation of C state.

The authors examined the built-up and decay process of both the 391.4 nm and 337.1 nm fluorescence on a time scale of tens of nanoseconds. The built-up process of both emissions could not be well determined due to the limited time resolution of their experiments. For the fluorescence decay process, the charactersitic decay time is on the order of 10 ns for a sample of 1.3% N₂ in helium buffer. To interpret the observations, the authors established rate equations for both the intersystem crossing and the dissociative recombination mechanism. Based on a comparison of experimental data and numerical simulations, the authors claimed that only the intersystem crossing contribution is sufficient to fit the case of low partial pressure N₂, while both ISC and dissociative recombination are necessary to reproduce the results obtained in pure N₂. It was therefore argued that the ISC is likely to be the dominant mechanism for populating excited N₂ while the dissociative recombination should be a minor contributor.⁴⁸

However, the experimental conditions of this study differ from the typical parameters of filamentation in air. The nitrogen gas was purged into He buffer gas and the concentration of N₂ was on the order of 1%. The electron density was on the order of 10¹³ cm⁻³, which is 3–4 orders of magnitude lower than that of plasma filaments. Therefore, the validity of this excitation scheme in the condition of filamentation is questionable.

2.4. Electron impact excitation mechanism

In 2014, S. Mitryukovskiy et al.⁴⁹ reported a backward nitrogen molecular lasing emission at 337.1 nm in pure nitrogen gas under 1 bar pressure. In this study, the authors employed an 800 nm femtosecond laser as the pump pulse. Through an investigation of the characteristics of the backward nitrogen molecular laser emission (refer to Section 3), it was discovered that the polarization of the pump pulse has a significant influence on the performance of the backward nitrogen molecular emission, as depicted in Fig. 8(c) and (d). Only with circularly polarized 800 nm femtosecond laser pulses, they observed a strong backward 337.1 nm radiation from nitrogen gas. Even slight deviation from circular polarization status results in a sharp decrease in the 337.1 nm signal. This unexpected sensitivity of the backward emission of neutral molecules to the pump pulse polarization has inspired researchers on thinking about the formation mechanism of the excited nitrogen molecules.

In the same work, S. Mitryukovskiy and co-workers argued that the nitrogen molecules excitation mechanism in the case of circularly polarized 800 nm pump pulses could be high-energy electron collisions with nitrogen molecules. The clue for this assumption lies in the fact that the distribution of electron kinetic energy strongly relies on the polarization of the pump laser during the ionization process of molecules using laser fields with circular and linear polarizations.^50,51 When a linearly polarized pump pulse is used, free electrons after tunnel ionization are accelerated back and forth along the direction of the laser polarization during each cycle, resulting in predominantly low kinetic energy at the end of the laser pulse, with only a few eV. In contrast, when a circularly polarized pump pulse is employed, electrons are continuously accelerated away from their nuclei throughout their motion, leading to a final kinetic energy approximately twice as large as the laser ponderomotive energy U_p. The ponderomotive energy obtained by an electron in a laser field is represented by

where ε₀, m_e, I, ω₀ are the vacuum permittivity, electron mass, laser intensity, and laser frequency, respectively. By combining the Newtonian equation of motion for electron and the rate equation of photoionization, they calculated the distribution of electron kinetic energy under different ellipticities, as illustrated in Fig. 3. The laser intensity considered was I = 1.4 × 10¹⁴ W cm⁻², a typical laser intensity found for filamentary laser pulses.⁵² For nitrogen molecules, the energy threshold for collisional excitation in C state is around 14 eV.⁵³ For a linearly polarized laser field (ε = 0), most electrons possess kinetic energies below 1 eV. With an elliptically polarized laser (ε = 0.5) between linear polarization and circular polarization, the electron energy distribution shifts to higher energies. In particular, with circular polarization (ε = 1), the peak of the electron's kinetic energy distribution occurs at 14.6 eV. This electron energy can lead to efficient transfer of nitrogen molecules from their ground state to the third excited state through the inelastic collision process:

N₂(X¹Σ_g) + e = N₂(C³Π_u) + e. (2.6)

Fig. 3 Calculated electron energy distribution for linear polarization (a), elliptic polarization (b), and circular polarization (c). Reproduced from ref. 51.

The authors further argued that population inversion between C and B states may be achieved, in view of the observed strong backward emission. The process is similar to that of a conventional nitrogen laser, where electrons acquire kinetic energy from an externally applied electric field and excite the nitrogen molecules by inelastic collisions. This interpretation is in agreement with the pronounced dependence on the polarization of the pump pulse and stimulated further studies in this direction.

Zheng et al.⁵⁴ theoretically and experimentally studied the formation mechanism of excited nitrogen molecules irradiated by 800-nm femtosecond laser. By modifying the electron energy distribution and, consequently, the electron collision cross section, the experimental observations are well reproduced theoretically for the dependences of N₂(C–B) fluorescence intensity as function of laser intensity and laser ellipticity. The study further verified that N₂(C) is formed due to electron collisions.

