A theoretical study of the signal enhancement mechanism of coaxial DP-LIBS

1.   Introduction

Laser-induced breakdown spectroscopy (LIBS) is a qualitative or quantitative analysis technique based on atomic and molecular emission spectroscopy, which can be used to analyze element composition in solid, liquid, and gaseous samples. Due to its fast, non-contact, and simple sample-preparation characteristics, it has been widely applied in industrial analysis [1], environmental monitoring [2], biochemical reconnaissance [3], and other fields. However, compared with other spectroscopic detection techniques, such as X-ray fluorescence spectroscopy (XRF) and inductively coupled plasma (ICP), LIBS still has relatively high detection limits (LOD) for some elements. In recent years, various spectral techniques have been proposed to enhance LIBS, including dual-pulse LIBS (DP-LIBS) [4], microwave-assisted LIBS [5], spatially constrained plasmas [6], and concentric multipass cell enhanced LIBS [7]. Among them, DP-LIBS is one of the most widely used techniques. It utilizes two ultra-short interval laser pulses to enhance the intensity of the spectral signal and achieve the detection of trace elements. As early as 1969, Piepmeier et al proposed the concept of DP-LIBS [8]. They believed that most of the laser energy was absorbed by the plasma plume, and the second laser pulse would further excite the species in the plasma.

Depending on the different optical structures, DP-LIBS mainly has two types of optical path structures: coaxial [9] and orthogonal [10]. In the coaxial structure, the two pulses have the same propagation axis, both perpendicular to the sample surface. In the orthogonal structure, it can be further divided into pre-ablation and re-heating modes based on the different excitation order of the dual pulses. In terms of the complexity of the optical path structure, the coaxial DP-LIBS structure is simpler and more practical for improving spectral signals.

In recent years, experiments with laser wavelengths ranging from infrared [9] to visible light, and even ultraviolet [11], have demonstrated that DP-LIBS can enhance element spectral lines by 1.5–33 times [12], reduce detection limits several times or even by one order of magnitude, and improve the signal-to-noise ratio (SNR) of spectral lines [13]. For example, Wang et al compared femtosecond DP-LIBS spectra at different pulse intervals [14] and found that the Fe I 427.18 nm line can be enhanced up to 3 times, which can be attributed to the plasma re-heating effects of the second laser pulse. Li et al utilized reheating DP-LIBS to analyze trace copper elements in micro-alloyed steel [15] and found that the enhancement degree of the spectral line is related to its excitation level, which indicates that the re-heating laser facilitates a larger and hotter plasma. In DP-LIBS-induced air plasma shielding and diagnostics, Zhang et al found that the plasma temperature is slightly higher than that of single-pulse LIBS [16]. In addition, in the area of laser metal processing, Forsman et al found that the quality removal rate of DP-LIBS is 3–10 times higher than that of LIBS [17]. For pulse laser deposition, DP-LIBS technology has been proven to achieve large-area and uniform thin film growth, which can be attributed to the axial expansion of the initial plasma size and increase in plasma temperature [18]. Mao et al found that the plasma temperature of DP-LIBS changes significantly with a delay between laser pulses of 100–200 ns. Once it exceeds 200 ns, the quality removal rate will increase significantly [19]. Babushok et al also summarized the mechanisms behind the signal enhancement effects of DP-LIBS from the perspective of the ablation process and laser heating of the plasma [20], suggesting an increase in plasma volume, temperature, expansion rate, ablation rate, and ion density in the plasma core as the possible sources. Furthermore, Scaffid et al also believed that the emission enhancement mechanism in DP-LIBS is the result of a combination of factors such as the heating of the sample before ablation, increased electron density and plasma temperature, and reduced atmospheric pressure [21].

