High-power femtosecond lasers pumped by laser diodes (LDs) play a significant role in industrial processing and scientific research. Femtosecond lasers are generated directly using mode-locked lasers. The components of a mode-locked laser include a gain medium, pump source, mode-locked device, and dispersion compensation device. The gain medium is the core of the laser; it provides population inversion and generates excited radiation. With the emergence of high-brightness and high-power semiconductor lasers, ytterbium ion (Yb³⁺)-doped solid-state laser materials have rapidly developed and become one of the most important gain media in the field of high-power and femtosecond lasers. High-power Yb-femtosecond lasers are mainly based on semiconductor saturable absorber mirror (SESAM) mode-locking technology and Kerr lens mode-locking (KLM) technology. Generally, both passively mode-locked and Kerr lens mode-locked femtosecond lasers need to introduce a certain amount of negative group delay dispersion (GDD) to balance the self-phase modulation in the cavity and produce stable femtosecond solitons. Particularly, as the average power increases, the intracavity self-phase modulation becomes stronger and more negative GDD is needed. It is well known that dispersion compensating devices include prism pairs, chirped mirrors, and Gires-Tournois interferometer (GTI) mirrors. Prism pairs lead to complex oscillator structures, while chirped mirrors and GTI mirrors are more expensive. Therefore, high-power Kerr lens mode-locked lasers without dispersion compensation devices are of great research significance for reducing the cost of femtosecond lasers. Based on the above background, this study evaluates the Kerr lens mode-locking technique using non-GDD-optimized broadband highly reflective mirrors for dispersion compensation. Because broadband highly reflective mirrors tend to be negatively dispersive in the band at wavelengths longer than their center wavelengths, we propose the use of broadband highly reflective mirrors instead of GTI mirrors to realize high-power Kerr lens-locked operation based on Yb∶CYA crystals.

The experimental setup is a dual-confocal cavity, and the pump source is a 50-W fiber coupled output LD at a wavelength of 976 nm with a beam quality factor (M2) of approximately 25. The pump is imaged into the crystal with a 104 μm-diameter spot by an imaging system. The laser spot size in the designed resonant cavity is simulated in the simulation software, and the beam waist radius size of the laser in the gain medium is calculated to be 70 μm. The spot diameter of laser mode is slightly larger than that of the pump light mode, which is conducive for the formation of a soft-aperture diaphragm. The cross-section area of 6-mm long Yb∶CYA crystal used in the oscillator is 3 mm×3 mm. The absorption slope of the pump is 93%. For the thermal load dissipation, the crystal is wrapped in indium foil and mounted tightly on a water-cooled copper heat sink maintained at a constant temperature. The nonlinear Kerr medium is a thin slice of CaF₂ with a thickness of 2 mm. The Kerr medium and the incident light are placed at the Brewster angle to compensate for the astigmatism introduced by the folding angle of the concave mirrors and maintain the linear polarization of the laser inside the cavity. Moreover, we use four broadband highly reflective mirrors covering 750-1100 nm in the cavity for dispersion management, because these highly reflective mirrors have negative dispersion in the bands at wavelengths larger than the central wavelength of 950 nm and positive dispersion in the bands at wavelengths smaller than the central wavelength. We measure the amount of negative dispersion introduced by the broadband high-reflective mirrors near the wavelength of 1030 nm, and each of them can provide GDD of approximately -550 fs2 for a single bounce; thus, the net dispersion in the cavity is -1520 fs2 using four high-reflective mirrors. The resonant cavity has a single cavity length of 1.85 m, corresponding to a repetition rate of approximately 81.1 MHz.

A stable mode-locked operation with an output power of 3.6 W, spectral full width at half-maximum of 15.2 nm, and pulse width of 92 fs is achieved at 18 W pumping using an output coupler with transmittance of 15%. The root mean square (RMS) of the average power fluctuation during the mode-locking operation is 0.46% over 100 min, and the beam quality factors of the mode-locked laser in x and y directions are 1.24 and 1.22, respectively.

Using broadband highly reflective mirrors instead of expensive GTI mirrors, a stable mode-locking operation with a high average power and short pulse duration is achieved, significantly decreasing the laser cost. Moreover, it is believed that such low-cost all-solid-state femtosecond lasers, which can directly produce high power, narrow pulse widths, good stability, and high beam quality, will become popular in frontier scientific research and industrial processing.

Diode-pumped solid-state lasers (DPSSLs) are widely used in many applications owing to their high energy, high repetition rate, and high efficiency. The gain medium is one of the core components of the DPSSL system; however, when the gain medium is subjected to a high-power pumping source, an uneven heat source is formed in it, resulting in an uneven temperature distribution. Furthermore, the cooling device can only dissipate heat to its surface, which in turn generates temperature gradients in different directions. The thermal deformation and stress caused by the temperature gradient in the gain medium eventually degrade the laser output power and beam quality. In this study, the finite element analysis (FEA) is used to optimize the design of a microchannel heat sink for laser amplifier cooling, and the effects of parameters such as microchannel bottom-plate thickness, channel height, channel width, channel wall thickness, and inlet velocity on the maximum temperature of the gain medium surface are investigated. The results are expected to provide accurate guidance for practical experiments.

To study the ability of the microchannel heat sink to cool the laser amplifier, a full-size model containing a slab-type gain medium and a microchannel heat sink is established (Fig. 1). The uppermost layer is the gain medium, the middle layer is the microchannel heat sink, and the bottom layer is the cover plate. The flow and convection-diffusion phenomena occurring in the inhomogeneous heat and microchannel heat sink within the slab-type gain medium are then studied by a flow-heat-solid multiphysical field coupling analysis. Finally, the coupling of heat and fluid under full-size model conditions is directly simulated using the ANSYS FLUENT module, in which the heat source within the gain medium is loaded through the UDF command. The pressure-velocity coupling is achieved using the SIMPLE algorithm, the flow parameter interpolation method is second-order windward, the heat sink material is purple copper, and the cooling medium is deionized water.

Pulsed pumping can be approximated as continuous pumping when the repetition rate is high (Fig. 3). When cooling the gain medium using a microchannel heat sink, the entire system can be simulated using the ANSYS FLUENT module under the set initial parameters (Fig. 4), and the distribution of thermal deposition in the gain medium can also be determined at this time (Fig. 5). When the microchannel bottom-plate thickness increases from 1 mm to 5 mm, the maximum temperature of the gain medium surface also increases (Fig. 6). The bottom-plate thickness cannot be too small, given that microchannel thermal deposition will be deformed by heat and must withstand a certain water pressure. Therefore, the optimal value of the bottom-plate thickness is set as 2 mm. When the channel height increases from 2 mm to 4 mm, the maximum temperature decreases significantly; when the height increases from 4 mm, the maximum temperature decreases, but the decrease is not significant (Fig. 7). Therefore, a channel height of 4 mm is selected. In the process of increasing the width of the channel from 0.3 mm to 1.2 mm, the maximum temperature and thermal resistance increase gradually. The pressure loss decreases significantly when the channel width increases from 0.3 mm to 0.6 mm, and the pressure loss decreases slowly when the channel width continues to increase from 0.6 mm. However, the pressure loss increases sharply when the width of the microchannel is too small. Therefore, the channel width is set at 0.4 mm (Fig. 8). The lowest temperature is observed on the surface of the gain medium when the channel-wall thickness is 0.3 mm (Fig. 9). The inlet velocity also affects the temperature of the gain medium surface (Fig. 10). When the flow rate increases from 0.5 m/s to 3 m/s, the temperature of the gain medium surface decreases, but the pressure loss increases. Therefore, the flow rate of 2.5 m/s is optimal. The equivalent heat transfer coefficient of the microchannel system is also calculated under the premise that the temperature of the system is known (Fig. 11). This value can be used to measure the cooling capacity of the microchannel cooling system under different parameters (Fig. 12). The analysis shows that the equivalent heat transfer coefficient of the microchannel system is up to 5000 W/(m²·K).

In this study, the temperature distribution characteristics of a high-repetition-rate and high-energy conduction cooling laser amplifier are numerically simulated by finite element analysis. The effect of each parameter within the heat sink of the microchannel on the maximum temperature of the gain medium surface is systematically discussed and analyzed, and the values of each parameter are optimized from the perspective of practical application and safety. The maximum temperature of the gain medium surface is the lowest when the bottom-plate thickness is 2 mm, channel height is 4 mm, channel width is 0.4 mm, and channel wall thickness is 0.3 mm. On this basis, the effect of the inlet velocity of the cooling fluid is further analyzed. The results show that the inlet velocity is not as high as possible, but its value is suitable; an extremely high inlet velocity is not conducive to a significant reduction in the surface temperature of the gain medium and will also cause a large pressure loss. Finally, the maximum temperature of the gain medium surface for specific microchannel parameters is determined. The equivalent heat transfer coefficient obtained can accurately and clearly reflect the cooling capacity of the microchannel system. The calculation results of this study can provide a strong numerical basis and theoretical foundation for practical fabrication and experiments on microchannel heat sink structures for slab laser amplifiers.

Recently, an increasing number of frequency-stabilized deep ultraviolet (DUV) lasers have been used in research on the laser cooling of atoms and ions, such as H, Hg, Cd, Mg, Be⁺, In⁺, and Mg⁺. Mercury atoms, which are the heaviest stable laser-cooled atoms, have been widely studied owing to their unique nature. Mercury atoms have a low sensitivity to blackbody radiation, and the mercury lattice clock is one of the recommended secondary representations of the second in the international system of units. It is also a good candidate to test the variation in the fine-structure constant and to measure the permanent electric-dipole moment of the electron. For the laser cooling of neutral mercury atoms, it prefers to adopt a two-dimensional magneto-optical trap (2D-MOT) plus three-dimensional magneto-optical trap (3D-MOT) configuration to improve the loading rate. This configuration requires a higher deep ultraviolet laser power, which is limited by DUV damage to optical elements. Here, we present a frequency stabilization laser system based on an optical phase-locked loop (OPLL) between infrared seed lasers, which can easily adjust the laser frequency over a wide range and efficiently use DUV laser power.

The ¹S₀→³P₁ transition at 253.7 nm is used for the laser cooling^{of mercury atoms. In the 2D-MOT plus 3D-MOT configuration, the frequencies of the 2D-MOT, push beam, and 3D-MOT must be independently adjustable. Therefore, in this study, two 253.7 nm frequency-quadrupled DUV lasers are used, and a frequency-stabilized DUV laser system with optical phase-locked loop technology is developed for the laser cooling of neutral mercury atoms. One DUV laser is locked on the saturated absorption spectroscopy and is used as the cooling laser of the 2D-MOT. Three acousto-optic modulators (AOMs) are used to set the detuning of each beam. Another DUV laser is frequency-stabilized by an OPLL between the semiconductor seed lasers at 1014.9 nm and is used as the cooling laser of the 3D-MOT without passing through any additional frequency shifter. A feed-forward method is adopted to reduce the frequency switch time because the cooling laser for 3D-MOT is also used for fluorescence detection.}

Two DUV cooling lasers are phase-locked by the OPLL method (Fig. 3), and the frequency drift in the long term is markedly suppressed. After being locked on the saturated absorption spectroscopy, the frequency fluctuation of the DUV laser is less than 350 kHz, and the relative frequency instability between the two DUV lasers is reduced to 30 mHz at an average time of 1000 s (Fig. 5) by the OPLL. A phase frequency detector (PFD) is used as the phase discriminator of the OPLL. It has a broad capture range, and the loop bandwidth can be easily controlled. Therefore, the frequency offset between the two DUV lasers can be adjusted within 2 GHz, and the DUV laser linewidth is measured with weak frequency locking (Fig. 4). Using the feed-forward method, the frequency switch time of the 3D-MOT cooling laser is found to be 0.15 ms with 100 MHz frequency shift, which is 1/23 of the original (Fig. 7). Therefore, the frequency stability and fast tunability of this cooling laser system meet the requirements of our 2D-MOT plus 3D-MOT configuration and the loading rate is 1×10⁶/s.