2.5. Time-resolved formation of the excited triplet state

With a streak camera of 30 ps time resolution, M. W. Lei et al. has captured the formation dynamics of the N₂(C) for low gas pressure of 4 mbar. They found that the N₂(C) was formed in 250 ps in this low pressure case, which was in line with the speculation of electron collision excitation.⁵⁵

In 2019, Danylo et al.⁵⁶ proposed a laser-induced fluorescence depletion technique to determine the primary formation mechanism of excited state nitrogen. This method successfully monitored the formation dynamics of excited nitrogen molecules with femtosecond time resolution and provided key information on their formation time. As mentioned in Section 2.3, with a gated ICCD it was only possible to record the formation and decay dynamics on the nanosecond time scale, while with a streak camera it is possible to obtain dynamics on the picosecond scale. In this experiment, after the circularly/linearly polarized 800 nm pump pulse, an ultraviolet probe pulse around 400 nm was injected into the plasma. Under the action of the ultraviolet probe pulse, molecules in the C state were ionized to the ionic state through a single photon excitation. By changing the relative delay between pump and probe pulse, fluorescence depletion establishment time was measured, and the formation dynamics of excited nitrogen molecule was obtained. Typical results obtained at different pressures are presented in Fig. 4. The experimental results show that the 337.1 nm fluorescence signal intensity reaches its minimum after approximately 4 ps under the pressure of 1 bar, as illustrated in Fig. 4(a), while it takes roughly 150 ps in case of 30 mbar nitrogen gas. In other words, the concentration of nitrogen molecules in the excited state attains its maximum within a time scale of around 4 ps for 1 bar gas nitrogen.

Fig. 4 Dynamics of 337.1 nm fluorescence formation and decay. Lateral fluorescence at 337.1 nm as a function of the pump–probe delay for different nitrogen gas pressures. The gas pressure for (a)-(d) is 1000, 300, 100 and 30 mbar. Reproduced from ref. 56.

How can one understand that the excited N₂ molecules are formed in less than 4 ps at atmospheric pressure? This ultrashort formation time is surprising for the dissociative recombination and ISC mechanism, because both reactions involve the collisions of molecules and ions, which occur on a much longer time scale. For a more quantitative analysis, they simulated the formation dynamics of excited neutral molecules using the rate equations for the different channels of neutral nitrogen excitation. An intersystem crossing scenario requires the presence of a high concentration of atoms such as He with a resonant level for energy exchange, which is not the case in pure nitrogen or air. Therefore, this mechanism was not considered.

According to the dissociative recombination model, the excited N₂ molecules are the product of cascaded impact reactions between ionized and neutral nitrogen molecules. The rate equations that describe the dissociative recombination mechanism are the following:⁵⁶

The second mechanism, electron impact excitation, is described by the following equation:The reader can find more information on the model and the parameters in ref. 57–59. The calculation results are shown in Fig. 5. In Fig. 5(b), the formation time of the triplet state based on the two mechanisms are presented. For the electron impact excitation, the formation time of ∼4 ps is observed. In contrast, when only the molecular path is considered, the formation time is around 125 ps (red line), much longer than the measured value. For a low pressure of 30 mbar, the electron impact excitation mechanism gives the formation time on the order of 100 ps, while the dissociative recombination predicts ∼10 ns. The formation time of the excited molecules has been calculated for different gas pressures and the results are compared with experimental observations in Fig. 5(a). Reasonable agreement is found between the calculation and experiment for all pressures ranging from 30 mbar to 1 bar, confirming the dominant role of electron impact excitation for the formation of the excited nitrogen molecules in filaments.

Fig. 5 (a) Experimentally measured (square dots) and calculated (solid circles) formation times of C state of neutral nitrogen molecules as a function of the nitrogen gas pressure. For 1 bar (b) and 30 mbar (c) nitrogen, calculated formation dynamic of the C state molecules based on the electron impact mechanism (blue line) and the dissociative recombination mechanism (red line). Reproduced from ref. 56.

As discussed in this section, after the observation of the clean fluorescence of the filaments in air, several different mechanisms have been proposed to explain the formation of the excited nitrogen molecules inside the filaments. The molecular pathways, including the dissociative recombination and the intersystem crossing, involve the collisions between molecules or ions, which necessities a relative long formation time. Electron impact excitation arises as the mechanism responsible behind the formation of the C excited state of neutral nitrogen molecules and the corresponding lasing effect.

3. Characteristics of forward and backward lasing

In 2003, Luo et al.⁶⁰ observed fluorescence radiation at wavelengths of 337.1 nm and 357 nm in the backward direction (opposite to the direction of the laser propagation) while investigating the plasma emission spectrum from a filament created by a femtosecond laser pulse in the atmosphere. They found that the intensity of backward fluorescent radiation shows a slight exponential increase with the calculated filament length. Based on this observation, the concept of “air lasing” was proposed for the first time. Studies of lasing in air provide an important route toward the application in optical remote sensing since “air lasing” can potentially create a coherent backward light source from the sky to the earth, without the need for airplanes or satellites. Nitrogen, abundant in the atmosphere, serves as the optimal gain medium for air lasing, thereby fuelling researchers' fervour to explore the intricate properties of nitrogen molecular lasing.