In addition to experimental studies, extensive theoretical research has been conducted on DP-LIBS. De Giacomo et al simulated underwater DP-LIBS by combining bubble dynamic codes and Euler equations describing plasma evolution [22]. They pointed out that adjusting the pulse interval can not only change the signal intensity, but can also affect the internal conditions (radius, pressure, and temperature) of the bubble induced by the first pulse, thus influencing the second pulse-induced plasma. Wang et al simulated the spatial distribution of plasma temperature and the enhancement effects of different pulse intervals under pre-ablation and re-heating modes [23], explaining the enhancement mechanism of spectral lines from the perspectives of plasma-plasma coupling and pressure effects. Ranjbar et al used Monte Carlo simulations to study the kinetic expansion process of plasma induced by three 266 nm pulse lasers [24], and explored the relationship between different beam sizes and plasma shielding effects. They found that the plasma shielding effects during multi-pulse laser ablation can be reduced when the laser beam size is in the tens of micrometers. Povarnitsyn et al proposed a dual-temperature hydrodynamic approach and used it to simulate the single and multi-pulse ablation processes in laser–metal interactions [25], considering laser energy absorption, electron–phonon coupling, and thermal conductivity. They demonstrated that the efficiency of re-heating is the highest when the pulse interval is 100 ps. Nosrati et al simulated the radiation of the DP-LIBS-induced plasma using a one-dimensional numerical model [26] and showed that the quality removal rate of DP-LIBS is significantly higher than that of LIBS, and the removal rate gradually increases with the reduction of the ablation plume. The enhancement mechanisms of coaxial DP-LIBS signals have been appropriately analyzed in these studies. However, further exploration is still needed to understand the enhancement mechanisms of spectral signals from various aspects, such as radiation fluorescence characteristics, spatial distribution of plasma temperature, and number density. Theoretical simulations can be conducted to investigate the spatiotemporal expansion process and behavioral characteristics of coaxial DP-LIBS-induced plasma, as well as to explore the enhancement mechanisms of dual-pulse excitation signals. Such simulations also offer valuable preliminary guidance for experimental design and parameter optimization.

In this work, numerical simulations were carried out to investigate the temporal and spatial evolution of plasma induced by co-axial dual-pulse laser-induced breakdown spectroscopy (DP-LIBS) in an argon environment, focusing on the fluorescence characteristics, spatial distribution of plasma temperature and density, and the shielding effects on the second laser pulse. The enhancement mechanism of spectral signals was also explored. The study provides important insights into the optimization of experimental parameters, by analyzing the plasma’s radiation and spatial expansion processes, and examines the effects of energy transfer, electron density, and temperature on plasma.

2.   Theoretical model

When the laser beam interacts with a sample, thermal conduction is the main heat transfer mechanism that transfers laser energy from the sample surface to its interior. Therefore, the heating process is usually described using a one-dimensional heat conduction equation [27]:

here, c_p, ρ, α, λ, R_f, T_t and v_t refer to the target material’s specific heat, mass density, absorption coefficient, thermal conductivity, reflectivity, surface temperature, and evaporation rate, respectively. The I_t is the laser irradiance on the target surface, while z is the coordinate along the normal direction to the surface.

In this study, the simplified process of laser ablation of magnesium–aluminum alloy to generate plasma is described as follows. Under the action of laser ablation, when the ablation zone on the target surface is heated to the boiling point of magnesium, magnesium vapor is generated. This vapor continues to absorb laser energy, becoming ionized and forming magnesium plasma. When the ablation zone reaches the boiling point of aluminum, aluminum vapor is also generated. The vapor then, under the combined action of subsequent laser energy and magnesium plasma, forms a mixed plasma of aluminum and magnesium particles. The magnesium–aluminum vapor causes the argon background gas to expand rapidly outward. This expansion process can be described by a two-dimensional axisymmetric fluid dynamics equation set containing the interaction between magnesium–aluminum vapor plasma and the background gas, including conservation equations of mass, momentum and energy [28]:

In the given equation, ρ_i and ρ represent the mass density of element i and the total mass density, respectively. Here, u_i and u represent the diffusion velocity of element i and the velocity of the plasma plume flow, respectively; p, q, e represent the local pressure, radiation power loss, and specific internal energy, respectively; α_IB and α_PI are the reverse bremsstrahlung absorption coefficient and photoionization coefficient of the excited atoms, respectively; λ and τ represent the thermal conductivity and viscous stress tensor [28], respectively; T represents the electron temperature; and I_t represents the laser irradiance.