In our frequency-stabilized laser system, the frequency of the DUV laser can be easily adjusted over a wide range, the DUV laser power is efficiently used, and the system complexity is reduced. This frequency-stabilization scheme not only satisfies the laser cooling requirements of neutral mercury atoms but is also applicable to other atoms, such as Cd and Mg. Moreover, it can produce coherent DUV lasers, which can be used in experiments such as electromagnetic induction transparency, Raman sideband cooling, and atom interferometry.

Laser-diode-pumped compact all-solid-state lasers with a high repetition frequency, short pulse width, and high beam quality have a wide application range in laser ranging, LIDAR detection, laser communication, and industrial processing. However, the thermal effect of solid-state lasers under high-power pumping is a crucial factor limiting the combination of the high single-pulse energy, high repetition frequency, and high beam quality characteristics of pulsed lasers. The burst-mode laser technology produces laser pulses in an intermittent mode, which alleviates the thermal effect of the continuous output of pulsed lasers to a certain extent. Common rod solid-state lasers are often end-pumped, which inevitably causes uneven heat distribution in the crystal. The slab laser reduces the temperature difference of the crystal by increasing the cooling area of the gain medium and makes the laser propagate along the zig-zag shape in the direction of the temperature gradient, which can reduce the thermal effect on the laser output to a certain extent. However, owing to the asymmetric shape of the slab gain medium, the output laser pulse is often elliptical or elongated in cross-section, resulting in a large difference in the beam quality in the x and y directions. In this study, beginning with the structure of the slab gain medium, we optimize the design of the gain medium size and aspect ratio and limit the range of the crystal doping region to reduce the thermal effect and optimize the laser spot. We hope that this method, which improves the beam quality of burst-mode lasers by optimizing the crystal structure of slabs, can also promote the development of high-energy, higher-repetition-frequency, and high-beam-quality burst-mode lasers.

In this study, Nd∶YVO₄ crystals with large stimulated emission cross-sections and short upper-energy-level lifetimes are side-pumped by an laser diode (LD), and both sides of the doped region are bonded with non-doped YVO₄ crystals to increase the heat dissipation area and constrain the pumping region, which facilitates heat dissipation and achieves high-repetition-frequency laser operation. By designing the crystal doping area aspect ratio to obtain a square beam exit surface, transmitting the laser pulse along the zig-zag shape in the doped region, and emitting the laser pulse perpendicular to the crystal end surface, the cavity mode optimization design is combined to limit and optimize the beam quality of the laser in the thickness and width directions to make both similar. In addition, the mode-selective effect of the small-aperture diaphragm is combined to further optimize the beam quality and obtain a pulse laser with the similar beam quality in the x and y directions. Electro-optical Q-switching technology is used to achieve a high repetition frequency and short pulse width output, and the transmittance of the output coupling mirror is optimized to obtain high-power burst-mode lasers.

Under the condition that the optimal transmittance of the output coupling mirror is 40% and the sub-pulse Q-switched repetition frequency is 80 kHz, a 1064-nm burst-mode laser with the highest average power of 5.03 W is obtained, with beam quality factor (M²) values of 2.67 and 2.43 in the x and y directions, respectively (Fig. 4). It can be seen that the beam qualities are similar in both directions, but there are certain higher-order-mode oscillations accompanied by stray light. By adding a small-aperture diaphragm with a diameter of 1 mm in the cavity to filter out stray light and suppress some of the higher-order-mode oscillations, a burst-mode laser with an average power of 2.56 W and a sub-pulse width of 7.2 ns is obtained (Fig. 5), and the M² values in the x and y directions are 1.42 and 1.49, respectively (Fig. 6). This indicates that a high-energy, high-frequency, high-beam-quality burst-mode laser with similar beam quality in the x- and y-directions is realized in this study. In addition, this study measures the output waveforms of the burst-mode lasers at different sub-pulse repetition frequencies (Fig. 7) and the variation in sub-pulse width with Q-switched frequency at maximum pumping power (Fig. 8).

By optimizing the aspect ratio of the high-gain Nd∶YVO4 slab crystal to limit the generation of higher-order modes in the doping region and constraining the M² values in the width and thickness directions to be approximately equal, a 1064-nm burst-mode laser with a high repetition frequency, short nanosecond pulse width, and high beam quality is obtained using LD-side quasi-continuous pumping and electro-optical Q-switching techniques. With the optimal transmittance of the output coupling mirror at 40%, the 1064-nm pulsed laser is obtained with an average power of 5.03 W and a sub-pulse Q-switched repetition frequency of 80 kHz, and the M² values in the x and y directions are 2.67 and 2.43, respectively. By adding a small-aperture diaphragm in the cavity to filter out stray light and suppress the oscillation of some higher-order modes, a burst-mode laser with an average power of 2.56 W and a sub-pulse width of 7.2 ns is obtained. The M² values in the x and y directions are 1.42 and 1.49, respectively. This approach provides a new research idea for the design of high-energy, high-frequency, and high-beam-quality burst-mode lasers.

High-power ultrashort pulse lasers operating in the picosecond and femtosecond time domains have important applications in strong-field physics, biomedical imaging, optical frequency conversion, and nuclear laser fusion. One approach for obtaining such high-power ultrashort pulses is the use of the amplification systems, such as chirped pulse amplification (CPA) or a master oscillator power amplifier (MOPA). However, amplifier chains produce amplified spontaneous emission (ASE), and the complex structure of the amplifier reduces the stability of the system. Another method is to use the direct output from the mode-locked oscillator, represented by a semiconductor saturable-absorber mirror (SESAM) mode-locked disk laser, which was demonstrated in 2000. The disk gain medium has a high area-to-volume ratio, which leads to excellent heat dissipation and therefore stabilizes the operation at high power. However, its low single-pass gain requires a complex multi-pass pump for improving the absorption efficiency of the pumped light, which can reduce the system stability. In 2022, our group reported a large core-size crystal waveguide mode-locked laser, providing a new solution for realizing high-power mode-locked lasers. Crystal waveguides used as gain media have good mode limiting capability and high heat dissipation capability, and they can achieve a stable high-power output. We believe that this new mode-locked oscillator has potential for power scaling. As studies related to dispersion compensation for crystal waveguide mode-locked lasers have been scarce, investigation of dispersion compensation to find ways to increase power is essential.

The semiconductor saturable-absorber mirror used for mode-locking introduces the tendency of the laser towards Q-switching instabilities; thus, the Q-switching mode-locking (QML) operation of the laser can be realized with a repetition frequency of the order of kHz. This leads to the generation of high-energy pulses that will cause irreversible damage to the SESAM. The cavity design follows the conditions proposed by H?nninger et al. with regard to achieving continuous-wave mode locking (CWML). We calculate the threshold powers for different spot radii on the SESAM and different cavity lengths (Fig. 1) and then select suitable cavity parameters. The spot radius on the SESAM is set as 200 μm, the cavity length is 4.5 m, and the theoretical value of power for CWML is 3.4 W. To achieve a stable CWML, a commercial SESAM with a small modulation depth is selected, an output coupler with a lower transmittance is used, multiple 4f systems are employed to increase the cavity length, and the focal length ratio of the last set of mirrors is changed to scale the spot radius on the SESAM. Furthermore, we analyze the main sources of dispersion in the cavity and experimentally implement dispersion compensation by inserting five Gires-Tournois-Interferometer (GTI) mirrors in the cavity (Fig. 3) and the -23500 fs² group velocity dispersion (GVD) per round trip is achieved. The experimental results show a significant improvement compared to the configuration without dispersion compensation, and no obvious saturation is observed in the output power curve [Fig. 5(a)], indicating further power expansion.

At a pump power of 160 W, the waveguide core absorbs a pump power of 84 W, the pump absorption efficiency is 52.5%, the output power is 21 W, and the optical-to-optical efficiency is 25%. The beam quality values in the x and y directions of the output beam are 1.17 and 1.05, respectively, which indicates impressive beam quality. The wide-span radio frequency (RF) spectrum and autocorrelation curve indicate single-pulse operation. Figure 6(a) shows a single-pulse shape, illustrating an autocorrelation trace with an full width at half-maximum (FWHM) of ～2 ps, corresponding to a time-bandwidth product of 0.4. The time-bandwidth product is closer to the Fourier limit compared with that of the configuration without dispersion compensation. We analyze the reasons for the low optical-to-optical efficiency and suggest ways for further power expansion: 1) No significant saturation is observed in the experiment and a higher output can be obtained when a high-power pump laser is used. 2) Using a crystal waveguide with a large core size as a double-cladding structure, optimizing the length of the crystal waveguide, or connecting multiple crystal waveguides in series can help to improve the pumping efficiency and increase the output power. 3) The focal length ratio of the last set of mirrors can be adjusted so that the spot area on the SESAM will also increase by a corresponding multiple; when the power in the cavity increases by a certain multiple, then stable mode locking can be achieved. 4) With an increase in the output power, the use of an output coupler with a higher transmission ratio can improve the slope efficiency of the laser.

An all-solid-state passively mode-locked laser based on a Yb∶YAG large-core-diameter crystal rectangular waveguide is reported. Using a GTI mirror to compensate the dispersion in the cavity as well as using a laser with average power of 16 W, a pulse width of 2 ps, time-bandwidth product of 0.4, and repetition rate of 31.7 MHz can be obtained. The mode-locked output characteristics of the large-core-diameter crystal rectangular waveguide mode-locked laser are experimentally studied. The main sources of intracavity dispersion are analyzed, and methods to expand the output power are proposed.

Mid-infrared lasers at approximately 3 μm can be used in many fields such as medical surgery, trace gas detection, remote sensing, and infrared countermeasures. Such laser source can be obtained via Dy³⁺-, Ho³⁺-, or Er³⁺-doped laser active medium. The development of Dy³⁺- and Ho³⁺-doped lasers is limited because of the lack of a suitable pump source. In contrast, there is a strong absorption band of Er³⁺-doped crystals at approximately 970 nm and they can be pumped by well-developed high-power InGaAs LDs. However, the transition of Er³⁺ ions at approximately 3 μm wavelength is self-terminating because the lifetime of the initial laser level is considerably shorter than that of the terminal laser level. To overcome this “bottleneck”, Er³⁺ ions with a high atomic fraction of 30%-50 % are typically required to depopulate lower laser level ⁴I_13/2. The thermal effects increase with increasing doping concentration. Cascading ⁴I_13/2→⁴I_15/2 near-infrared laser emission can achieve a 3-μm-laser output at an extremely low doping concentration but at the expense of reducing the conversion efficiency. In our recent study, it has been proven that the cyclic cascade can improve the efficiency of a 3-μm-laser in Er∶YAG crystals, with a low doping concentration at room temperature. However, the maximum slope efficiency does not exceed 10%. On the basis of the cyclic cascade, improving the slope efficiency is a meaningful attempt.