As already mentioned in Section 2.1, dipole optical transitions from ground state X¹Σ_g of N₂ to triplet states are prohibited. Thus, optical excitation cannot pump ground-state nitrogen molecules into excited states for N₂ air lasing. Nitrogen molecular lasing primarily relies on the collisional excitation to achieve population inversion through two different schemes: collisional transfer of the excitation energy of argon atoms^61–63 or collisions of high-energy electrons with nitrogen molecules as mentioned in Section 2.4.^49,59,64 In subsequent sections, we will review research progress on these two mechanisms.

3.1. Resonance transfer excitation of the nitrogen molecules

In 2012, Kartashov et al.⁶¹ shined high-power mid-infrared laser pulses at 3.9 μm or 1.03 μm wavelength into a high-pressure mixture of nitrogen and argon gases. From this nitrogen–argon mixture under high pressure, the researchers observed stimulated radiation in the backward direction at wavelengths of 337.1 nm and 357 nm, as shown in Fig. 6. By optimizing the pressure of nitrogen and argon, they achieved an output energy of the nitrogen lasing reaching 3.5 μJ, with an energy conversion efficiency of 0.5%. This efficiency is comparable to that achieved by traditional electric pumped N₂ laser (0.1%).

Fig. 6 Measured backward emission spectra of N₂–Ar mixed gas induced by mid-infrared femtosecond filaments (insert shows the energy level diagram of N₂ lasing excited in collisions with Ar atoms). Free-space nitrogen gas laser driven by a femtosecond filament. Reproduced from ref. 61.

The researchers explained the population inversion mechanism between the C and B states as a conventional Bennet mechanism, wherein metastable Ar atoms in state 4³P₂ play a crucial role in establishing N₂ population inversion through the following processes: Ar⁺ + 2Ar → Ar₂⁺ + Ar, Ar₂⁺ + e → Ar(4³P₂) + Ar. This collisional process produces Ar atoms in state 4³P₂, which then collide with N₂ resulting in a resonance energy transfer that excites N₂ from its ground state X¹Σ⁺_g to its excited state C³Π_u: Ar(4³P₂) + N₂(X¹Σ_g) → Ar + N₂(C³Π_u). This ultimately leads to population inversion between states C and B of N₂ molecules. Hence, the excited argon atoms serve as a collisional pump for the laser transition of N₂ in the plasma generated by laser-induced filaments, playing an analogous role to that of hot electrons in conventional discharge-pumped nitrogen lasers.

The temporal and spatial properties of observed radiation are shown in Fig. 7. The duration of emission at wavelengths of 337.1 nm and 357 nm reach the nanosecond due to the long lifetime of the metastable excited state (4³P₂) of Ar atom. The lasing beam profile exhibits a super-Gaussian shape with a divergence angle approximately equal to 1.6 mrad. Additionally, they also confirmed an excellent coherence of the nitrogen molecular lasing by observing interference fringes on both the front and rear surfaces of a 2 mm glass plate. In this mechanism, the internal energy of excited argon atoms is transferred to nitrogen molecules through collisional processes, resulting in nitrogen molecule excitation. Therefore, a higher concentration of argon (>3 bar) is required, which is unrealistic for air conditions.

Fig. 7 (a) Temporal profiles of the 337.1-nm (blue solid curve) and 357-nm (magenta dashed curve) laser pulses from the nitrogen–argon mixture. (b) UV-lasing beam profile. The red dotted line shows a 6th-power super-Gaussian fit. Inset is a CCD image of interference in the beam from a 2-mm-thick CaF₂ parallel plate. Free-space nitrogen gas laser driven by a femtosecond filament. Reproduced from ref. 61.

Subsequently, in 2015 Xie et al.⁶³ employed a 800 nm femtosecond laser to pump a mixture of N₂ and Ar gases. By comparing the gain dynamics of forward and backward N₂ lasing, they concluded that the gain lifetime of the nitrogen molecular lasing generated by collisions with excited argon atoms could reach several nanoseconds. They claimed that the minimum gain time necessary for achieving backward nitrogen molecular lasing emission was approximately 0.8 ns.

3.2. Observation of neutral nitrogen lasing pumped by circularly polarized pulses

In 2014, S. Mitryukovskiy et al.⁴⁹ reported that effective amplification of backward 337.1 nm signals can be achieved from filaments generated from high-energy circularly polarized near-infrared femtosecond laser in nitrogen gas. In the experiments, the authors employed a commonly used femtosecond pump source, an 800 nm femtosecond laser from Ti:sapphire amplifier, which holds a significant potential for generating backward air lasing in atmosphere. This discovery has sparked a new wave of research on nitrogen molecular lasing, with detailed descriptions of the properties of both backward and forward radiation provided in subsequent sections.