If the electrons follow the Maxwellian velocity distribution, then the total amount of energy emitted per unit volume per unit time is given by [28]:

where k_B is the Boltzmann constant.

The aforementioned conservation equation also needs to be combined with expressions for the local pressure and internal energy density of an ideal gas [29]:

where M is the molar mass of the element, R is the ideal gas constant, and IP is the ionization potential.

By applying the boundary conditions of the Knudsen layer [30] and the equilibrium conditions at the sample surface, the fluid dynamics model can be coupled with the heat transfer model to obtain the surface temperature, evaporation rate and initial plasma parameters of the sample, including the total number density, velocity, and plasma temperature. By combining the Saha equation and the charge conservation equation, the number density of each atom and ion can be obtained.

Based on the plasma parameters obtained from the fluid dynamics equations, the emission intensity of the species in the plasma under the local thermal equilibrium conditions is given by:

The plasma generated at the target surface absorbs a portion of the laser beam energy, known as the plasma shielding effect [31]. This absorption includes two parts: the inverse bremsstrahlung absorption (α_IB) and the photoionization absorption (α_PI), of which the former includes the electron–neutral absorption (α_en) and the electron–ion absorption (α_ei):

Here, n_e, n_0，n_j and n_v represent the electron density, atomic number density, ion number density, and vapor number density, respectively; Q is the cross-section for electron absorption of light (10⁻³⁶ cm⁵) [32]; z_j is the charge number; ε is the minimum excitation energy for photoionization; v is the laser frequency; and c, k_B and h represent the speed of light, Boltzmann constant, and Planck constant, respectively. The cross-sectional area ${\sigma }_{\mathrm{P}\mathrm{I}}=7.9\times {10}^{-18}{\left({E}_{\mathrm{I}}/ hv\right)}^{3}{\left({{I}_{\mathrm{H}}/ {{E}_{\mathrm{I}}}}\right)}^{1/2}$ [33], where E_I is the ionization potential of the excited state and is considered equivalent to the photon energy of the laser, and I_H is the ionization potential of hydrogen.

Assuming that the initial laser irradiance is I₀, accounting for the plasma shielding effect, the laser irradiance at position $z$ can be expressed as:

This study conducted numerical simulations on the induced plasma of aluminum–magnesium alloy in argon gas using a coaxial DP-LIBS setup shown in figure 1. The laser used was a Gaussian pulse with a width of 31 ns, and the pulse intervals were set at 50, 100, 200, 500, 1000, and 1500 ns. The laser power density on the target surface in the interaction region was set at 5×10⁹ W cm⁻², as well as a double energy density of 10×10⁹ W cm⁻². A numerical model was established, including laser–solid interaction, vapor plume expansion, plasma formation, and laser–plasma interaction. The initial temperature of the model was set at 300 K, and the initial pressure of the argon gas was 1.01×10⁵ Pa. The boundary temperature and pressure were set to 300 K and 1.01×10⁵ Pa, respectively. The time step was 1 ns, with horizontal and vertical grid steps of 0.1 mm and 0.05 mm, respectively. The parameters for the aluminum–magnesium alloy target are shown in table 1.

Table  1.  The performance of the alloy target material.

Parameters	Values
Specific heat, cρ (J g−1 K−1)	0.90
Mass density, ρt (g cm−3)	2.70
Thermal conductivity, λt (W cm−1 K−1)	2.37
Reflectivity, R	0.90
Absorption coefficient, α (cm−1)	1.5×106
Melting point, Tm (K)	921 (Mg), 934 (Al)
Boiling point, Tb (K)	1363 (Mg), 2792 (Al)
Heat of fusion, Hf (J mol−1)	9.04×103 (Mg), 1.04×104 (Al)
Heat of vaporization, Hv (J mol−1)	1.16×105 (Mg), 2.55×105 (Al)
First ionization potential, IP (eV)	7.65 (Mg), 5.99 (Al)

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Figure  1.  A schematic diagram of the one-dimensional coaxial DP-LIBS.