In this study, we theoretically analyzed the two main factors influencing the mid-infrared (MIR) laser slope efficiency in Er∶YAG crystals, namely, quantum efficiency and overlapping efficiency. We analyzed the mechanism of improving the quantum efficiency by a cyclic cascade. For the overlapping efficiency, we simulated the distributions of the pump light and laser mode field and analyzed their influence on the overlapping efficiency. Next, the coating parameters of the cavity mirror were designed according to the relevant characteristic wavelengths in the cyclic cascade process. Er∶YAG crystals with doping concentrations (atomic fractions) of 7.5%, 10%, 15%, and 25% were used in the experiment and cut along their〈111〉crystal direction, with cross-sections of 3 mm×3 mm. The lengths of the Er∶YAG crystals with atomic fractions of 7.5%, 10%, and 15% were 10 mm and 2 mm, and the lengths of Er∶YAG crystals with atomic fraction of 25% were 5 mm and 2 mm. The pumping source was a stable wavelength fiber-coupled laser diode with a central emission wavelength of 976 nm. A spectrometer was used to measure the laser output spectrum and determine whether a cascade oscillation was formed. An energy meter was used to measure the output energy and other related parameters. Then, the laser output slope efficiency was calculated to analyze the influence of improving the overlapping efficiency by optimizing the crystal length on the slope efficiency.

In the output spectra of the crystals with four doping concentrations, two emission peaks in near-infrared (1469 nm) and mid-infrared (2937 nm) bands can be observed (Fig. 5), showing that the near-infrared light and mid-infrared light have formed a cascade oscillation in the cavity. For Er∶YAG crystals with lengths of 10 mm and 5 mm, the threshold is greater than 23 mJ, whereas for Er∶YAG crystals with a length of 2 mm, the threshold is lower than 17 mJ. The threshold of Er∶YAG crystals with a larger length is generally higher than 2 mm (Fig. 6 and Table 1). In terms of the 2937-nm mid-infrared laser output slope efficiency, under the same doping concentration, the laser slope efficiency of the 2-mm long crystal is significantly improved compared with that of the longer laser crystal. In particular, for Er∶YAG crystals with an atomic fraction of 10%, when the crystal length is 10 mm, the mid-infrared laser threshold is 23.4 mJ, and the slope efficiency is 23.5%; when the crystal length is 2 mm, the mid-infrared laser threshold is 11.4 mJ, and the slope efficiency is 36.5%. Compared with the 10-mm long crystal, the threshold is reduced by 51.3%, and the slope efficiency is increased by 55.3%. To the best of our knowledge, this is the first time that a slope efficiency exceeding the Stokes limit has been obtained for low-doped Er∶YAG crystals at room temperature (Fig. 6 and Table 1).

A high-efficiency cyclic cascade Er∶YAG mid-infrared pulsed laser at room temperature is reported. Based on the cyclic cascade, using the optimized cyclic cascade cavity, the influence of optimizing the crystal length to improve the beam overlap on the slope efficiency of the mid-infrared laser is explored. The experimental results show that by appropriately shortening the crystal length, the threshold of mid-infrared laser oscillation is reduced considerably, and the slope efficiency is significantly improved. Slope efficiencies of 2937 nm mid-infrared lasers up to 36.5% and 37.2%, exceeding the Stokes limit of 33.2%, are achieved in Er∶YAG crystals with a length of 2 mm and Er atomic fractions of 25% and 10%, respectively. To the best of our knowledge, this is the first time that an Er∶YAG crystal with a low doping concentration (atomic fraction of 10%) is used for a high-efficiency 3-μm mid-infrared laser output exceeding the Stokes limit at room temperature. Moreover, Er∶YAG crystals with an Er atomic fraction of 10% can produce less thermal effect than Er∶YAG crystals with an Er atomic fraction of 25% and is expected to obtain a higher average output power. This study can help to promote the development of 3-μm mid-infrared high efficiency high average power lasers.

As an ideal light source for 3D cameras, 940 nm vertical cavity surface emitting lasers (VCSELs) have broad application prospects and can be used in virtual reality and car-assisted driving. The optimal design of the distributed Bragg reflector (DBR) is crucial for improving the performance characteristics of 940 nm VCSELs. In traditional research, there are few studies on DBRs in the 940 nm band. To provide guidance for the design and optimization of DBR structures in 940 nm VCSELs, we systematically study the reflection properties of various DBR structures. In the present study, we apply the transmission matrix method (TMM) to multilayer dielectric films to calculate and analyze the influence of different stacking methods and periods on the DBR reflection spectrum. The model is modified and the influence of the incident angle on the DBR reflection spectrum is calculated and analyzed. A linear fitting model between the refractive index of Al_xGaAs and Al atomic fraction x at a wavelength of 940 nm is established. The effect of the gradient layer on the reflectance spectrum characteristics of the DBR is calculated and analyzed using the multilayer division equivalent method. Through our research analysis, the relationship between the DBR structure and its reflective properties can be understood more clearly.

In this study, we choose Al_0.89GaAs as the DBR low-refractive-index layer material (L) and Al_0.09GaAs as the DBR high-refractive-index layer material (H) with refractive indices of 3.497 and 3.040, respectively. The reflection characteristics of different DBR structures are analyzed using the TMM. First, we use the transmission matrix of the multilayer dielectric film to study the effects of different stacking methods and periods on the reflection characteristics of the DBR structure. Subsequently, considering the influence of the incident angle on the reflection spectrum, we modify the transmission matrix and study the influence of different incident angles on the reflection characteristics of the DBR. Finally, to simplify the calculation of reflection spectrum characteristics of the gradient layer structure, we linearly fit the relationship between the refractive index of Al_xGaAs material and the aluminum atomic fraction x, and we adopt the multilayer division equivalent method by dividing the Alx1-x2GaAs gradient layer into sufficiently small ultra-thin and equal thickness layers; when the divisions are sufficiently large, this stepped layered structure can truly replace the gradient layer structure.

The highest reflectivity (99.86%) of the DBR structure arranged using the LH stacking method is significantly greater than that (98.32%) of the structure arranged using the HL stacking method, but the reflection spectral bandwidths of the two structures are basically the same (Fig. 5). When the number of DBR periods is 15, the reflectivity can reach 98.3%; when the number of periods is >17, the reflectivity of the DBR is >99%; when the number of periods is >20, the reflectivity is >99.5%; and when the number of periods is >40, the reflectivity is >99.99% (Fig. 6). As the incident angle increases, the optical path difference of the dielectric layer decreases, and the DBR reflection spectrum shifts to the short-wavelength direction as a whole. When the incident angle is 0 (normal incidence), the central wavelength of the DBR reflection spectrum is ~940 nm, and when the incident angle is π/3, the central wavelength of the DBR reflection spectrum shifts to 910 nm; that is, the central wavelength is greatly affected by the incident angle (Fig. 7). When the reflectivity is >99.4%, the stop bandwidth of the mutant DBR (D=0 nm) is 89 nm, the stop bandwidth of the DBR with D=10 nm is 88 nm, the stop bandwidth of the DBR with D=20 nm is 85 nm, the stop bandwidth of the DBR with D=30 nm is 81 nm, and the stop bandwidth of the DBR with D=40 nm is 75 nm (Fig. 9). The maximum reflectivity of the gradient DBR gradually decreases with an increase in the thickness of the gradient layer. The highest reflectivity of the mutant DBR exceeds 99.85%, and the highest reflectivity of the DBR with D=40 nm is still >99.6% (Fig. 10).

In this study, using the transfer matrix model, the effects of the DBR stacking method, number of DBR periods, incident angle, and thickness of the gradient layer on the reflectance characteristics of an Al_0.89GaAs/Al_0.09GaAs DBR are investigated. At a wavelength of 940 nm, the refractive index of Al_xGaAs has a linear relationship with the aluminum atomic fraction x, which can be expressed as nAlxGaAs=-0.572x+3.550, which is consistent with the calculation result of the Sellmerier formula. When the incident medium is GaAs and the output medium is air, the DBR with the LH stacking method has greater reflectivity. To study the relationship between the incident angle and the DBR reflection spectrum, the TMM is modified. It is found that, with an increase in the incident angle, the reflection spectrum of the DBR structure moves in the short-wavelength direction, and the reflectivity of the DBR increases. Using the multilayer division equivalent method, the refractive index gradient structure is replaced by a refractive index stepped structure, and the reflection spectrum characteristics of the gradient DBR are analyzed. It is found that, with an increase in the thickness of the gradient layer, the reflection bandwidth of the DBR narrows and the reflectivity at the center wavelength is essentially unaffected. In follow-up research and device preparation, our calculation results can provide a useful guide for the design and optimization of the DBR structure in 940 nm VCSELs.

There are increasing demands for mid-infrared lasers at 3-5 μm, which overlaps with the transparency window of atmosphere, for their potential applications in various fields, including laser surgery, spectroscopy, infrared countermeasures, environmental monitoring, and laser communication. There are lots of approaches to achieve lasers at 3-5 μm band, which can be roughly divided into two major categories. The first category is based on population inversion, namely the linear method, which includes HF/DF gas lasers, semiconductor cascade lasers, fiber lasers, and solid-state lasers (typically Fe∶ZnSe or Fe∶ZnS lasers). The second category is based on the nonlinear effect, including optical parametric oscillators (OPO, typically using PPLN and ZGP crystals as nonlinear media), difference frequency generation (DFG), and frequency doubling. Compared to these lasers, the Fe∶ZnSe or Fe∶ZnS lasers, emitting at the mid-infrared range of 4-5 μm, enjoy several advantages, including high efficiency, wide wavelength-tuning range, and compactness of optical cavity. As a consequence, lots of efforts have been made in the development of Fe∶ZnSe/Fe∶ZnS lasers in the past decade. For some practical applications, continuous-wave (CW) Fe∶ZnSe/Fe∶ZnS lasers are required. Several CW Fe∶ZnSe lasers, all of which operates at the wavelengths of over 4 μm, have been demonstrated by using various CW pumping sources, including the Cr:ZnSe laser, Er:YAG laser, Er:ZBLAN fiber laser, and Er:Y₂O₃ laser. Limited by matured pump sources at ~3 μm, CW Fe∶ZnSe lasers were seldom domestically reported. In this paper, a CW Fe∶ZnSe laser at ~4 μm is demonstrated by using a self-developed continuous-wave Er-doped fiber laser at 2.8 μm.

The pump source used in our study is a continuous-wave Er-doped fiber laser at ~2.8 μm developed in our lab. It has a maximum output power of about 4 W. The gain medium, i.e., the Fe∶ZnSe crystal is 3.5 mm in length and has a cross section of 10 mm×10 mm, with the Fe²⁺ ion concentration of 1.0×10¹⁹ cm^-3. For obtaining effective CW lasing, the crystal is wrapped in a piece of indium foil and clamped to a copper mount cooled to ～77 K by liquid nitrogen in a cryostat, owing to the lifetime of the upper laser level in a Fe∶ZnSe crystal being as short as 370 ns at room temperature while around 57 μs at 77 K. Longer lifetime of upper laser level makes continuous-wave emission much easier. The faces of the gain crystal are anti-reflection coated at 2.7-4.8 μm. Windows of the cryostat are 3 mm CaF₂ plates with AR coated at 2.7-4.8 μm. In the laser cavity arrangement, the feedback is a special coated CaF₂ plano-concave mirror, while the output mirror is another CaF₂ plano-concave mirror with a coupling ratio of ~35%. The radius of each cavity mirror is identical at 50 mm. A dichroic mirror is placed with an incidence angle of ~45° to separate the pump beam and output laser beam. An uncoated CaF₂ lens with a focal length of 50 mm is used to couple the pump beam into the crystal. Unlike the previous demonstrations of CW Fe∶ZnSe lasers, the pump direction in our experiment is counter-pumping, i.e., the pump beam and laser beam propagate in opposite directions.