S. Mitryukovskiy et al. focused an 800 nm laser pulse with a duration of 40 fs and an energy of 8.5 mJ into a gas chamber using a focussing lens with focal length f = 1 m, resulting in the formation of a long plasma filament (∼10 cm). The chamber was filled with pure nitrogen at a pressure of up to 1 bar. Optical emission corresponding to transitions between the C and B states was observed in both forward and backward directions, with the results for the backward emission shown in Fig. 8(a). In Fig. 8(b), emissions at wavelengths of 315, 337, 357, and 380 nm correspond to transitions between C and B states with different vibrational levels, initial and final vibrational quantum numbers are shown in the figure. Notably, when changing from linear polarization to circular polarization for the pump pulse, there was no significant change in signal strength for the 357 and 380 nm emissions. In contrast, the backward 337.1 nm signal increased by nearly forty-fold (Fig. 8(b)), which is a strong signature of stimulated emission. Furthermore, it is worth mentioning that with circularly polarized pump pulses, the forward emission at 337.1 nm was three orders of magnitude higher compared to backward direction emission.

Fig. 8 Backward emission spectra from filament plasma generated by circularly (a) and linearly (b) polarized pump pulses. (c) Dependence of the backward emission on the polarization of the pump pulse. (d) Spatial profiles of 337.1 nm emission measured in backward for linearly (above) and circularly (below) polarized pump pulse. The pump energy is 9.3 mJ. Reproduced from ref. 49.

In further investigations, it was observed that a significant enhancement of the 337.1 nm signal only occurred for the pump pulse of circular polarization. When the polarization of the pump pulse deviated even slightly from circular polarization, as depicted in Fig. 8(c), the signal was a sharply decreased. This means that the lasing phenomenon at 337.1 nm is highly sensitive to the pump pulse polarization. A comparison of emission linewidths revealed that with circularly polarized pump pulses, the 337.1 nm signal is narrowed by one-third compared to the fluorescence emission. As shown in Fig. 8(d), an iCCD camera was employed to capture the spatial pattern of backward nitrogen molecular emission. Only with circular polarization could one observe a Gaussian-shaped radiation with a divergence angle of 9.2 mrad. Further measurements confirmed that the backward radiation is unpolarized.

Then, an external seed pulse was introduced in the nitrogen plasma to confirm the presence of optical amplification.⁶⁵ With appropriate spatial overlap and temporal ordering, an optical signal amplification exceeding two orders of magnitude was observed in both forward and backward directions. The experimental results for the backward emissions are presented in Fig. 9. The backward 337.1 nm signal obtained with only pump laser is shown in Fig. 9(a). The profile of the seed pulse is presented in Fig. 9(b). Strong amplification is evident in Fig. 9(c) when both pump and seed pulses were present. The amplified 337.1 nm signal retained the polarization state of the seed pulse. Based on these characteristics, S. Mitryukovskiy et al. concluded that stimulated radiation at 337.1 nm occurs exclusively under excitation by circularly polarized pump pulse—a process enabled by population inversion between C and B states of nitrogen molecules. In view of the characteristic features mentioned above, the authors attributed the nature of this directional backward and forward emission to Amplified Spontaneous Emission (ASE).

Fig. 9 Spatial profile of backward ASE (a), seed pulse (b), and amplified 337.1 nm radiation (c). The angle of each picture is 12.5 mrad × 10 mrad. Reproduced from ref. 65.

The above results were obtained in pure nitrogen gas. In the ambient air, the forward propagating 337.1 nm coherent radiation was observed to be approximately 250 times weaker than in the nitrogen.⁴⁹ Unfortunately, up to now no backward 337.1 nm lasing emission has been reported under atmospheric conditions with circularly polarized pump lasers. This quenching effect is attributed to the presence of oxygen in air and will be elaborated in Section 5.

3.3. Dynamics of the neutral nitrogen lasing: measurements and modelling

In order to understand the formation of the optical gain inside the plasma, it is crucial to perform gain dynamics measurements and time-resolved characterization of this ASE radiation. The gain dynamics was characterized by recording the amplified signal, while changing the delay between the seed and pump pulse.⁶⁶ By investigating the gain dynamics of the 337.1 nm radiation under different nitrogen pressures, it was observed that it exhibits an ultra-fast establishment time and relatively slow relaxation, as depicted in Fig. 10(a). For instance, the establishment time for gain is 4 ps while the decay time is 20 ps at a pressure of 1 bar. Additionally, it is evident that the establishment time for gain is closely related to the gas pressure. A lower gas pressure results in a longer time for gain establishment. The dependence of the gain built-up time on the pressure rules out the possibility that population inversion of the system is achieved directly through optical pumping mechanism, which occur on the time scale of the pulse duration of 40 fs.

Fig. 10 Upper row: (a) Measured forward amplified 337.1 nm lasing signal as a function of the relative time delay between the pump and seed pulse. Measured temporal profile of (b) forward and (c) backward 337.1 nm signals. (d)–(f) Shows the numerical simulation results. The ASE signal (blue curves in subfigure b) is enlarged by 10 times for the sake of comparison with the amplified seed. Reproduced from ref. 66.

