2.1.

Experimental Setup

The experimental setup was like those used in GIBS⁴⁶ or MIBS,⁵⁰ except that all three fs laser beams were aligned to interact in the same plane. A Ti:S fs laser operated at 800 nm with a maximum pulse energy of 2 mJ and pulse duration of 40 fs was used as the excitation laser source in our experiments. Its repetition rate was fixed at 1 kHz. As single filaments were used to ablate aqueous solutions, the plasma excitation efficiency was quite low, and it was impossible to obtain observable plasma spectral line emissions for trace element analyses. Therefore, we used an auxiliary method of a fluid jet to help improve plasma excitations. As shown in Fig. 1(a), we set up a syringe to form a fluid jet by utilizing the gravity of the water itself and installed a water pump to pump the flowing water back to the syringe so that the fluid jet could form a stable laminar flow. In this way, we avoided the influence of the surface fluctuation of the liquid sample on the spectral line signal and formed a distinct plasma in the excited region. When the fluid jet was ablated with 2D plasma gratings formed by three noncollinear and noncoplanar filaments, violent plasma explosions were normally accompanied to form obvious water splashes to scatter the fluorescence, which not only affected the stability of the plasma-grating induced breakdown but also dramatically reduced the intensities of the plasma spectral line signals. To minimize detrimental influence from plasma explosions, the MIBS setup was modified to sustain noncollinear interactions of three or multiple coplanar filaments. Such noncollinear couplings of coplanar filaments established plasma gratings of 1D microstructures in the common plane rather than formation of 2D plasma gratings used in MIBS.⁵⁰ The schematic of the spatial alignment of the interacting fs pulses is shown in Fig. 1(b). The angle between pulses A and B was 20 deg, and pulse C was aligned to propagate along the bisector of A and B. Pulses A and B were synchronized to form 1D plasma gratings, whereas pulse C was adjusted by means of a delay stage to reach the plasma-grating region with a positive or negative delay, corresponding to pulse C propagating behind or ahead of the synchronized pulses A and B, respectively. Temporal and spatial overlapping of three filaments was aligned as follows. At first, we cross-overlapped filaments A and B in space (with a cross angle of 20 deg) and then scanned the time delay between the two filaments. By monitoring the plasma fluorescence from the side of the plasma channels, we determined the temporally overlapping position as the plasma fluorescence reached its maximum. Plasma gratings were generated as the two filaments underwent nonlinear interactions. Afterward, the third filament (C) was steered in the same plane to propagate along the bisector of filaments A and B. We spatially cross overlapped the third filament with filaments A and B and adjusted their relative time delay. Temporal synchronization of the third filament with the as-formed plasma gratings was determined by monitoring the enhancement of the plasma fluorescence induced by the third filament to reach its maximum. By adjusting the three-dimensional position of the fluid jet, we could realize that part of the plasma gratings was formed in air before they entered the fluid jet,⁴¹ as schematically shown in Fig. 1(c). It should be noted that the plasma gratings were established in the area where two filaments cross-overlapped and interfered. Accordingly, the as-formed plasma gratings typically had a length $L$ significantly shorter than single filaments. Based on the typical filament diameter of $100\mu \mathrm{m}$ in air and the angle between the interacting filaments A and B, it could be easily calculated that plasma grating modulation covered a width $D$ slightly smaller than the fluid jet diameter $2R$ [as denoted in Fig. 1(c)]. In addition, filaments and plasma gratings reached their automatic balance between Kerr self-focusing and plasma defocusing. Single fs pulses underwent filamentation in the region where they were focused to reach the so-called self-focusing thresholds, whereas two synchronized fs pulses interfered in their cross-overlapped region, where self-focusing took place along the constructive interference fringes and was then automatically balanced by local plasma defocusing, generating wavelength-scale structures of plasma modulation. Since such interference could in principle enable the self-focusing threshold to be reached in the constructive interference fringes, periodic plasma channels could be established beyond the single filamentation region as determined by the spatially localized self-focusing along the corresponding interference fringes. Hence, the width [$D$ in Fig. 1(c)] of the plasma gratings became larger than the typical diameters of single filaments. As a result, excitation of plasma gratings could be readily controlled to cover the whole fluid jet. Even though the plasma gratings covered a large area, plasma modulation therein could well confine the laser energies in the wavelength-scale periodic structures and avoid breakup of high-energy filaments into multifilaments especially during their propagation across the air–aqueous interface, and thus more efficient excitation could be achieved in aqueous solutions. Moreover, using plasma gratings with multiple plasma-modulated channels to interact with the aqueous solutions, strong and stable breakdown of spectral lines could be achieved. In our experiments, the signal acquisition mode of the intensified charge-coupled device (ICCD) was set to the so-called on-chip integration mode, and the acquisition gate was set with a width of 500 ns and gate delay of 100 ns. The exposure time of the ICCD was set to 200 ms, corresponding to an accumulation per spectrum of 200 laser shots of ablation with an fs laser of 1 kHz repetition rate used in our experiments.