An optical spectrum analyzer is used to monitor the lasing of the 4 μm signal. When the pump power is increased to about 0.4 W, there is a little peak in captured spectrum. Subsequently, fixing the pump power slightly higher than the threshold, we adjust the cavity mirrors and the coupling lens to maximize the output power. The output power as a function of pump power is recorded and shown in Fig. 3. The maximum power is 0.97 W, which is limited by the pump capability. The slope efficiency is fitted to be ~38.6%, which nearly approaches the limited efficiency of the current laser. The measured laser spectra are shown in Fig. 4. The central wavelength shifts from 3747.1 nm at low output power to 3773.3 nm at high output power with a signal to noise ratio (SNR) of as high as 40 dB, which is also named with “red-shift” and is common in free-running solid-state lasers. The wavelength in this laser is approximately 3.8 μm. The laser spot indicates that the beam profile has a desirable fundamental Gaussian distribution.

A watt-level high efficiency 3.8 μm mid-infrared all-solid-state continuous wave laser is demonstrated in this study. The output power of 0.97 W with a central wavelength at 3.8 μm with a slope efficiency of 38.6% from Fe∶ZnSe crystal is obtained by employing a self-developed continuous-wave Er-doped fiber laser at 2.8 μm as the pump source. The pump source is employed under liquid nitrogen cooling, and the beam profile has a desirable fundamental Gaussian distribution.

High power, high beam quality, and compact miniaturization are the development goals of fiber lasers. Spectral beam combination is an effective means to overcome the bottleneck of single-fiber output power and can achieve a high power output of fiber lasers. In most existing spectral beam combining systems, the gap between adjacent subfibers is generally of the order of millimeters or even larger; consequently, the entire system occupies a large space. Therefore, a compact spectral beam combining system based on a precision fiber array is proposed in this study. Many factors affect the beam quality of a combined laser in a spectral beam combining system, including lens aberration, laser line width, grating thermal distortion, and fiber array disturbance, which degrade the beam quality of the combined laser. Research on the influence of fiber array disturbance deviation on beam quality is relatively scarce. Therefore, this study focused on the effects of fiber array disturbance on beam quality factor of a combined laser. Quantitative analysis of the effects of fiber array displacement and pointing disturbance deviation on beam quality factor of the combined laser provides a means of realizing effective control of combined laser beam quality. Unlike in similar studies, this study conducted error analysis of the axial displacement deviation of the fiber array by the M² factor of the combined laser, which makes the theoretical model more practical.

Diffraction propagation theory enables us to derive the light field distribution at each position of a subbeam affected by displacement and pointing deviation. In the observation plane where the combined laser is formed, the near- and far-field light intensities of each subbeam are incoherently superimposed based on the incoherent superposition principle. The traditional intensity second-moment method is used to caclulate beam quality factor of the beam by fitting the relationship between the beam width and propagation distance. Due to the limitations of computer memory and performance, large calculation errors are introduced in the results, resulting in low calculation efficiency. Therefore, based on the Heisenberg uncertainty principle, the expression of beam quality^{factor of the combined laser under the effects of horizontal displacement, axial displacement, and horizontal pointing deviation was derived in this study.}

Under the condition of a constant number of subbeams, variations in beam quality factor of the combined beam with displacement and pointing disturbance deviation of a single-channel/multi-channel beam were simulated and analyzed, and error analysis of beam quality factor of the combined laser with different numbers of subbeams under a certain random displacement and pointing disturbance deviation was conducted. The results are as follows. 1) The beam quality factor of the combined laser is the most sensitive to the disturbance along the horizontal (x-axis) direction of the end face of the optical fiber, which must be controlled in the order of microns (Figs. 4, 5, 7, and 8). 2) The quantitative relationship between the different disturbances of the optical fiber array and beam quality factor of the combined laser was determined, and the specific control requirements of the displacement and pointing accuracy of the optical fiber array were described (Figs. 4, 5, 7-9). 3) When the number of subbeams in the beam combination exceeds 23, under a specific random disturbance, the statistical means of the beam combining laser beam quality factor tend to their respective stable values of 1.37, 1.34, and 1.25, and the standard deviations tend to 0.05, 0.06, and 0.04, respectively (Fig. 9).

In this study, a compact spectral beam combining system is proposed, and an error analysis of the optical fiber array disturbance deviation of the combined laser beam quality is theoretically conducted. The rationality and feasibility of the compact spectral beam combining system are explained to some extent, where these can be extended to other spectral beam combining systems. The specific control requirements of various errors are described. This study provides guidance for the development of high-power and high-beam-quality fiber lasers.

Traditional supersonic flameholders, such as cavities and struts, face severe thermal protection problems. Recently, some scholars have investigated methods for plasma supersonic flameholding in scramjet combustors without flameholders. However, the main flame remains concentrated near the boundary layer, which leads to the same thermal protection problem. Laser-induced plasma (LIP) presents many potential benefits over conventional plasma generation methods, such as non-intrusion of the flow field and availability of easily changing energy deposition locations. Thus, the use of LIP is a novel solution for the study of plasma flameholding methods under supersonic conditions. Research on the evolution characteristics of a multi-point LIP in quiescent air is the basis for studying and optimizing its supersonic ignition and flameholding effects. Owing to the limitations of measurement techniques and equipment in experimental research, it is challenging to obtain sufficient information of the flow field after applying multi-point LIP in quiescent air. Numerical simulation has become an important approach for studying LIP in quiescent air. Therefore, the instantaneous energy deposition model was used in this study to numerically investigate the evolution characteristics of multi-point LIP in quiescent air.

Although plasma is the fourth state of a substance, it can be considered as a Newtonian fluid in numerical simulations. In this study, high-temperature and high-pressure effects of LIP were mainly studied so that the Navier-Stokes (N-S) equations could be used to describe its control equations. The study was based on an improved instantaneous energy deposition model proposed by Dors, who simplified the region after LIP in air at the laser focus into regions of high-temperature and high-pressure gas in the experiment. Dors assumed that after the LIP in quiescent air at the laser focus, the temperature was exponentially distributed in the laser direction and normally distributed in the direction perpendicular to the laser direction. The pressure distribution can be defined using the ideal gas state equation. In this study, the laser wavelength was set to 532 nm, pulse width was set to 10 ns, static temperature was set to 291 K, and static pressure was set to 100 kPa. The size of the calculation domain was 20 mm×20 mm×10 mm. The grid independence was verified by comparing the pressure distribution at y=0 at 10 μs. Subsequently, the reliability of the model was verified by comparing it with the experimental schlieren diagram.

The shock wave and plasma kernel are generated by multi-point LIP in quiescent air at the laser focus, and the plasma kernel completely fuses at 10 μs (Fig. 4). Although the shock wave shapes vary in different laser focal layouts, the development trend and time for complete fusion remain similar. The average temperature and volume of the plasma kernels vary with different focal layouts. However, they are approximately inversely proportional to each other within 5-30 μs (Figs. 9 and 11). The time for complete fusion of the plasma kernel is shorter when the distance between adjacent focal spots (D_s) is 2 mm. However, the plasma kernel cannot fuse when D_s=4 mm (Fig. 14). D_s significantly influences the ignition and flameholding characteristics of the multi-point LIP. A D_s of 3 mm is more conducive to the ignition and pursuit of the previous flame kernel in a supersonic flow (Fig. 15).

In this study, an improved instantaneous energy deposition model based on the model proposed by Dors was used to numerically simulate the evolution characteristics of a multi-point LIP in quiescent air. From the results of the multi-point LIP with the linear focal configuration when D_s=2 mm, we confirm that a shock wave is generated by the multi-point LIP, and the shock wave pressure remains stable during the propagation stage. The fusion of the plasma kernel can reduce energy dissipation when its size increases, which is beneficial to the survival and pursuit of the previous flame kernel in a supersonic flow. In addition, the shock wave generated by the LIP can deflect the supersonic flow, which can build a low-speed region behind the shock wave. By comparing the average temperature, volume, specific surface area, and pressure at the characteristic position of the plasma kernel, we determine that the evolution characteristics of the multi-point LIP are mainly affected by D_s. When D_s is extremely small, the advantages of multiple points cannot be fully utilized. When D_s is extremely large, the plasma kernel cannot fuse. Under such conditions, D_s should be set to approximately 3 mm to achieve better survival ability and pursue the previous flame kernel in supersonic flow for the initial flame kernel generated by the multi-point LIP.

The power scaling of mid-infrared (mid-IR) fluoride fiber lasers is difficult to realize because of the low melting temperature of fluoride glass and immature fabrication techniques of mid-IR fiber devices. Mid-IR laser output powers of 30.5 W and 41.6 W at 2.94 μm and 2.82 μm based on single-end and dual-end pumping configurations (Table 1), respectively, have been previously reported. Although fiber Bragg gratings (FBGs) written in fluoride fibers have been developed as cavity mirrors in mid-IR fiber oscillators, the thermal degeneration of grating reflectivity, mismatch of the reflective wavelength, and severe splicing losses with silica fiber create new problems for the power scaling of FBG-based mid-IR fiber lasers. This study introduces a high-power erbium-doped fiber laser at 2.8 μm based on a single-end pumping scheme, where a high-reflective (HR) mirror and Fresnel reflection from the end face of a homemade end cap are used to provide cavity feedback.

Figure 1 shows the experimental setup of the high-power 2.8 μm erbium-doped fiber laser. The active fiber has an erbium dopant mole fraction of 7%, core and inner/outer cladding diameters of 15 μm and ~250 μm/290 μm, and core and inner cladding numerical apertures of 0.12/0.45; the fiber is butt-coupled to an HR mirror on one end and spliced to a 500-μm-long AlF₃ fiber end cap on the other end. An end cap with core and cladding diameters of 200 μm and 240 μm, respectively, can efficiently decrease the power density of the high-power mid-IR laser while isolating the water vapor diffusion from the end face of the active fiber, which is essential for high-power laser output. A multimode laser diode with a wavelength stabilized at 976 nm and a maximum output power of 128 W is coupled to the inner cladding of the fluoride fiber using two lenses with optimized focal lengths, where one is for pump light alignment and the other is for focusing light into the fiber. A dichroic mirror, which transmits the pump laser and reflects the back-propagation mid-IR laser, is inserted between the two lenses. Water cooling is applied to the pump coupling end of the erbium-doped fiber for appropriate heat dissipation under a high laser power, while the rest of the optical system is passively cooled.

When the output power is less than 10 W, the laser slope efficiency is 32.8% with respect to the launched pump power, and the lasing wavelength is red-shifted from 2800 nm to 2818 nm with increasing laser power. The slope efficiency decreases gradually as the laser power increases because of the pump excited-state absorption (⁴I_11/2→⁴F_7/2). A maximum output power of 33.8 W is achieved at a launched pump power of 128 W, and dual-wavelength lasing at 2865 nm and 2871 nm is obtained owing to the wide reflection band of the HR mirror and high laser gain of the cavity. Because no damage is observed from the AlF₃ end cap at the maximum output power, further power scaling of this fiber laser is limited by the available pump power delivered from a 105 μm/125 μm multimode fiber.

With a homemade AlF₃ end cap, a 33.8 W erbium-doped fluoride fiber laser operating at 2.8 μm is demonstrated under the appropriate thermal management of the fluoride fiber. A high optical-optical conversion efficiency of 26.4% is achieved at the maximum output power using high-precision spatial pump coupling. To the best of our knowledge, this is the highest output power achieved using a single-end pumping mid-infrared erbium-doped fiber laser.