The authors of ref. 65 have employed the cross-correlation method to characterize the seed, the ASE, as well as the amplified 337.1 nm signal in the temporal domain for both the forward and backward emission. The forward amplified spontaneous emission (ASE) in Fig. 10(b) exhibits a pulse duration of approximately ∼20 ps, with its peak position delayed by 26 ps relative to the pump laser. Upon injection of a forward directed seed pulse, the amplified radiation presents a narrower pulse width of about 4 ps, accompanied by an advance of the peak position compared to ASE, occurring approximately 3 ps after the pump pulse. The results for the backward emission are presented in Fig. 10(c). The amplified radiation shows a delay of 14 ps relative to the seed pulse while exhibiting a long-lasting tail up to 100 ps. Utilizing a photodiode for energy measurements, it was revealed that the backward amplified radiation is roughly 150 times weaker than the forward radiation. In fact, for backward-propagating photons, because the lifetime of the gain is only τ_g = 13 ps, the effective gain length that can amplify photons is l = cτ_g = 4.2 mm, which is much smaller than the geometric length of the plasma ∼30 cm.

In order to understand the different temporal dynamics of the forward and backward 337.1 nm emissions observed in experiments, the one-dimensional time-dependent Maxwell–Bloch code DeepOne⁶⁷ and the three-dimensional time-dependent Maxwell–Bloch code Dagon⁶⁸ were adapted to model these experiments. These codes solve a Maxwell wave equation for the electric field enhanced with a constitutive relation derived from Bloch equations:

where E₊, E₋ are the electric fields propagating in the forward and backward directions respectively, P₊, P₋ are the corresponding polarization densities of the medium, Γ is a stochastic source term with vanishing correlation time modeling the spontaneous emission, γ is the depolarization rate due to collisions, z_ul is the corresponding dipole matrix element (that can be deduced from Einstein's A coefficient), N_u, N_l are respectively the population of the upper and lower levels of the lasing transition, ω₀ is the laser frequency and ω_p the plasma frequency.

The populations of different levels were computed using rate equations

where i = u, l and C_ki are the collisional (de)excitation and radiative de-excitation rates. These rates are computed from the cross sections reported in ref. 58. Other parameters can be found in ref. 57 and 59. With this model, numerical simulation results on the optical gain dynamics agree well with the experiments, as shown in Fig. 10(d). The temporal dynamics of both the forward and backward emissions were also well reproduced based on this model, presented in the lower row of Fig. 10(e) and (f).

Indeed, the different temporal profiles of forward, Fig. 10(b), and backward, Fig. 10(c), amplified seed unveils the temporal dynamics of electron collisions inside the filament. The duration of the amplified seed pulses depends on the depolarization rate γ. Higher rates result in shorter pulses and, conversely, lower ones result in longer pulses. The fact that the forward amplified seed is shorter than the backward amplified seed is the signature of a depolarization rate decreasing in time: the forward seed pulse, which is synchronized with the IR pump, always finds a plasma with hot and relative dense electrons. This is not the case for the backwards seed. Due to its counterpropagating nature, the electrons have cooled and recombination has taken place. When the depolarization is driven by electron collisions, it takes the form and its value decreases in time, resulting in shorter pulses when they are amplified in the forward direction.⁶⁷

4. Application

The fluorescence of filaments in air, which is quite visible for human eyes, is a spectacular manifestation of the femtosecond laser filamentary process, especially in case of long filaments (see Fig. 1). This emission in the visible light range provides a direct and very simple characterization of the onset, length and width of the filaments. Actually, researchers have widely employed the photos of the plasma filaments as a basic tool in the study of filamentation. For example, W. Liu and co-workers have used the plasma emission to identify the onset of filaments, in order to determine the critical power for self-focusing.⁶⁹ A kilometre-long nonlinear propagation of terawatt femtosecond laser pulses in atmosphere was confirmed by its plasma fluorescence.⁴ S. Mitryukovskiy et al.⁴⁹ took advantage of this method to calibrate the width of the filaments and confirmed that the filaments width increases with higher power input pulses. In recent studies of air lasing, two kinds of applications have been demonstrated. One application aims at remote spectroscopy, while another one demonstrates detection of external electric field.

4.1. Detection of electric field with fluorescence or lasing emission

As discussed in Sections 2.3 and 2.4, the plasma fluorescence intensity of neutral nitrogen inside filaments originates from inelastic collisions of energetic electrons with the N₂ molecules in ground state. Therefore, the fluorescence can be used to detect an electric field since the electron motion and its resulting kinetic energy can be manipulated by the electric field.