Fig. 1

(a) Photo of plasma-grating excited fluid jet stream. (b) Schematic of the spatial configuration of three filaments generated by pulses A, B, and C. The parallel structure represents plasma gratings generated by the nonlinear interactions of coplanar filaments A, B, and/or C. (c) Schematic of the top view of the plasma grating interacting with the fluid jet.

2.2.

Sample Preparation

In our experiments, three kinds of mineral salts with an analytical reagent grade, ${\mathrm{CuCl}}_2$, ${\mathrm{CrCl}}_3·6{\mathrm{H}}_2\mathrm{O}$, and NaCl (all from Sinopharm Chemical Reagent Co., Ltd.) were used. They were dissolved together in deionized water with a concentration of $500\mathrm{mg}/\mathrm{L}$ for each mineral salt. The concentrations of analytical metal elements were thus in 237 ppm for Cu, 97 ppm for Cr, and 196 ppm for Na, respectively. The configured solution was stirred on a magnetic stirrer at $600\mathrm{rad}/\mathrm{s}$ for 5 min and mixed uniformly.

3.1.

Time Evolution of the F-GIBS Spectrum

Figure 2(a) shows the variation trend of the F-GIBS full spectrum with the acquisition gate delay. It can be seen from Fig. 2(a) that in the early stage of plasma formation, the plasma emission involved strong continuous background signals from free electron recombination (free-bound emission) and bremsstrahlung radiation (free–free emission). On the continuous background signals, there were emission lines of neutral atoms and ions. In the range from 0 to 200 ns, with the increase of the detection delay, the continuous background signals rapidly dropped to negligible, and the spectral line signals emitted by atoms or ions became sharp. However, in the range from 200 to 400 ns, the spectral line signals emitted by atoms or ions continued to decrease as the detection delay was prolonged, which was not conducive to analysis. Therefore, there existed an optimal detection delay. We selected Cu I 324.7 nm to optimize the detection delay. The variation trend of the intensity and signal-to-noise ratio (SNR) of this spectral line with the detection delay is shown in Fig. 2(b). It is obvious from Fig. 2(b) that the intensity of the spectral line decayed exponentially with the increase of detection delay, but the SNR showed a trend of increasing first and then decreasing. The optimal spectral line SNR occurred when the detection delay was 100 ns. In addition, under this detection condition, the relative standard deviations of the obtained five spectral line intensities were around 3% to 5%. The stable and reproductive spectral line evidenced that our proposed F-GIBS scheme greatly improved the plasma excitation and removed detrimental effects of bubbles caused by plasma explosions in the liquid as expected.

Fig. 2

Time evolution of a typical F-GIBS spectrum: evolution of (a) a typical F-GIBS with the detection delay and (b) the intensity and SNR of Cu I 324.7 nm excited by F-GIBS.

3.2.

Nonlinearly Coupled Excitations with Filament and Plasma Gratings

In order to establish efficient plasma excitations, the F-GIBS protocol should be optimized by carefully adjusting the interpulse delay between the third filament formed by pulse C and the plasma gratings formed by pulses A and B. Negative interpulse delay refers to that pulse C excited the sample ahead of the plasma gratings, and vice versa is positive interpulse delay.

Figure 3 shows the variation trend of the intensities of the spectral lines Cu I 324.7, Cr I 425.4, and Na I 588.9 nm with the interpulse delay. Unlike traditional DP-LIBS, which typically showed the time evolution lasting tens of microseconds through plasma expansion and cooling or reheating,^30,31 the spectral line intensity of F-GIBS changed with the interpulse delay via “M-type” intensity-variation trends within typical durations of a few hundred picoseconds, and reaching their maxima as the delay was about $\pm 50\mathrm{ps}$. Such optimum interpulse delays involved in F-GIBS, at least 5 to 6 orders of magnitudes shorter than that in the nanosecond DP-LIBS,^30,31 was comparable to the typical lifetimes of the plasma gratings and plasma in filaments.⁵⁴ Within such ultrashort time delays, there existed observable nonlinear interaction between the plasma gratings and the third (synchronized, ahead, or delayed) filaments. It is interesting to note that the plasma excitations and breakdown spectral line emissions manifested intrinsically different mechanisms for plasma gratings interacting with synchronized, ahead, or delayed filaments, respectively.