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3.   Results and discussion

3.1   Emission line intensity

The relationship between the intensity of the Al I 308.2 nm line and the pulse interval in both LIBS and coaxial DP-LIBS obtained from theoretical simulations is shown in figure 2. It can be seen that the variation trend of spectral line intensity is the same under both conditions. After the laser pulse action, the intensity rapidly increases to its maximum value and then gradually decreases. Compared to LIBS, the enhancement ratio of the spectral line intensity in DP-LIBS is 1.25–2.25 times higher, and the curve has two peaks. The spectral line intensity of double-pulse energy density LIBS is still lower than that of DP-LIBS under short pulse intervals. From the decay rate of the spectral line intensity after reaching the maximum value, it can be observed that the decay rate of coaxial DP-LIBS is slower than that of LIBS. Therefore, coaxial DP-LIBS can generate stronger and more persistent spectral lines, thereby reducing the LOD (limit of detection) of elements and improving detection sensitivity. The main mechanism for the enhancement of spectral lines by the second pulse laser in coaxial DP-LIBS is mainly attributed to the plasma absorbing laser energy due to shielding effects, resulting in an increase in plasma temperature. The remaining laser energy will then re-ablate the target material to replenish and enhance the plasma. This conclusion will be discussed in detail in the subsequent analysis of plasma temperature and number density.

Table  2.  Spectroscopic details for characteristic spectral lines of different species.

Spectral line	E (eV)	g	A (×107 s−1)
Al I 308.2 nm	4.021	4	5.87
Al I 396.2 nm	3.143	2	9.85
Al II 466.3 nm	13.256	3	5.81
Mg I 285.2 nm	4.346	3	49.1
Mg II 279.6 nm	4.434	4	28.0

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Figure  2.  The time evolution of Al I 308.2 nm line intensity in LIBS and coaxial DP-LIBS at different pulse intervals.

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Figure 3 displays the dual-pulse emission enhancement graph relative to the single-pulse results, showing the relative intensity as a function of the pulse delay time for several spectral lines. The emission characteristics of vapor species (Al I, Al II, Mg I, Mg II) in the plasma were analyzed. The spectroscopic parameters for each spectral line listed in table 2 are sourced from the NIST database. Through simulated studies, it was found that compared to single-pulse results, an enhancement in the DP-LIBS spectral line signals was observed, and all spectral lines exhibit similar behavior with respect to the pulse delay time. By examining the variation of signal enhancement for several spectral lines with respect to the pulse delay time, two main states were observed: relatively strong (∆t < 1000 ns), and relatively weak (∆t > 1000 ns). Figure 3 indicates that at a short pulse delay (∆t ≈ 100 ns), the maximum signal gain is observed, reaching approximately 2.25 times. However, at longer pulse delays, the enhancement of the second laser pulse on the plasma emission intensity becomes less pronounced, at 1.14 times. These simulation results align with other experimental findings, as reported in [34], where certain elements in DP-LIBS exhibited maximum signal gain around a pulse delay of 200 ns.

Figure  3.  The impact of the interpulse delay on the intensity of multiple spectral lines.

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3.2   Laser irradiance in the presence of plasma shielding