The high clamping laser intensity inside the filament can ionize molecules and fragment them into plasma because of multiphoton ionization or tunneling ionization. Filamentation occurs in solids, liquids, and gases. The dynamic energy exchange between the filament core and background energy reservoir, as well as the dynamic balance of self-focusing and defocusing propagate filaments over hundreds of kilometers. Nevertheless, filaments can also overcome complex atmospheric environments. The self-healing and replenishment from background energy reservoir and the generation of acoustic waves make filaments penetrate fog and clouds. The nonlinear effect of filaments can restrain the beam wander induced by turbulence. These unique properties make femtosecond laser filamentation applicable to remotely detecting atmospheric pollution, such as gases, aerosols, metals, and biological matter.

The lateral spatial distribution of fluorescence induced by the femtosecond laser filamentation is significance for measuring the parameters of laser intensity and plasma inside the filament, studying the physical process, and controlling the filament. It is a non-invasive and in‐situ measurement method. The backward fluorescence distribution is useful for filament-based Lidar to promote the remote signal intensity and signal-to-noise ratio. Forward and backward air lasers are ideal light sources for remote sensing. Studying the far-field spatial distribution characteristics, such as the divergence angle and directivity, is important. This paper reviews the research progress of the spatial distribution of fluorescence induced by the femtosecond filamentation from lateral, backward, and forward spatial orientations.

The laser polarization, repetition rate (Fig. 2), and the molecule alignment (Fig. 3) affect the lateral distribution of fluorescence, in addition to laser energy, chirp, and external focusing condition. Measuring the lateral distribution of fluorescence is a noninvasive and in‐situ filament visualization method (Fig. 1); it measures the laser intensity (Fig. 5), plasma density, and temperature (Fig. 6) inside the filament. It is a simpler and more sensitive method than measuring electrical conductivity, acoustic waves, and other pump-probe methods. Different physical phenomena have been discovered by measuring the lateral distribution, such as anti-correlated plasma density and THz pulse generation during two-color laser filamentation (Fig. 4). Controlling the filament is important for different filament-based applications, including controlling the laser intensity and plasma density inside the filament, controlling the spatial position and filament length, and organizing multiple filaments. Spatiotemporal phase modulation is used to enhance and elongate the filament (Fig. 8). Different spatial phase modulation methods, such as axicon, deformable mirror, phase plate, and beam ellipticity, are used to control the generation of multiple filaments (Fig. 9).

An amplified spontaneous emission inside the filament has been observed for different compositions, such as N₂, O, CN, OH, and NH (Fig. 10). Thus, the amplified spontaneous emission (ASE) phenomenon has gained considerable attention for air laser applications; furthermore, the backward spatial distribution and divergence angle are important remote sensing characteristics (Fig. 11). Backward N₂ lasers are generated with an energy conversion efficiency of 0.5% and a small divergence angle of 1.6 mrad (Fig. 11) by electron impact excitation. Different pump-probe methods have been proposed to generate forward air lasers, including self-generated harmonic waves, white light, and external probe beams. The forward spatial distribution is also analyzed with an annular profile (Fig. 15). The forward divergence angle is sensitive to the gas pressure and external focus length.

For filament characterization and control, understanding the physical process inside the filament, and generating air lasers, the spatial distribution of fluorescence induced by filaments is reviewed from lateral, backward, and forward spatial orientations. Challenges remain with the application of filamentation-based remote sensing. First, the physical mechanism of the interaction between filaments and molecules, dust, and aerosols, and the mechanism of fluorescence emissions still need to be studied. The mechanisms of gain and amplification inside the filament are also important. Second, the influence of complex atmosphere conditions on the spatial distribution is still unclear, including the turbulence, pressure, and temperature distribution in the atmosphere and atmosphere scattering and absorption. Third, controlling long-distance filaments and promoting remote signal intensity and the signal-to-noise detection ratio are also practically important.

When a femtosecond laser is sufficiently strong to undergo filamentation in air, perturbation theory cannot be used to analyze the interaction because the laser intensity inside the filament is comparable to the Coulomb field intensity inside the molecule. The interaction between the strong laser field and molecule then produces a series of nonlinear phenomena, such as molecular alignment, ionization, high-order harmonics, terahertz radiation, and fluorescence radiation. These nonlinear phenomena are closely related to particle motion under strong fields. For example, by collecting the resulting high-order harmonics, ionized electrons, and dissociated ion signals, the internal structure of the material or dynamic process can be experimentally detected. In addition, these nonlinear phenomena have broad application prospects; for instance, filament-induced fluorescence can be used for atmospheric remote sensing, and high-order harmonics generated by laser-molecule interactions can be used to obtain high-intensity purple rays and attosecond lasers. Therefore, an in-depth study of molecular dynamics under a strong field can facilitate the elucidation of the nonlinear mechanism in the filamentation process as well as provide a theoretical basis for innovation and application.

This study presents a review of the main research progress concerning strong field molecular dynamics of femtosecond laser filamentation in air, including molecular alignment, molecular strong field ionization, electron-ion recombination, and population of molecular energy levels. As regards molecular alignment, researchers have conducted extensive research on its basic mechanism and have successfully used many methods to improve the alignment of molecules in experiments. Therefore, increasing research focus has been placed on more complex molecular alignment problems, such as three-dimensional alignment. In the field of molecular strong field ionization, there are many methods and models for calculating single-electron ionization, and the theoretical and experimental results are in agreement. With regard to filament-induced fluorescence radiation, substantial research has been conducted on measuring the spatial distribution of fluorescence radiation, and new technologies for environmental monitoring and atmospheric remote sensing have been proposed using this mechanism, such as filament-induced nonlinear spectroscopy. In the study of high-order harmonics, researchers can now directly generate high-order harmonics inside the filament and extract relevant information. Finally, in the study of air lasers, a series of methods have been proposed to realize the population inversion of particles, thus driving the experimental generation of air lasers.

Although strong-field molecular dynamics in the background of filamentation has been widely studied, many problems remain unsolved. As regards molecular alignment, combining molecular alignment with other technologies remains a problem worth considering. For molecular strong field ionization, there is no ideal model or method that can completely restore the ionization behavior of multiple electrons. In addition, the study of the complex motion of electrons after molecular ionization in filaments is crucial for the generation of new extreme ultraviolet or terahertz waves using common laser light sources, and its regulation must be further optimized. For filament-induced fluorescence radiation, the reason for the fluorescence gain in the filament is still controversial, and research has mainly focused on common gas molecules. Further research is needed to apply filament-induced fluorescence to practical application scenarios, such as large pollutant detection. With regard to higher harmonics, the basic mechanism of its generation needs to be elucidated, and improving its conversion efficiency is currently a difficult problem. Finally, regarding air lasers, many methods can be used to generate population inversion; however, these methods often have significant limitations. For example, an atomic air laser must be excited by a high-intensity ultraviolet pump laser; however, ultraviolet light is easily absorbed in air, thus limiting its application prospects. Although a few researchers have suggested that the rare gas argon with weak absorption of ultraviolet light can be used as the gain medium, prior studies have shown that the argon atom laser can be observed only when the mole fraction of argon reaches more than 10%, which is evidently different from that in the real air environment. In addition, the phenomenon of air laser reflects the quantum coherence of molecules under the action of a strong field. However, few studies have combined quantum optics with ultrafast laser, and further exploration and research are required in this field. Therefore, many unknowns remain to be explored regarding strong field molecular dynamic problems in filaments.

Intense femtosecond laser pulses propagate far beyond the diffraction limit in air, producing high-intensity filaments and low-density plasma along with the radiation of supercontinuum white light. The properties of filamentation have attracted significant attention owing to their potential applications in many areas, such as lighting control, remote sensing of atmospheric pollution, terahertz emission, and rainmaking. To achieve these goals, a filament with a long-distance transmission is required. However, the variety of complicated environments, for example, cloud, fog, aerosol, and rain, has strong influence on the propagation of filamentation. The atmospheric turbulence and inhomogeneous energy distribution of the initial beam profile result in the generation of multiple filaments, which can shorten the filament length, reduce the spot quality of the beam, and limit various applications of the laser filamentation. Therefore, the generation and control of long-distance filamentation are crucial. In this study, the research progress on the long-distance propagation of femtosecond laser pulses for space-based remote sensing applications is summarized, including the basic research methods of filament propagation, producing long-distance filaments, and modulation of filament characteristics. Furthermore, the advantages of femtosecond laser filaments in atmospheric remote sensing applications and the fundamental science problems to be solved are summarized.

The propagation of laser filament in air relies on a dynamic balance between Kerr self-focusing, which causes laser intensity to be clamped at a level of 10¹³-10¹⁴ W/cm², and plasma defocusing due to laser-induced ionization, with typical peak electron densities limited to 10¹⁶-10¹⁷ W/cm^-3. The high intensity filament persists over many diffractions in this process, providing a great opportunity for various applications, particularly remote sensing. Currently, numerous methods have been developed to manipulate the filamentation. The filament lengths can be extended by simply increasing the input power. While the incident pulse exceeding the critical power by an order of magnitude will quickly lead to multifilamentation, which is unstable both in space and time, incorporating certain external conditions can optimize the characteristics of the optical filament. Using a phase plate, spatial light modulator, and axicon (Fig. 1) to reshape the phase of the laser beam, the formation of multiple filaments can be effectively suppressed, and the filament length can be extended. In addition, the onset and length of the filament and the intensity of the laser and plasma density can also be controlled by numerous other methods, such as using optical systems of certain lens combinations (Figs. 2 and 4), introducing an initial pulse chirp, changing the wavefront phase of the Gaussian beam to obtain the Bessel beam (Fig. 7), phase-nested beam (Fig. 8), and annular beam (Fig. 9), externally refuelling the energy of the filaments (Figs. 10 and 11), and adopting a technique with two- or multiple-pulse (Figs. 12 and 13). The studies conducted on the methods of long-distance propagation of filamentation provide a great opportunity for remote sensing applications.

Since Braun et al. observed the self-guided propagation of intense femtosecond laser pulses in air, the generation of long-distance filaments has attracted much attention. Subsequently, an optical filament was transmitted over more than 50 m in the Laboratoire d’Optique Appliquée, and then La Fontaine et al. obtained a propagation distance of several hundred meters. In 2004, Méchain et al. showcased horizontal filamentation over a distance greater than 2 km. Then, the Teramobile group observed a filamentation that was generated by the vertical propagation of high-power femtosecond pulses and emitted in a supercontinuum from the ultraviolet to the infrared regions, which was detected from an altitude of more than 20 km (Fig. 14). Furthermore, the linear absorption spectra of some molecules, such as water (humidity) and ozone, were measured by filament-based LIDARs in an atmospheric environment from several km to tens of km. Moreover, the proof-of-concept of spaceborne laser filamentation for atmospheric remote sensing was presented by the European Space Agency (ESA) group. They numerically simulated the remote generation of filaments from an Earth-orbiting satellite, as well as a white light continuum extending from 350 nm to 1.1μm (Fig. 15). Spaceborne laser filamentation might offer promising applications for atmospheric science and chemistry studies. Recently, the characteristics of the filaments generated by propagating a femtosecond Gaussian beam in a 2 m long gas cell with continuously varying pressures at different focal distances have been numerically investigated. It was demonstrated that maintaining a large pressure (1 atm) and changing to a larger pressure (such as 0.3-1.0 atm) benefit filament propagation and spectral broadening (Fig. 16). Although a large refractive index gradient was present in our calculation, we predict that the similar impact induced by the pressure variations is also applicable to propagating a femtosecond laser pulse over a real atmosphere. In addition, we also numerically simulated the propagation of a femtosecond laser pulse from a 400-km altitude towards the ground (Fig. 17). It is crucial to improve the simulation precision and perfect the theoretical model in the future.