Fig. 3

F-GIBS signals of Cu I 324.7, Cr I 425.4, and Na I 588.9 nm attained under different interpulse delays.

Figure 4 shows the top view of the noncollinear interaction area between pulses A and B to create plasma gratings without [Fig. 4(a)] and with [Fig. 4(b)] the third filament (pulse C) entering the plasma grating at $+50\mathrm{ps}$ delay, respectively. When the interpulse delay was 50 ps, the plasma gratings were formed at first to excite the liquid sample. Both in air and in liquid jets, the laser intensity and electron density exhibited periodic modulations, which allowed the laser energy to be concentrated in the corresponding area, thereby helping to break through the peak-intensity-clamping effect of the fs filament to achieve better ablation.^52,53 In our experiments, pulse C was aligned to propagate along the bisectors of A and B [see Fig. 1(b), which could be regarded as the zeroth-order Bragg angle]. Bragg diffraction occurred when pulse C propagated through the plasma gratings,⁵⁵ so that its energy was no longer uniformly distributed but exhibited a periodic distribution, which made the pulse directly self-focus along the as-formed plasma gratings.^52,53 This stands for a novel nonlinear coupling mechanism for the plasma gratings and delayed filaments. That is, the pulse C underwent filamentation by following the same plasma modulation structures of the as-formed plasma gratings. Thereby, even the pulse C itself could experience a breaking-through of the peak-intensity-clamping of single filamentation in air. Within the lifetime of the as-formed plasma gratings, the still-lasted plasma modulation functioned as modulation seeds for the pulse C, and zeroth order Bragg diffraction of the delayed pulse C enforced the as-formed plasma gratings to be regenerated, with plasma density and plasma modulation contrast enhanced therein regeneratively. Such regenerative formation of plasma gratings elongated the as-formed plasma gratings. Intriguingly, this equivalent lifetime-elongation could be implemented repeatedly with multiple pulses of appropriate delays and thus elongated plasma grating excitations, which might produce plasma excitations comparable to long-pulse ablation. Such nonlinear couplings of plasma gratings with multiple delayed pulses inaugurate a technique to overcome the bottleneck intrinsically arisen from the short plasma lifetime of fs filament ablation. As a result, the regenerative formation of plasma gratings benefits to achieve breakdown spectral lines of improved SNRs, better than those excited by the long double pulses used in traditional DP-LIBS,^56–58 single filaments used in FIBS,^59–61 or nonregenerative plasma gratings used in GIBS.⁴⁶ Note that such regenerative nonlinear couplings exhibited quite an interesting variation with the delay of the third filaments. At the beginning stage of plasma grating expansion (or plasma modulation decay), pulse C should pass through a plasma background (nonmodulated plasma generated by pulses A and B) before being coupled into the modulated plasma grating channels, its self-focusing should balance the defocusing arisen from the plasma background of a relatively high plasma density. It has been demonstrated that the plasma expanded faster than the plasma gratings.^{38,40–42,47,48} As the interpulse delay increased, pulse C experienced reduced defocusing losses from the nonmodulated background plasma of rapidly decreased plasma density, and thus it could easily start self-focusing to undergo filamentation, increasing the effective coupling into the long-lasted plasma modulation channels and making the plasma gratings regenerate with increased efficiencies. The spectral lines attained with such an F-GIBS protocol increased accordingly. Anyhow, the as-formed plasma grating structures also experienced their own decays (although slower than the nonmodulated plasma background), their regenerative nonlinear couplings with the third filament were pronounced only at those delays that there still existed plasma modulation structures. If the third filament were delayed up to a few hundred picoseconds, the as-formed plasma modulations almost disappeared and hence could not be regenerated any longer. Accordingly, the F-GIBS was degraded to double-pulse plasma excitations from the plasma gratings and the delayed filaments without any observable nonlinear couplings. Even under such circumstances, the attained spectral line signals were still much larger than the summation of those attained by the plasma gratings and single filament C alone. This was consistent with the spectral line enhancement with double-pulse plasma excitations.