Due to the shielding effects of the plasma, the laser irradiance reaching the target surface will inevitably be reduced after passing through the plasma. Figure 4 compares the initial irradiance of the second laser pulse with the calculated irradiance after the plasma is induced by the first laser pulse. It can be seen that due to the shielding effects of the first laser pulse ablating the plasma, the irradiance of the second laser pulse reaching the target surface is always lower than the initial irradiance. When the pulse interval is 100 ns, the plasma shielding effect is severe, and the remaining laser energy passing through the plasma is very low. The remaining energy is insufficient to re-ablate the target surface and generate plasma. At this time, the enhancement of spectral line intensity is mainly due to the plasma directly absorbing laser energy and increasing its temperature. When the pulse interval is 200 ns, the plasma shielding effect is still significant, and the remaining laser energy passing through the plasma is very low. The remaining energy can only generate a small amount of lower-temperature plasma after re-ablating the target surface. At this time, the enhancement of spectral line intensity is mainly due to the direct absorption of laser energy by the plasma to increase its temperature. However, after extending the pulse interval to 500 ns, a considerable amount of laser energy can pass through the plasma, and the laser, after being shielded by the plasma, will re-ablate the target surface to generate plasma. At this time, the enhancement of spectral line intensity is a combined effect of the plasma directly absorbing laser energy and the laser re-ablating the target material. Therefore, in the following discussion, we mainly focus on the irradiance of the laser reaching the target surface, as well as the plasma temperature and particle number density under the conditions of a 500 ns pulse interval.

Figure  4.  Comparison of initial laser irradiance and irradiance after plasma shielding at different pulse interarrival times in co-axial DP-LIBS.

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Figure 5 depicts the temporal evolution of irradiance on the target surface for the second laser pulse with a pulse interval of 500 ns. Initially, the actual irradiance of the laser reaching the target surface is identical to the irradiance after being shielded by the initial generated plasma. However, after a few nanoseconds, there is a steep decrease in the proportion of the actual laser irradiance. This phenomenon indicates that the remaining energy of the second laser pulse, after passing through the initial plasma, causes further ablation of the target material and generates a large number of species that enter the plasma plume. Consequently, the density of aluminum–magnesium neutral atoms, ions, and electrons in the plasma increases rapidly, resulting in most of the laser absorption occurring in the plasma plume layer near the target surface. As a result, the absorption effect intensifies rapidly. Bogaerts et al [32] also conducted a comparison of the temporal distribution of pulsed laser propagation through plasmas before and after plasma formation at different laser irradiance levels. They found that, initially, a single laser pulse was not shielded by the plasma, and at equivalent laser irradiances, the absorption trends were similar to those observed in this study.

Figure  5.  The actual laser irradiance reaching the target surface at a pulse interval of 500 ns.

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3.3   Plasma temperature

The temperature of the plasma is an important parameter that characterizes the plasma and directly affects its fluorescence characteristics, determining the distribution of its energy. To visually compare the spatial distribution of internal plasma temperature induced by LIBS and DP-LIBS, contour plots of plasma temperature are shown in figure 6. The plasma temperature here is treated according to the local thermal equilibrium (LTE) state. In figure 6(a), the spatial distribution of plasma temperature for single-pulse LIBS with a delay time of 500 ns is presented. In figure 6(b), the plasma temperature distribution for DP-LIBS with a pulse interval of 500 ns and the same delay time of 500 ns (i.e., after the second laser pulse at 500 ns) is shown. It can be observed that in single-pulse mode, the temperature distribution exhibits a symmetrical arch shape, with high-temperature regions concentrated in the middle of the plasma. By contrast, in dual-pulse mode, the temperature distribution shows a symmetric wing-like shape. This is because the second laser pulse will reheat the already generated plasma and further ablate the target surface after passing through the plasma, resulting in the concentration of high temperatures at the top of the plasma. Furthermore, the plasma temperature induced by coaxial DP-LIBS is significantly higher than that of single-pulse LIBS. From the legend in the figure, it can be seen that the highest temperature under LIBS mode is 3.10 eV, while under DP-LIBS mode, the highest temperature reaches 8.08 eV, which is 2.6 times higher than that of the single pulse with the same delay time.

Figure  6.  Spatial distributions of plasma temperature at 500 ns under different conditions.

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From figure 7, it can be observed that after the plasma is induced by the pulsed laser, its average temperature rapidly decreases. However, when another pulse laser beam is incident with a 500 ns interval, the average temperature of the plasma is significantly increased. The partial energy absorption of the second laser beam and the re-ablation of the target material both contribute to the increase in plasma temperature, greatly enhancing the radiation signal of the plasma. The additional thermal energy quickly converts into the kinetic energy of particles, resulting in a high expansion and diffusion speed of the plasma. This aspect will be discussed in detail in the following study regarding the spatial distribution of the number density of Mg and Al particles.