In 2009, Liu et al.²⁹ reported a scheme for detecting terahertz radiation using plasma fluorescence. By observing the lateral fluorescence signal of the plasma emission, such as the 337, 353, 357, 375, 380 nm transitions of the nitrogen molecule's second positive band system, they found through theoretical calculation and experimental analysis that under the irradiation of terahertz radiation on laser-induced plasma in gas, the fluorescence intensity can be significantly enhanced due to the heating of electrons by the terahertz pulse through inverse Bremsstrahlung effect and the consecutive excitation of gas molecules or ions through electron collisions. Moreover, this enhanced fluorescence intensity is proportional to the square of the terahertz electric field intensity, as shown in Fig. 11. This discovery opens a new route to applications of plasma fluorescence for terahertz wave detection.

Fig. 11 (a) Scheme of the interaction of a THz wave and a laser-induced plasma. (b) Measured fluorescence spectra versus THz field amplitude. (c) Measured quadratic THz field dependence of the 357 nm fluorescence emission line. Reproduced from ref. 29.

Inspired by the previous works in which plasma fluorescence was employed for detection of THz fields, Zhang et al.⁷⁰ demonstrated the standoff detection of electric fields using the nitrogen molecular lasing effect. In this experiment, detection of electric fields was achieved by exploiting the bidirectional stimulated radiation signals generated by nitrogen molecular air lasing. By employing a circularly polarized 800 nm pulse to pump nitrogen, they generated both backward and forward lasing emission at 337.1 nm, as shown in Fig. 12. In the presence of an external DC electric field, they found that both the forward and backward 337.1 nm signals were significantly modulated. The experimentally detected emission signals in both forward (12.5 m away) and backward direction (3 m away) are shown in Fig. 13. In the presence of a positive electric field, it was observed that both forward and backward signal were enhanced up to between 20% and 50%, with a saturation effect appearing for E > ∼2 kV cm⁻¹. A linear dependence of the bidirectional signal provides the basis for a sensitive detection of electric fields.

Fig. 12 Scheme of the bidirectional nitrogen lasing for detection of an external electric field. Reproduced from ref. 70.

Fig. 13 Influence of external electric field measured at 12.5 m (a) forward and 3 m (b) back of plasma on 337.1 nm signal. The blue rectangle indicates the heterodyne detection area. Reproduced from ref. 70.

An interesting observation was that the lasing signals present a decrease for a negative electric field up to ∼1 kV cm⁻¹ followed by a signal recovery, as shown in Fig. 13. Consequently, monitoring changes in this signal not only enables amplitude detection but also facilitates determination of the actual direction of external DC electric fields, providing a sensitive method for characterizing both their magnitude and orientation at remote locations. However, this decrease of the signal was unexpected since the electron motion is believed to be symmetric in the transverse plane for the circularly polarized 800 nm pump pulse and the direction of the DC field is expected to be trivial. In the experiments, the authors observed that a weak residual linearly polarized second harmonic pulse was generated in the quarter-wave plate. The presence of this second harmonic pulse breaks the symmetrical motion of electrons in the plane perpendicular to the laser propagation direction. Numerical simulations based on the two-dimensional time-dependent Schrodinger equation and the classic Newton equation for electrons confirmed that the kinetic energy of the electron can be either enhanced or suppressed by a few eV, depending on the direction of the DC electric field. Therefore, the increased or decreased electron kinetic energy leads to a modulation of the population inversion, resulting in either enhancement or attenuation of the 337.1 nm signal when applying a DC electric field in different directions at the plasma filament.

Compared to the works based on plasma fluorescence, the authors employed the directional stimulated lasing beam as the information carrier, instead of the fluorescence signal emitted in the 4π solid angle, which facilitates remote detection. Also, the lasing signal modulation is expected to be more sensitive than the technique based on the modulation of fluorescence signal of nitrogen molecules,²⁹ due to the fact that the lasing signal depends exponentially on the population difference between the C and B states, while the fluorescence depends linearly on the C state population. This is in line with the observation that electric field on the order of 1 kV cm⁻¹ has a significant influence on the lasing signal, while THz field of ∼100 kV cm⁻¹ was used to achieve modulation of fluorescence signal.²⁹

4.2. Spectroscopy study with air lasing

Air lasing can be generated remotely and possesses unique characteristics, such as bidirectional propagation, high collimation, and high coherence, opening up new possibilities for applications in remote sensing. The air lasing effect produced by nitrogen, the main component of air, has been employed in several experiments. For example, for the forward-propagating air lasing of nitrogen ions, the natural alignment of the pump laser with the air lasing pulse provides advantages such as a narrow linewidth and high coherence. Air lasing-assisted coherent Raman spectroscopy was used to excite coherent Raman vibrations in pollutant molecules and greenhouse gases.^71–73 Various molecular components and their concentrations in ambient gases can be inferred from the Raman scattering spectrum.

The backward air lasing has the advantage of bringing the remote information towards the observer, which may greatly improve the detection sensitivity of optical remote sensing in comparison with the omnidirectional fluorescence. This approach addresses the challenges posed by the full spatial diffusion of the scattered light from traditional laser remote sensing and the quadratic attenuation of the signal collected by ground-based observation stations with increasing transmission distance.