Based on remote sensing applications, we review the major advances in the long-distance transmission of laser filament, including the basic research methods, the generation and modulation of the long-distance filaments, and the transmission of a femtosecond laser pulse over an ultra-long-distance. After more than 20 years of continuous exploration, research on femtosecond laser filament has made great progress in both theoretical mechanism and practical application. However, numerous scientific problems remain to be explored regarding the ultra-long distance transmission of filaments, such as the intensity of the filament and peak plasma density not being high enough, developing a laser technique with high power for complicated atmospheric conditions, and establishing a complete theoretical model for the atmospheric environment. Although laser filamentation and remote supercontinuum generation from orbital altitudes are in the theoretical proof-of-concept stage, an earth-orbiting white-light LIDAR might become a new remote sensing tool for atmospheric research.

Ultrafast laser propagation in transparent media can lead to long-range diffraction-free filamentation. The laser filament has numerous nonlinear optical effects such as the Kerr effect, self-phase modulation, four-wave mixing, and self-steepening. Supercontinuum covers the ultrabroad range from microwave to ultraviolet. Supercontinuum generation from femtosecond laser filaments has an ultrabroad band, high directionality, and tunability. Therefore, the supercontinuum can be used in absorption spectroscopy, remote gas detection, pulse compression, and few-cycle pulse generation. The supercontinuum is mainly induced by self-phase modulation, which considerably broadens the spectrum. The generation and regulation technology of the supercontinuum have matured gradually owing to the development of the commercial femtosecond laser. The supercontinuum is excellent broadband coherent radiation that can be extended to multiple octaves. The supercontinuum is applicable to absorption spectrum detection. The directionality of the supercontinuum benefits from the spatial directivity of the filament. Therefore, the supercontinuum can realize the remote sensing and detection. The spectrum-broadening and abundant nonlinear effects during supercontinuum generation can compensate for the dispersion to realize pulse self-compression. The conventional scheme generally undergoes two processes: spectrum broadening and pulse compression, which is inefficient and extremely limited by the compression elements for large energy pulses. The supercontinuum from the filaments provides a new way to solve this problem, simplifying the pulse compression process with great efficiency.

In specific application scenarios, the multi-dimensional modulation of the supercontinuum is essential for certain spectral distributions and conversion efficiency. In past decades, various schemes, including spatial shaping, pulse shaping, polarization modulation, focusing conditions modulation, and material modulation, were developed. Spatial shaping can directly adjust the spatial energy distribution of the input laser pulse. Supercontinuum conversion efficiency can be considerably improved by multiple filament generation, which overcomes the energy saturation effect compared to a single filament. Pulse shaping modulates the time-domain profiles of the laser pulse, which is useful for obtaining specific band supercontinuum generation. The polarization state of the laser field affects the nonlinear polarization process of the nonlinear medium, thereby changing the spectral range, spectral intensity, and polarization state of supercontinuum radiation. The focusing condition or physical properties and arrangement of the transmission medium are direct and convenient methods for controlling supercontinuum generation by changing the length and intensity of the filament.Recently, the supercontinuum has been widely studied and important progress has been achieved. The modulation schemes are summarized in Section 3. Researchers proposed the control of the energy distribution of the filament through beam spatial shaping to optimize the femtosecond laser filamentation and generation of a supercontinuum (Figs. 2-6). The time-domain characteristics of the femtosecond laser, such as pulse width, chirp, and initial spectrum, can directly affect the filament supercontinuum. Pulse shape regulation has important applications in the research of femtosecond laser filamentation and optimization of the supercontinuum (Figs. 7 and 8). Because the nonlinear coefficient, plasma density, and clamping light intensity are related to the ellipticity of the driving laser, incident laser polarization is also used for regulating the filament supercontinuum (Figs. 9-11). Additionally, it is demonstrated that the effective regulation of the supercontinuum in femtosecond laser filamentation can be achieved by controlling the focusing conditions and material (Figs. 12-14). This review focuses on physical mechanisms and modulation methods, and systematically summarizes the latest progress in the supercontinuum based on femtosecond laser filaments.

In summary, with the development of ultrafast laser technology and nonlinear optics, the physical mechanism of supercontinuum generation has been gradually clarified. Relevant experiments have been extended from solid and liquid to gas and applied to remote gas detection and sensing. This review summarizes the physical mechanism and multi-dimensional regulation scheme of filament-induced supercontinuum and briefly introduces the application scenarios of the supercontinuum, including transient absorption spectrum systems, remote sensing systems, and the seed of the mid-infrared and air lasers. At present, most of the experiments and simulations of the supercontinuum are limited to the laboratory; complex environmental conditions, such as turbulence, temperature, and humidity changes, should be considered in remote sensing. In addition, although the supercontinuum can also provide a direct seed source for an air laser, it must be optimized further and the generation distance, wavelength, and energy conversion efficiency of future air lasers must be controlled. In addition, the backscattering mechanism and spatial distribution of air lasers must be studied to develop related applications.

Laser-induced fluorescence spectroscopy (LIFS) is a novel spectroscopic technique with several advantages, such as multi-elemental simultaneous detection, rapid response, and real-time online monitoring; hence, it is a powerful tool for remote sensing. However, single-beam laser filamentation remains limited, including the limitation of fluorescence signal intensity and detection sensitivity owing to the influence of intensity clamping. Several methods have been proposed to address these problems. For instance, the fluorescence signal can be enhanced by the interaction between two or more filaments, which is crucial in improving the sensitivity of substance detection. Previous studies about the interactions between co-propagation filaments often adopted multiple femtosecond pulses to form plasma gratings in the medium and increase the fluorescence signal intensity. However, such methods rely on the spatial interference effect of an ultrafast light field. They have high requirements for parameters such as the excitation beam’s spatial angle and pulse delay. To circumvent the aforementioned problems, we study the interaction mechanism of collinear counter-propagating filaments and their influence on fluorescence properties. Experiment results demonstrate that although its enhancement effect on fluorescence can be comparable to that of the co-propagating filament, it is almost not affected by the laser polarization. Applying this technology to the spectroscopic detection of metal ions in compounds is expected to provide a novel approach to detecting trace contaminants by studying the linear relationship between characteristic spectral intensity and substance concentration.

We establish a collinear counter-propagating filaments (CPF) system, which comprises two collinear beams propagating in the opposite direction and focusing on the same focus through a lens, thereby forming two spatially overlapping counter-propagating filaments near the focus. We make precise adjustments using the electronic translation platform to better control the relative pulse delay of the two light beams. The atomized sample interacts with the filaments to excite the fingerprint fluorescence and the fingerprint fluorescence is transmitted to a spectrometer using an optical fiber. In addition, we configure brine solution samples of KCl, Na₂SO₄, and MgSO₄ with different mass fractions to establish calibration curves and analyze the detection sensitivity of this system.

First, we compare the signal intensities induced by the CPF and single filament (SF) under the same total excitation pulse energy and successfully obtain an enhancement factor of approximately 4. Furthermore, we compare the relationship between the intensity of induced fluorescence and the pulse energy of the two filamentation systems. When the laser energy increases from 0.5 mJ to 1.5 mJ, the increase in the CPF excited signal is significantly higher than the increase in the SF excited signal; this indicates that the collinear counter-propagating filaments can obtain higher fluorescence intensity. In addition, we study the evolution of fluorescence signal intensity with time and infer that the filament interaction will prolong the fluorescence decay time of excited molecules. Simultaneously, by changing the relative pulse delay of the two lasers, fluorescence enhancement can be observed in the pulse delay range of -3-3 ps, with an excitation pulse width of 50 fs. Finally, we obtain the detection sensitivity of CPF by establishing the calibration curve of metal ions (K⁺, Na⁺, and Mg²⁺) in the brine solution. The experiment result demonstrates that the detection sensitivities of K⁺, Na⁺, and Mg²⁺ are 9.3×10^-6, 4.3×10^-6, and 16.7×10^-6, respectively, and their corresponding determination coefficients of the calibration curves are 0.99 (KCl), 0.98 (Na₂SO₄), and 0.97 (MgSO₄), respectively; this implies that the method adopted in this study exhibits optimal linearity in concentration measurement and can be utilized for the quantitative analysis of compound samples within a specific concentration range.

This study introduces a fluorescence spectroscopy detection technique induced by collinear propagation filaments. The interaction of counter-propagating filaments prolongs the fluorescence decay time of excited state molecules and enhances fluorescence signals. The fluorescence intensity excited by counter-propagating filaments is 4 times stronger than the fluorescence intensity excited by the single filament under the same pulse energy. Compared with the co-propagation filament-induced fluorescence enhancement technology, the proposed method has loose requirements for the delay control of the two excitation pulses. More importantly, this method can effectively improve the detection sensitivity of metal ions in compounds and exhibits optimal linearity; hence, it provides a novel approach to detecting trace contaminants and other applications.

Aerosol is the general term for solid, liquid, and other particulate material in the atmosphere. The possible sources of aerosol include the combustion of biological substances and fossil fuels, mineral dust, and other harmful pollutant particles. When the concentration of NaCl aerosol in the atmosphere is higher than a threshold concentration, it inhibits plant growth, corrodes metals, harms the respiratory, cardiovascular, and cerebrovascular systems of human beings.

When a femtosecond laser is transmitted in the air, owing to the nonlinear self-focusing effect, the focused light intensity reaches 10¹³ W/cm². At this intensity, any substance in air is ionized and the fluorescence spectrum corresponding to the chemical composition of the substance is released. The composition and concentration of atmospheric pollutants can be detected based on this property by collecting and analyzing the fluorescence spectrum excited by the femtosecond laser filament, realizing air pollution monitoring and providing basic data for the formulation of air pollution control programs.

Compared with the grating spectrometer, the light intensity collected by the Fabry-Perot interferometer (FPI) is 2-3 orders of magnitude larger than that of the grating spectrometer with the same spectral resolution. Simultaneously, because the aperture of the FPI is large, the spectrum of the extended light source can be measured directly, thus reducing the requirement of light-collecting elements. Based on the above characteristics, FPI is an ideal device for remote weak-light spectrum measurement.

A Fresnel lens is considerably lighter and less expensive than the traditional spherical lens, which is suitable for the large-aperture low-light collection system. In this study, a Fresnel lens with an aperture of 1.1 m is used to converge remote low-light sources. Although the size of the focusing spot is large, it still can form a remote low-light spectrum detection system with the large-aperture FPI.

The Fresnel lens used in this study is made of polymethyl methacrylate (PMMA) whose diameter and focal length are 1.1 m and 1.31 m, respectively. The Fresnel lens has a ring spacing of 0.5 mm, and each ring has a different depth. The Fresnel lens used in this study has an average transmittance of 94% in the visible light range. The FPI used in this study consists of two partially reflective mirrors with diameters of 1 inch (1 inch=2.54 cm) and three 2-mm-thick piezoelectric ceramics (PZT). The reflectivity of the mirrors is 90%, the applied voltage range of the PZT is 0-60 V, and the maximum displacement of the PZT is 3 μm. The PZT used in this study has good linearity between the displacement and applied voltage, the resolution of the PZT is 0.5 nm, and the free spectrum range of FPI is 9 nm.