Figure  7.  The average temperature of plasma in DP-LIBS.

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3.4   Species number density

The spatial distribution of species number density is the most direct characteristic for an accurate understanding of the dynamic features of the plasma. For convenient visual comparisons, figures 8 and 9 respectively show the spatial distribution of Mg and Al species in the plasma induced by LIBS and DP-LIBS at 500 ns and 1000 ns (i.e., 500 ns after the second laser pulse). It can be seen that the distribution of species number density for both Mg and Al is very similar and symmetric. However, the number densities of ions are far less than those of their corresponding atoms (by 2–3 orders of magnitude), because ionization requires a higher energy level. The number density of Al atoms is lower than that of Mg atoms because Al has a higher boiling point than Mg, and therefore requires a higher target surface temperature to form Al atoms. However, for ions, the number density of Al is higher than that of Mg due to its lower ionization energy. It is also noticed that the magnitude of the vapor in various species at 1000 ns is almost twice that of 500 ns, which is related to the plasma temperature. The second laser pulse increases the plasma temperature, and the species acquire greater kinetic energy, resulting in a quite considerable vapor size. The second laser pulse will ablate the sample surface again after passing through the plasma shield, generating new species on the target surface together with the diffusion of vapor, further enhancing the plasma radiation.

Figure  8.  Spatial distribution of the number density of Mg and Al species at 500 ns in plasma induced by LIBS.

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Figure  9.  Spatial distribution of the number density of Mg and Al species at 500 ns in plasma induced by co-axial DP-LIBS.

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4.   Conclusion

This study utilized the fluid dynamics model theory to investigate the evolution of spectral line intensity and laser irradiance with time, as well as the spatial distribution of temperature and particle number density in co-axial DP-LIBS and single LIBS-induced plasmas. The simulation results reveal that, in co-axial DP-LIBS with pulse delays ranging from 50 to 1500 ns, the spectral intensity can be enhanced by 1.25–2.25 times. Different elemental spectral lines exhibit similar behavior concerning pulse delay, although optimal delay times vary. The irradiance from the second laser, after passing through the plasma, indicates that the shielding effect consistently results in lower irradiance compared to the initial values. At 10 ns, a sharp decrease in actual laser irradiance suggests that the second laser re-ablates the target material through the existing plasma, releasing a significant number of particles into the plume. This infers that the shielding effect primarily occurs in the plume layer near the target surface. In co-axial DP-LIBS mode, the plasma’s peak temperature is 1.6 times higher than that in single-pulse LIBS. The average temperature increases under the influence of the second laser, attributed to direct energy absorption by the plasma and the re-ablation of the target material. The additional thermal energy rapidly converts into particle kinetic energy, leading to a high expansion and diffusion rate of the plasma. With larger particle kinetic energy, a considerably greater plume size is observed in co-axial DP-LIBS compared to single-pulse LIBS at 500 ns, nearly doubling the sizes of various particles. It was deduced that the signal enhancement mechanism of co-axial DP-LIBS could be attributed to the absorption of the second laser beam’s energy by the plasma, leading to an increase in its temperature, and the generation of new plasma through re-ablation. This theoretical simulation of plasma evolution in co-axial DP-LIBS can explain phenomena, such as enhanced spectral line intensity at different delay times, a slowed decay rate of spectral line intensity, increased plasma temperature caused by double-pulse excitation, accelerated sample ablation rate, and an enlarged area. It provides theoretical support for conducting experimental research and parameter optimization in DP-LIBS.

Acknowledgments

This work was supported by the National Key R&D Program of China (No. 2017YFA0304203); the National Energy R&D Center of Petroleum Refining Technology (RIPP, SINOPEC); Changjiang Scholars and Innovative Research Team at the University of the Ministry of Education of China (No. IRT_17R70); National Natural Science Foundation of China (NSFC) (Nos. 61975103, 61875108 and 627010407); 111 Project (No. D18001); Fund for Shanxi (No. 1331KSC).