P. N. Malevich et al.⁷⁴ reported the first demonstration of a coherent standoff signal using remotely generated backward-propagating molecular nitrogen lasing in a mixture of nitrogen and argon gas. They employed a beam consisting of an intense mid-IR femtosecond pulse and a wavelength tunable picosecond pulse in the forward direction. The intense mid-IR femtosecond pulse interacts with the gas mixture of nitrogen and argon gases, in which a backward-propagating nitrogen lasing is remotely generated, as shown in Fig. 14. The forward-propagating tunable picosecond pulse and the backward-propagating nitrogen lasing provide a scheme of stimulated Raman scattering (SRS) for the gas sample. The coherent SRS signal from a CH₄ gas was detected without any use of reflection mirrors or optics. This proof of principle experiment shows that the backward air lasing has the potential for optical remote sensing in a coherent manner.

Fig. 14 Experimental setup for stimulated Raman gas sensing by backward UV lasing from a femtosecond filament. Reproduced from ref. 74.

5. Quenching effect and challenge

In the first observation of nitrogen lasing driven by circularly polarized 800 nm pulses, S. Mitryukovskiy et al.⁴⁹ have reported the impact of oxygen on backward 337.1 nm lasing. By introducing oxygen into nitrogen gas and employing a circularly polarized 800 nm pulse pump, they observed a significant decrease in signal strength at 337.1 nm. When the oxygen concentration exceeded 13%, a complete suppression of the 337.1 nm lasing signal was observed. Later, Yao et al.⁷⁵ also reported a similar quenching effect of oxygen. This quenching effect is illustrated in Fig. 15(a). However, considering that atmospheric oxygen concentration is approximately 21%, this quenching poses important challenges for practical applications of nitrogen molecular lasing in atmosphere.

Fig. 15 Dependence of the backward 337.1 nm signal strength on O₂ (a), Kr (b), Ar (c), and He (d) pressure. Reproduced from ref. 76.

Several mechanisms have been considered for this quenching effect. First, an intermolecular collision mechanism was proposed.^75,77 The collision between nitrogen in excited C state and oxygen molecules in ground states can lead to dissociation of oxygen molecules, which can be expressed as N(C³Π_u) + O₂ = N₂(X¹Σ_g) + O + O. This collision process reduces the concentration of nitrogen molecules in excited states and consequently diminishes the intensity of the 337.1 nm radiation signal. Second mechanism considers collisions between energetic electrons and oxygen molecules that lead to electron cooling.⁷⁸ High-energy electrons present in plasma filaments collide frequently with oxygen molecules, potentially causing vibration and rotation excitation of oxygen molecules or even their dissociation. These inelastic collisions rapidly decrease the average electron energy. Low energy electrons are unable to effectively excite nitrogen molecules from the ground state, which results in quenching of nitrogen laser radiation. Third mechanism suggests that the presence of oxygen may alters the laser peak intensity inside the filament. Since oxygen (ionization energy U_i = 12.1 eV) is mixed with nitrogen (U_i = 15.6 eV), the clamping intensity within plasma filaments is reduced because its ionization energy is relatively lower than that of nitrogen.⁷⁹ As the kinetic energy of electrons is proportional to the laser intensity, a reduction of laser intensity will lead to a decrease of the kinetic energy for electrons, possibly diminishing collisional excitation efficiency and consequently inducing a quenching effect on lasing.

The mechanism of intermolecular collisions can be excluded based on later experimental observations. As mentioned above, it has been observed that the gain dynamics and lasing emission occur on the time scale of tens of picoseconds. In contrast, molecular collisions have a much longer time scale due to the slow thermal velocity of the molecules compared to the electrons. Therefore, this mechanism should not be important for this quenching effect.

In 2020, Gui et al.⁷⁶ performed systematic experiments to examine the other two mechanisms. They mixed oxygen and different noble gases into nitrogen and examined the dependence of the backward and forward lasing signal on the added gas pressure. They increased the gas pressure of oxygen, argon, helium, and krypton from 20 mbar to 200 mbar with nitrogen at a fixed pressure of 800 mbar. The results for the backward emission are presented in Fig. 15. With noble gases introduced into nitrogen, the excitation of vibrational and rotational degrees of freedom or the dissociation of molecules (the second mechanism) are no longer possible. However, for both forward and backward 337.1 nm radiation, it was found that krypton exhibited a pronounced quenching effect on the lasing signal. In contrast, the intensity of the backward 337.1 nm radiation remained nearly constant at pressures up to 200 mbar in the case of helium, as shown in Fig. 15(d). Based on these observations, the authors attributed the quenching effect of oxygen to a reduced laser intensity inside the plasma. The reduced laser intensity results in a decrease of the free electron energy, and leads to less efficient collision excitation of nitrogen molecules. Helium mixed with nitrogen makes less impact on the 337.1 nm emission intensity because the laser intensity remains almost unchanged within the plasma filament, owing to helium's higher ionization potential (24.5 eV).