Using the industrial CCD as the detector, the spectrum of the mercury lamp can still be detected even when the distance between the lamp and FPI increases to 30 m (Fig. 10). In this case, the illumination on the Fresnel lens surface is only 6.5 μlx.

The self-built FPI combined with the Fresnel lens is used to detect the fluorescent spectrum of the NaCl aerosol induced by the femtosecond laser optical filament at a distance of 10 m (Fig. 11). In the experiment, the pulse energy of the femtosecond laser is 4 mJ, and the pulse width is 50 fs. The NaCl aerosol with mass fraction of 13×10^-6 is generated by the aerosol generator. In this case, an intensified complementary metal-oxide semiconductor (CMOS) camera is employed as the detector. The emission lines of Na⁺ at 589 nm are detected.

The spectrum of the mercury lamp placed at a distance of 8 m away from the Fresnel lens and FPI is determined when an industrial charge coupled device (CCD) is employed (Fig. 7). By applying different voltages to the PZT, the wavelength of the emission spectral line of the mercury lamp is calculated using the relationship between the wavelength and radius of the interference ring. The wavelength error measured by the FPI is less than 1 nm, which is mainly originated from the radius error of the interference ring obtained from the picture taken by the CCD camera.

In this study, a Fresnel lens with a diameter of 1.1 m and a self-built FPI are used to construct a remote spectral detection system. With the efficient light-collecting characteristics of the Fresnel lens and large light-collecting aperture FPI, an industrial CCD camera can detect the spectrum of the micro-lux light sources. Using an intensified CMOS camera, the system can measure the fluorescence of NaCl aerosol with mass fraction of 13×10^-6 excited by the femtosecond laser filament at a distance of 10 m. In the future, by further improving the fitting method of FPI and designing more matching optical elements for the light coupling between the FPI and Fresnel lens, the spectral resolution and low-light detection capability of the spectral detection system can be further improved to play a greater role in the long-range measurement of atmospheric pollutants.

Quantitatively analyzing aerosol composition is key to monitoring air pollution. In this study, filament-induced fluorescence spectroscopy (FIFS) technology is used to detect NaCl aerosols remotely based on intense femtosecond laser pulses that excite materials and induce their fingerprint fluorescence. However, the fluorescence intensity does not vary linearly with the different mass concentrations of NaCl aerosols because of the self-absorption effect. Thus, a one-dimensional convolutional neural network (1D-CNN) is proposed for predicting the mass concentration of NaCl aerosols with FIFS spectra because deep neural networks can well fit non-linear relationships. In the future, FIFS technology with deep neural networks might be key for the development of next-generation laser lidar for remote air pollution detection systems.

An FIFS system with ultra-short, ultra-intense laser pulses that generate high-intensity filaments is first built. The method based on the use of a filament focused by a combined lens in air can be employed for the multi-component, remote, and rapid quantitative analysis of atmospheric aerosols. Next, a spectrum collection system based on FIFS is designed (Fig. 1) to acquire aerosol fluorescence spectra. The system uses a Coherent commercial Ti∶sapphire femtosecond laser amplifier (Legend Elite) with a pulse wavelength of 800 nm, a pulse energy of 6 mJ, and a frequency of 500 Hz. Using the telescope focusing system, the filamentation position of the femtosecond laser is fixed in the cloud chamber at 30 m. Moreover, a NaCl aerosol is chosen as the experimental sample to simulate aerosols in the air. Specifically, an aerosol generator is used to generate the NaCl aerosol in the cloud chamber, where the femtosecond laser excites it and induces thin filaments. Fluorescent signals are collected using a spectrometer. Finally, a 1D-CNN model (Fig. 5) is designed to collect the FIFS spectra and predict mass concentration of the NaCl aerosol. To construct distinguishable features of the spectra, the 1D-CNN is set up with two convolution and two pooling layers, and the constructed features are inserted into the full connection layer to obtain the predicted value. To prevent gradient explosion, ReLU is selected as the activation function of the 1D-CNN.

A 10-fold cross-validation comparison experiment was conducted with traditional quantitative models, back propagation neural network (BPNN), and 1D-CNN on the full and characteristic spectral data. Generalized prediction experiments were performed for each model to further verify the reliability of the proposed model. According to the results of the 10-fold cross-validation experiments on NaCl spectral data (Tables 1 and 2), the 1D-CNN outperforms the other models in all prediction performance measures on the full spectrum dataset. It can achieve a root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R²), relative percentage deviation (RPD), and accuracy (ACC) of 0.110, 0.073, 0.997, 18.478, and 0.99, respectively. Its performance is further improved when executed on the characteristic spectrum dataset. This result indicates that the 1D-CNN can fit a non-linear relationship. When comparing the results on the full and characteristic spectra, most of the models perform better on the characteristic spectrum than on the full spectrum (Fig. 6). In the generalization experiments (Tab. 5), the 1D-CNN performs poorly only on the lowest concentration (0.33 mg/m³) but performs well when predicting higher mass concentrations. The RMSE, MAE, and ACC of the 1D-CNN on the characteristic spectrum dataset are 0.34, 0.31, and 0.87, respectively, in the generalization experiments. The 1D-CNN outperforms the other models when predicting mass concentrations that have not appeared in the training data (Tables 3 and 4). The results indicate that the 1D-CNN model can be generalized to NaCl aerosols with unknown mass concentrations.

An experimental system is built to collect the FIFS spectra of NaCl aerosols and predict its mass concentration based on the proposed 1D-CNN. Compared with baseline models, the convolution and pooling layers of the 1D-CNN can generate spectral characteristics to improve prediction accuracy. The results of 10-fold cross-validation experiments show that the 1D-CNN and BPNN models have unique advantages over CR, MLR, and PLSR. In addition, the 1D-CNN performs significantly better than the other models in the generalization experiments. This indicates that FIFS technology and 1D-CNNs are suitable for the quantitative analysis of FIFS spectra of NaCl aerosols. Hence, they can be the core technology of next-generation laser lidar for monitoring air pollution.

In recent years, femtosecond laser filamentation has attracted much attention and has shown great potential in atmospheric remote sensing owing to its unique characteristics. Femtosecond laser filamentation characterization is the basis of filament regulation and application. However, the high laser intensity and electron density in the plasma channel make it challenging to measure the filament directly. Fortunately, the energy conversion effects among light, acoustic, and thermal signals during filamentation enable studies into the exploration and diagnosis of filaments using acoustic and optical methods. Owing to difference in the microscopic physical mechanism of acoustic waves and fluorescence radiation during the filamentation process, there is a difference in the quantitative relationship between the two signals and the physical parameters of the filament. However, there is still a lack of comparative research on the accuracy of the two methods. This study investigates the effect of pulse energy on the spatial distribution of filament, and the differences and similarities between acoustic and fluorescence methods for characterizing filament are systematically compared. The reasons for the differences between the two methods are theoretically analyzed.

The longitudinal plasma profile of filament induced by the propagation of an intense femtosecond laser pulse in air is measured simultaneously by employing acoustic and fluorescence methods. Acoustic emissions from the filament are detected by a directional microphone at a distance of 1 cm from the filament. To measure filament fluorescence, a convex lens (focal length f =50 mm) is employed to collect and focus the filament fluorescence onto the entrance slit of a monochromator. The dispersed fluorescence is detected by a photomultiplier tube placed at the exit slit of the monochromator. The triple standard deviation of the background noise is used as the reference for the appearance of the filament, and the differences and similarities between the acoustic and fluorescence methods in the spatial characterization of the filament are studied experimentally and theoretically.

In order to calibrate the spatial resolution of the acoustic and fluorescence detection systems, the beam is focused by a single lens with 50 mm focal length to produce a point source. By measuring the spatial distribution of such a point source, it is determined that the spatial resolution of acoustic and fluorescent methods is 0.76 cm [Fig. 2(a)] and 0.84 cm [Fig. 2(b)], respectively, which are in agreement with the results reported previously (within one centimeter). The differences and similarities between acoustic and fluorescence methods in the spatial characterization of filament are compared and analyzed. Compared with the fluorescence method, the start position of the filament measured by the acoustic method is closer to the focusing lens and the length is larger [Figs. 2(c) and (d)]. This difference increases with an increase in filament length (Figs. 3 and 4). The analysis of the physical mechanism shows that the kinetic energy of free electrons in the filament is low owing to the low intensity of the light field at the start and end of the filament, which is much less than the kinetic energy (11 eV) of electrons needed to produce N₂ fluorescence through electron collision (Fig. 5).

We present a simultaneous multi-parameter measurement on filament using acoustic and fluorescence methods, and the effect of pulse energy on the spatial distribution of the filament is studied. The experimental results show that the filament length increases with increasing laser energy. Simultaneously, the start and peak positions of the filament move toward the lens. Both methods can characterize the spatial characteristics of filaments. Compared with the fluorescence method, the start position of the filament measured by the acoustic method is closer to the focusing lens, and the length is larger. A study of the physical mechanism shows that the dependence of the free electron kinetic energy in the filament on the intensity of the light field is the main reason for the difference in the characterization results. The acoustic method shows higher sensitivity to the start and end positions of the filament, which is more conducive to the experimental characterization of the weak filament.

Excess heavy metals in soil can seriously affect the growth of crops, among which chromium is considered to be one of the most toxic heavy metals. Excess chromium levels can lead to retarded plant growth and reduced yields, and can affect human health when consumed. Therefore, chromium detection in soil has become an important research element in the field of agriculture. Laser-induced breakdown spectroscopy (LIBS) can be used for the detection of heavy metals in soil. This technique has the advantages of simultaneous detection of multiple elements, online detection, and simple sample preparation methods. Conventional nanosecond laser-induced breakdown spectroscopy has poor reproducibility due to the influence of background continuum spectra and matrix effects during the detection process. Improved methods include filament-induced breakdown spectroscopy (FIBS) based on femtosecond filament, plasma-grating-induced breakdown spectroscopy (GIBS) based on the non-collinear superposition of two femtosecond filaments, multidimensional-plasma-grating-induced breakdown spectroscopy (MIBS) based on the superposition of three non-coplanar femtosecond filaments, and triple-filament interaction induced breakdown spectroscopy (TIBS) based on the coplanar and non-collinear superposition of three femtosecond filaments. All these methods do not require the introduction of additional equipment and complex sample preparation methods. Among these improved methods, GIBS and MIBS have been well-studied. However, studies on TIBS are still lacking, especially regarding the detection of heavy metals in soil.

In this study, a TIBS system based on the superposition of three coplanar and non-collinear femtosecond beams, a GIBS system based on the superposition of two noncollinear femtosecond beams, and a FIBS system based on one femtosecond beam are developed to study the heavy-metal detection capability of these three systems in soil. Standard soil samples are doped with various mass fraction Cr elements and pressed into sheets. To ensure that the position of the sample being excited remains the same, the sample sheet is placed on a three-dimensional translation table. The fluorescence signal generated by the excited sample is transmitted to a step spectrometer equipped with an intensified charge-coupled device (ICCD). In addition, we use three systems for the detection of standard soil samples doped with different mass fraction Cr elements and determine the detection limits.