Fig. 4

Top view of the noncollinear interaction area between pulses A and B to create plasma gratings (a) without and (b) with the third filament (pulse C) entering the plasma grating at 50 ps delay, respectively. The plasma grating fluorescence photos are shown in the inset pictures.

As the interpulse delay was set at $-50\mathrm{ps}$, conceptually different nonlinear couplings occurred between the plasma gratings and filament of pulse C. The top view of the noncollinear interaction area between the ahead pulse C ($-50\mathrm{ps}$ delay) and plasma grating induced by pulses A and B is shown in Fig. 5. In this case, pulse C experienced filamentation at first that created self-guiding plasma channels of about $100\text{-}\mu \mathrm{m}$-diameter in air, which in turn made the fluid jet and air–aqueous interface be ablated, i.e., filament excitation occurred at first. Although the femtosecond laser pulses were temporarily confined within the pulse duration (e.g., about 40 fs in our experiments), the plasma channel typically lasted tens of picoseconds, which helped to effectively improve the plasma density of filaments formed later. It has been well demonstrated that there existed observable nonlinear interactions among delayed filaments.⁶² When synchronized pulses A and B overlapped upon the filament channels as-formed by pulse C, both pulses A and B established their own filaments under the circumstance of the already existed plasma from the ahead pulse C, plasma defocusing effects were altered and laser self-focusing should be changed accordingly to reach a new region of balance. Consequently, filaments of pulses A and B interfered differently in the presence of plasma defocusing from the ahead pulse C, and nonlinear filament interactions resulted in the formation of plasma gratings under the influence of the still-lasted plasma channels of the ahead filament C. Plasma grating ablation and excitation were also reasonably different from that without filament C. As plasma gratings were established with additional plasma defocusing from the ahead pulse C, their electron densities were further increased, plasma ablation and excitation efficiency of the liquid sample was thus further improved. Appropriate delay at $-50\mathrm{ps}$ for the best spectral line enhancement implied that plasma gratings were best formed under properly expanded plasma channels of the ahead pulse C. This was consistent with the fact that plasma gratings were established in an area larger than the well-confined single filaments, and that the as-formed filamentation channels with an approximately lifetime duration of plasma expansion could support better filament interactions of pulses A and B.

Fig. 5

Top view of the noncollinear interaction area between the ahead pulse C ($-50\mathrm{ps}$ delay) and plasma grating inducing by pulses A and B.

As all the three filaments were synchronized and shown in Fig. 6, their interactions generated novel kinds of plasma gratings that exhibited quite different microplasma structures. As the synchronized pulse C participated the coplanar noncollinear interference in the cross-overlapped region, the interference patterns differed from that of two noncollinear fs laser beams (pulses A and B), and thus plasma gratings were formed in accordance with the change of interference patterns, giving rising to periodic plasma channels of fine structures in which electron density and peak intensity could be further enhanced using more synchronized pulses to interfere noncollinearly.

Fig. 6

Top view of the noncollinear coplanar filament interaction area as the three filaments are synchronized.

3.3.

Signal Enhancements of Breakdown Spectral Lines

To further analyze the plasma breakdown enhancements, we used GIBS (pulse A and pulse B, total laser energy at 1.4 mJ) and FIBS (pulse C, total laser energy at 0.6 mJ) techniques to acquire spectral line signals, respectively, to compare with F-GIBS (total laser energy at 2.0 mJ). Figure 7 shows the comparison results in which Figs. 7(a)–7(d) represent the spectral lines of the Cu, Cr, H, and Na elements, respectively. FIBS hardly excited aqueous solutions, as indicated by blue curves in Figs. 7(a)–7(d), almost no obvious spectral line signals were observed, except for the easily excited Na element. FIBS spectral lines could not increase further as the input fs laser energy was adjusted to reach a saturated excitation, indicating that filaments and the accompanied filament excitations reached peak-intensity-clamping limits. In all aqueous solutions containing small amounts of elements, filamentation was mainly limited by the optical nonlinearity of water as the major constituent, and plasma channels generated therein could guide laser pulses without filamentation breakups of much lower peak intensities than those in air. As a distinct contrast to FIBS, GIBS spectral line intensities were significantly improved, and all elements (Cu, Cr, and Na) were excited to emit sharp spectral lines. The GIBS protocol allowed for further increase of laser energies (pulses A and B) beyond the intensity clamping limits of single filaments and exhibited the pronounced advantage in evading breakups of the plasma grating channels in the fluid jet stream. In air, fs laser pulses were tightly guided in the plasma gratings, the nonlinearly coupled filaments (pulses A and B) entered the fluid jet through the air–aqueous interface and established plasma gratings in the aqueous solutions, which excited the fluid jet completely differently from single filaments alone. As all the three pulses A, B, and C were synchronized to excite the liquid samples (F-GIBS at 0 ps), an interesting phenomenon was observed. The spectral line intensities were significantly improved, much greater than the summation of FIBS and GIBS. In addition, further spectral line signal enhancement occurred when the interpulse delay was about $-50\mathrm{ps}$ (F-GIBS at $-50\mathrm{ps}$) and 50 ps (F-GIBS at 50 ps), respectively. It should be noted that at these interpulse delays, the filament formed by pulse C did not interact directly with the other filaments. However, as aforementioned, the plasma grating formed by the interference of pulses A and B exhibited different nonlinear couplings with filaments formed by pulse C at positive or negative delays, to achieve better excitation and improved spectral line signals.