In view of this mechanism behind oxygen-induced quenching of nitrogen molecular lasing, it is anticipated that optimization of focusing conditions together with utilization of stronger femtosecond laser pulses will enable achievement of higher laser intensity inside the filaments in atmospheric air and thus allow the generation of backward lasing in atmosphere. Another possible strategy entails utilizing a powerful nanosecond laser pulse to dissociate initially oxygen molecules, minimizing thereby energy losses during injection of circularly polarized pulses at 800 nm wavelength. To manipulate the kinetic energy of the electrons for effective collision excitation, D. Kartashov et al. proposed to employ a microwave pulse to heat further the electrons after ionization by a femtosecond pulse.⁸⁰ Pumping with longer wavelength femtosecond pulses can also be beneficial for the realization of lasing in air since the ponderomotive energy of electrons scales quadratically with the wavelength of the laser field.

6. Conclusions

In this review, we concentrated on one of the most spectacular aspect of the filamentation process, the fluorescence emission and the recently discovered cavity-free lasing radiation of excited neutral nitrogen molecules inside filaments. The fluorescence of filaments plasma excited by femtosecond laser pulses differs significantly from that of air plasma produced by nanosecond and sub-nanosecond laser pulses. This fluorescence is featured by a series of “clean” molecular emission lines without the continuum background due to the different electron density and temperature inside the plasma and different excitation mechanism of molecules and atoms inside the filaments. Following its first observation, this “clean” fluorescence emission has been widely employed for the characterization of filaments, but its mechanism has been debated and not settled until recently. For the fluorescence-emitting excited neutral nitrogen molecules, several mechanisms, including dissociative recombination, intersystem crossing, and electron impact excitation, have been proposed by different groups. With the recently demonstrated time-resolved measurements with femtosecond time resolution, it has been shown that the excited C nitrogen molecules are formed within ∼4 ps in atmosphere conditions. This ultrafast formation time provides an essential criterion for the above different mechanisms, since the molecular pathways (dissociative recombination and ISC) predict much longer sub-nanosecond formation time due to the small collision rate between molecules while the electron collision excitation can well reproduce the observed picosecond temporal dynamics. Therefore, it became clear that the collisional excitation of nitrogen molecules by energetic electrons is the dominant pathway for the formation of the excited neutral nitrogen molecules.

Due to the presence of large amount of excited nitrogen molecules, it was surprisingly found that the filaments can emit UV lasing radiation along its propagation axis in both forward and backward directions. No optical cavity is necessary for this lasing effect due to the large single-path optical gain. This cavity-free lasing effect has attracted much attentions in recent years since it holds the unique potential to create a virtual laser source in the sky, which emits coherent radiation from the sky to the ground observer. It was expected that this backward-propagating coherent laser emission can lead to revolutionary improvement for optical remote sensing since coherent optical spectroscopy methods can now be applied for trace gas detection. With the widely used 800 nm femtosecond laser pulses, it has been demonstrated that circular laser polarization is necessary due to the distinct electron kinetic energy distribution after photoionization inside the filaments. Both the forward and backward lasing signal at 337.1 nm have been systematically characterized in the temporal domain and the corresponding gain dynamics has been investigated. It was found that the optical gain and lasing emission occur on the time scale of tens of picosecond, depending on the gas pressure. The experimental observations are compared with numerical simulations based on Maxwell–Bloch equations and it was revealed that the fast cooling of electrons due to collision excitation plays a decisive role for the temporal dynamics. The much weaker and longer backward emission with respect to the forward one was also attributed to the limited lifetime of the optical gain and the smaller depolarization rate.

The applications of the plasma fluorescence for the characterization of filaments have been explored since the beginning of the filamentation study. Later, the enhanced fluorescence in presence of external electric field was exploited to measure the waveform of intense terahertz pulses, which holds the advantage of standoff and omnidirectional detection. For the coherent lasing emission from the filaments, its potential for trace gas detection with stimulated Raman spectroscopy and sensitive DC field have been recently demonstrated.

In the meantime, for the practical applications of the cavity-free lasing effect from filaments, the achievement of backward lasing in atmosphere is crucial. Nowadays, it was observed that the presence of oxygen molecules results in a significant quenching effect of this cavity-free lasing effect and the backward lasing was entirely suppressed in ambient air. The reason for this quenching effect has been attributed to the reduced laser intensity inside the filaments due to the smaller ionization energy of oxygen molecules. Several possible methods to overcome this quenching effect are now actively exploited by different groups for the realization of backward lasing in atmosphere, which will provide a conceptually new coherent light source in the sky and breed revolutionary improvement for optical remote sensing.

Data availability

No primary research results, software or code have been included and no new data were generated or analyzed as part of this review.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The work is supported in part by the National Key R&D Program of China (no. 2023YFA1406801), National Natural Science Foundation of China (no. 12034013, 92250305), Fundación BBVA (Beca Leonardo a Investigadores y Creadores Culturales 2021), Ministerio de Ciencia e Innovación (grant CNS2023-144058) and Agencia Estatal de Investigación (MCIN/AEI/10.13039/501100011033) and European Union “NextGenerationEU”/PRTR, grant CNS2023-144058.

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