We first compare the spectral line signal intensities of the FIBS, GIBS, and TIBS systems under the same experimental conditions. As shown in Table 2, the signal intensity of the TIBS system is enhanced by 2 times compared with that of the GIBS system and 7-11 times compared with that of the FIBS system. Then, we compare the changes in the spectral line intensity under the three systems by varying the sample position. As shown in Fig. 4, the TIBS, GIBS, and FIBS systems exhibit stable excitation in the spatial scale of 0.30, 0.35, and 0.15 mm, respectively. This implies that the plasma grating formed by the superposition of multiple filaments has more stable excitation. The spectral signal intensity decreases rapidly after the excitation is far from the corresponding region because the filaments are not superimposed in this case. Finally, we measure the calibration curves of the Cr samples in soil with the three systems and calculate the corresponding limits of detection. As shown in Fig. 5, the limits of detection for the FIBS, GIBS, and TIBS systems are 22.18×10^-6, 8.68×10^-6, and 5.06×10^-6, respectively. The TIBS system exhibits higher detection sensitivity compared with the GIBS system, and the coefficients of determination of the calibration curves for all three systems exceed 0.99.

In the comparative analysis of the soil samples doped with various mass fraction Cr₂O₃ under the same experimental conditions, the spectral signal of the TIBS system is significantly enhanced compared with those of the GIBS and FIBS systems; specifically, the spectral intensity achieves an enhancement of 2 times and 7-11 times, respectively, which is due to the more intense electron-ion collision in the interaction region of three filaments than that of two filaments, thereby leading to a further enhancement of the fluorescence. Compared with the GIBS system, the TIBS system has similar excitation stability and maintains in the best excitation region when the sample is moved within 0.30 mm. The calibration curves of Cr in soil are established under FIBS, GIBS, and TIBS systems, and the detection limits are 22.18×10^-6, 8.68×10^-6, and 5.06×10^-6, respectively. These results show that the TIBS technique can further improve the sensitivity of the detection compared with the GIBS system, and can be used as an effective method for the detection of heavy metals in soil.

To collect long-distance and wide-spectrum signals of laser filament-induced plasma spectroscopy, a high-efficiency collecting system with a large-aperture Fresnel lens is necessary so that the fluorescence spectrum signals can be converged and coupled into a fiber spectrometer. Although conventional non-imaging Fresnel lenses have superior energy collection efficiencies, the focusing performance of the lens is affected by spherical aberration and dispersion, which are induced by the increased aperture. This leads to difficulties in spectrum analysis at high resolution. Therefore, optimizing the ring shape of the Fresnel lens and improving the performance by considering source parameters, volume size, and lens specifications are crucial to the design of the collecting system.

A large-aperture Fresnel lens collecting system is designed using loop optimization of each ring with multiple software programs. The system consists of seven Fresnel lenses with a diameter of 300 mm and a focal length of 670 mm. To optimize the energy collection efficiency and the focusing spot size in the Zemax sequence mode, a multi-ring aspheric Fresnel lens is designed using Code V and MATLAB softwares, and the lens is modeled and analyzed using the LightTools software. This method reduces the spherical and chromatic aberrations of the large-aperture Fresnel lens, making the efficiency of energy coupling into the optical fiber improved and the convergence spot size reduced. Therefore, the signal intensity of the fiber spectrometer can be raised effectively.

The surface shape of the single-ring band is optimized in the Code V software by controlling the light spot radius and the convergence angle (Fig. 4). The loop optimization of multi-ring bands is carried out in the MATLAB software using the same optimization method (Table 2) and the focusing spot size is analyzed in the Code V software. In addition, the Fresnel lens model is constructed in the LightTools software (Fig. 7), and the full width at half maximum of the focus spot and the energy collection efficiency are calculated (Fig. 8). Finally, the tolerance of the lens is analyzed according to the manufacturing process (Fig. 9). In the simulation, the Fresnel lens energy collection efficiency and the spot diameter are 52.2% and 2.051 mm, respectively. In contrast, the energy collection efficiency measured in the experiment and the light spot diameter are 34.9% and 2.260 mm, respectively. The differences between the simulation and experiment results are possibly owing to the errors in manufacturing and assembly.

In this study, the large-aperture Fresnel lens is investigated according to the requirements of the collecting system of laser filament-induced plasma spectroscopy. A design method of large-aperture Fresnel lenses is proposed using several software platforms, which improve the collection efficiency and reduce the influence of aberration. After the design and optimization of the multi-ring using Code V and MATLAB softwares, along with modeling and analysis using LightTools software, a collection efficiency of 52.2% for the lens and a focusing spot size of 2.051 mm are achieved. Due to the errors in manufacturing and measurement, the collection efficiency is 34.9% in the experiment, which meets the application requirements of the system. The simulation and experiment results show that the design method can reduce the aberration of a large-aperture Fresnel lens and facilitate collection of long-distance and wide-spectrum signals efficiently.

To meet the requirements for using an optical fiber spectrometer to detect weak signals over long distances and across a wide spectrum, and considering the sensitivity of the spectrometer, a large aperture optical system is needed so that sufficient optical signals can be obtained. In addition, the aperture of the receiving surface of the optical fiber bundle is small, making it difficult for the lens to match the numerical aperture of the optical fiber bundle. Therefore, the focal spot size and convergence angle should be as small as possible to efficiently couple optical signals into the optical fiber bundle and improve energy utilization efficiency. The traditional design of an optical system based on imaging optics increases the weight and volume of the system, ultimately affecting the overall performance of system. Therefore, determining the size of the spot and angle of beam convergence is crucial for improving the system's light energy utilization efficiency.

A large aperture Fresnel lens condensing system is designed based on a hybrid design method of imaging and non-imaging optics. The system consists of a 1.1-m-diameter Fresnel lens, a beam homogenizer, a total reflection collimator, and a relay lens group. The receiving surface is a fiber bundle with a diameter of 2 mm and a numerical aperture of 0.22. The problem of traditional large aperture lenses' large volume and weight is solved using large aperture Fresnel lenses. To achieve uniform energy distribution and reduce the convergence angle of the light bundle, the rear group of non-imaging optical elements, composed of a beam homogenizer and a total reflection collimator, are designed to reduce the spherical and chromatic aberrations of large aperture Fresnel lenses. The relay lens group also controls the beam divergence angle and spot size, allowing the optical signal to be efficiently coupled into the optical fiber and improving the light energy utilization efficiency of the system.

First, a large aperture Fresnel lens condensing system based on imaging and non-imaging optics is designed (Fig. 2). Subsequently, the optical device is modeled and designed using the ZEMAX software, and the overall parameters of the condensing system are achieved (Table 1). The optical system model is established in ZEMAX software to verify the focusing performance of the Fresnel lens condensing system, and simulation results are obtained (Fig. 8). The light energy utilization efficiency of the condensing system is 6.5% according to ray tracing, and the light energy utilization efficiency of the condensing system with a rear group is five times that of the system without a rear group. In addition, the experimental system is built based on the condensing system' s design results (Fig. 9). The experimental light energy utilization efficiency of the condensing system is 3.8%, which is lower than the simulation results. This is because the experimental device parameters and spectral power distribution of the light source are inconsistent with the theoretical simulation. In contrast, the light energy utilization efficiency of the Fresnel lens condensing system without the rear group is only 1.8%. The simulation and experimental results indicate that the rear group system based on the hybrid design method of imaging and non-imaging optics can effectively improve the light energy utilization efficiency of the Fresnel lens condensing system.

In this study, based on the hybrid theory of imaging and non-imaging optics, the large aperture Fresnel lens condensing system is examined, and the design scheme of the rear group system composed of a beam homogenizer, total reflection collimator, and relay lens group is devised. Through the simulation and optimization by ZEMAX software, a theoretical light energy utilization efficiency of 6.5% is obtained for the system. The experimental system is built based on the design results. The light energy utilization efficiency of the Fresnel lens condensing system with the rear group is 3.8%, which is 2.1 times that of the system without the rear group. Given that the experimental device parameters are not completely consistent with the theoretical simulation parameters, the experimental result is essentially reasonable. The theoretical simulation and experimental test prove that the rear group can reduce the influence of aberration, and control the spot size and the convergence angle. The hybrid design method efficiently couples the optical signal into the optical fiber bundle, allowing for the detection of weak signals over long distances and across a wide spectrum.

With the development of ultrashort and ultra-intense laser, it has been revealed that when a femtosecond laser pulse propagates in air, filaments, referred to as “filament laser”, would occur owing to nonlinear effects. Traditional spaceborne air-pollution monitoring devices rely on spectral imaging and LiDAR technology, which cannot realize real-time monitoring of atmospheric multi-component pollutants, identify unknown pollutants, and detect the chemical composition of various pollutants. The filament laser system in orbit emits a femtosecond laser pulse into the atmosphere, and the intensity of the femtosecond laser pulse is sufficient to ionize molecules in the atmospheric environment. Ionization excites the fluorescence spectrum carrying the information of the material composition, which can determine the various material components, species, and content in the area of the filament laser. To aid the research on space-based filament lidar technology, this study explored the optical system design of a space-based filament lidar spectrometer for remote sensing applications and realized the optical system configuration design. The spectral range and resolution of the spectrometer are 320-950 nm and 2 nm, respectively, and it has applicability in high resolution spectral detection of atmospheric pollutant composition.

First, the application requirements of space-based filament lidar spectrometer were analyzed. On the basis of the characteristics of pollutants and the corresponding spectra of the substance elements, the working spectrum of the spectrometer and the spectral resolution were designed to be 320-950 nm and 2 nm, respectively. Using filament laser propagation simulation software, the filament laser diameter was found to be approximately 6 mm after 400 km orbital propagation. The filament laser diameter can be constrained to a small spatial scale after ultralong-distance propagation. To conform to the spectral range and resolution requirements, the size of CCD detector is 1024×1024, with 13 μm×13 μm pixel size. The minimum spectral sampling interval was designed to be 0.67 nm/pixel. Considering the signal-to-noise ratio requirements of the spectrometer, the relative aperture of the optical system was determined as D/f '=1/3.5, and the aperture of the spectrometer system was set as 0.5 m. Then, considering the requirements of engineering and the space environment, the optical design and optical-mechanical design of the spectrometer were performed so as to provide an effective load scheme for space-based filament laser atmospheric detection.

The optical system of the spectrometer mainly comprises a telescopic system, slit, collimating system, plane grating, and imaging system; the collimating system, dispersion element, and imaging system constitute the spectrometer. The front telescopic system adopts a total reflection Cassegrain structure without chromatic aberration correction, and the root mean square (RMS) value of the diffuse spot radius of its imaging point is within 14 μm. The spectrometer uses a reflective plane grating; the number of plane grating lines was determined to be approximately 263 lp/mm, and the grating aperture was 22 mm. A spectral resolution of 2 nm was achieved using first-order diffraction light. The maximum RMS diameter of the spectrometer system imaging slit is less than 17 μm. The modulation transfer function (MTF) is greater than 0.99@3.7 lp/mm, and the maximum color distortion is 1.1 μm. The energy concentration in three pixels is over 96%, which can be used for spaceborne high-resolution spectral detection of atmospheric components. The spectrometer system adopts a damping truss-unlocking mechanism for three-point support and is installed on the bottom plate of the satellite load compartment. The front lens tube is made of a carbon fiber composite material to ensure the thermal stability of the primary and secondary lens spacing. The main bearing frame and connecting plate are made of a titanium alloy. The design of stray light adopts the combination of “secondary mirror mask and primary mirror central hole baffle” with the simplest structure, which can ensure that the stray light coefficient of the camera is less than 0.5%. The statistics of various light paths that could reach the image surface were also obtained, and no abnormal stray light paths were found.

For space-based applications of the filament LiDAR spectrometer system, the optical system was designed and examined, and the main technical indicators of the optical system were determined. The designed spectrometer system can achieve a spectral resolution of 2 nm in the spectral range of 320-950 nm and thus provide a reference for the design and development of spectrometers used in filament LiDAR systems.