Fig. 7

Comparison of FIBS, GIBS, and F-GIBS at different delays (0 and $\pm 50\mathrm{ps}$) in aqueous solutions for spectral lines of (a) Cu, (b) Cr, (c) H, and (d) Na elements.

In order to better compare the spectral line emission differences and effects arisen from nonlinear couplings of filaments with plasma gratings in different excitation protocols, we define the ratio of the spectral line intensities of GIBS and F-GIBS versus FIBS as the enhancement factors: $E_{\mathrm{GIBS}}=I_{\mathrm{GIBS}}/I_{\mathrm{FIBS}}$ and $E_{\mathrm{F}\text{-}\mathrm{GIBS}}=I_{\mathrm{F}\text{-}\mathrm{GIBS}}/I_{\mathrm{FIBS}}$, where $I_{\mathrm{FIBS}}$, $I_{\mathrm{GIBS}}$, and $I_{\mathrm{F}\text{-}\mathrm{GIBS}}$ denote the spectral line intensity attained with FIBS, GIBS, and F-GIBS, respectively. Filament excitations induced quite low breakdown emissions in liquids, and beyond the filamentation threshold, FIBS did not increase any more by merely increasing the excitation pulse energy due to the peak-intensity clamping of single filaments,^46,50 i.e., $I_{\mathrm{FIBS}}$ reached saturation under filament excitation and even worse, single filaments randomly broke up into multiple filaments in liquids as the excitation pulse energy increased further. Although in GIBS and F-GIBS, laser pulses were confined in the plasma grating channels and total pulse energy could be increased beyond the filament breakup limits. The enhancement factors calculated from the measured spectra are summarized in Table 1. As FIBS was replaced by GIBS, two synchronized pulses with a total energy of 1.4 mJ entered the aqueous solutions; instead of multifilamentation breakup, plasma gratings were formed. $I_{\mathrm{GIBS}}/I_{\mathrm{FIBS}}$ ranged from 3 to 5 for Cu and Na elements and reached more than 22 for the Cr element. This enhancement could be ascribed to the enhanced peak intensity and plasma density in the as-formed plasma gratings. By coupling the third filament into the plasma gratings, F-GIBS achieved more prominent enhancements. At the interpulse delay of 0 ps, F-GIBS intensities were enhanced about 6, 28, and 99 times for Na, Cu, and Cr elements, respectively. At the interpulse delay of $\pm 50\mathrm{ps}$ (i.e., F-GIBS at $\pm 50\mathrm{ps}$), nonlinear couplings between the filament and plasma gratings further enhanced the spectral lines of Na, Cu, and Cr elements up to 12, 87, and 195 times, respectively. Note that F-GIBS at $-50\mathrm{ps}$ was slightly larger than that at 50 ps and that the asymmetric enhancement was pronounced for the Na element. This could be readily understood by the mechanism difference of nonlinear couplings between the third filament and the plasma gratings under positive and negative delays. In addition, the measured enhancement factors differed among the three elements tested in our experiments, which may be mainly related to the reactivity difference of elements. F-GIBS contained efficient multiphoton excitations directly from fs laser pulses as well as electron collisions in the elongated plasma gratings, nonlinear couplings of filaments with plasma gratings hence induced prominent enhancements of breakdown emissions for heavy metal elements, such as Cu and Cr, that require high laser intensity and electron density to excite.

Table 1

The enhancement factors of various spectral lines attained by GIBS and F-GIBS excitation protocols versus FIBS.