A nanosecond Nd:YAG laser was used to study the laser ablation of aluminum foil in the phase explosion regime at a laser intensity range of 0.63–3.61 × 10 12 W / cm 2. Laser ablation and plasma characteristics were studied using microscopic ablation crater images, plasma emission spectra, and plasma plume images. Measured plasma density using a Stark width of Al I (396.2 nm) showed a strong linear correlation with crater size, with a Pearson correlation coefficient (r) of 0.97. To understand the origin of this linear correlation, plasma temperature was estimated using Bremsstrahlung emission from 512 to 700 nm. The estimated plasma temperature and aspect ratio of the plasma plume were negatively correlated, having r = 0.76. This negative correlation resulted from a laser-plasma interaction, which heated the plasma and increased its hydrodynamic length. The percentages of laser energy used for plasma heating ( E p / E L) and Al foil ablation ( E Al / E L) were estimated from plasma temperature. Increased E Al / E L, such as crater size, with increasing laser intensity, confirms that greater mass ablation is the fundamental reason for the strong linear correlation between crater size and plasma density.

Pulsed laser ablation (PLA) is a method of mass ejection of a target material. During PLA, the surface of the material absorbs the laser energy, and as a result of the rapid rise in temperature, plasma is generated, and materials are ejected in their gas phase. In the past two decades, PLA has been extensively studied and is a hot topic of research due to its wide range of applications, such as nanoparticle production,1 laser micromachining of materials,2,3 laser-assisted bioprinting,4–6 pulse laser propulsion,7 laser-induced breakdown spectroscopy (LIBS),8–11 EUV generation lithography,12 among others. The ablation process of liquid13 and solid materials14,15 has been thoroughly investigated for optimized PLA applications. However, the fundamental understanding of PLA is still incomplete due to the complexity of light–matter, light–plasma, and plasma-ambient medium interactions.16,17

Developing a comprehensive PLA simulation model is a challenging task because the model must account for numerous nonlinear processes, such as energy exchange between the laser and the target material, material heating, melting, and vaporization, plasma formation and expansion, and laser pulse interactions with plasma.18 For this reason, in addition to numerical simulations, microscopic imaging of the ablation crater19 and characterization of laser-produced plasma (LPP)20 are widely used to understand the fundamental physical principles behind PLA. Characterization of LPP includes analysis of plasma plume dynamics, determining plasma temperature, and electron density.

To characterize the LPP, techniques, such as shadowgraphy,21 schlieren imaging,22 interferometry,23 and optical emission, absorption, and fluorescence spectroscopy24 have been used. Shadowgraphy and schlieren imaging can be used to study the plasma plume and laser-induced shock wave dynamics.25 Imaging plasma plume based on interferometry provides information about density gradient, hence refractive index variation of plasma.26 From the LIBS spectrum, the elemental composition of target material, plasma electron density, and temperature can be determined.8 Analysis of microscopic images of laser-produced craters on the target material gives essential information about the mass ablation rate.27 

The existing literature has investigated variations in crater size and depth as a function of laser fluence or intensity to determine ablation threshold fluence.28–31 These works reported that the craters’ morphology and plasma characteristics are highly dependent on the target material,28 laser pulse duration,29,31 repetition rate,29 number of shots,32 wavelengths,30,33 ambient environment,34 and pressure.34 Considering only the research works related to nanosecond (ns) metal ablation, the majority of previous work has studied the ablation process near the ablation threshold fluence ranging from 0.5 to 50  J / cm 2 (intensity 10 9 W / cm 2).28,29,35 In this regime, the metal ablation is dominated by the vaporization process.30,36 In the vaporization regime, the electrons near the surface of a metal are excited due to the focused laser beam. These excited electrons redistribute the energy in a metal via electron–phonon relaxation, causing lattice vibration and heating of a metal. In this heating process, the temperature reaches the vaporization temperature, and mass is ejected into the surrounding atmosphere.36 

Stoichiometric ablation using laser intensity greater than 10 9 W / cm 2 is required for chemical analysis of solids using LIBS.8,37–41 Therefore, mass ablation and crater size studies using laser intensity 10 9 W / cm 2 are useful for optimizing LIBS for elemental analysis and quantifying the destructiveness of the LIBS. However, few studies of metal ablation exceeding laser intensity 10 9 W / cm 2 exist.30,31,33,36 Yoo et al. studied the ns ablation of silicon for laser intensities ranging from 10 9 to 10 11 W / cm 2.36 They showed that the ablation volume of silicon drastically increased for laser intensities greater than 2.2 × 10 10 W / cm 2. This drastic increase in mass ablation occurs due to the transition from the vaporization to the phase explosion regime.30,36 In the phase explosion regime, a melted liquid metal can be heated above boiling temperature, becoming a superheated liquid. When the temperature of the liquid metal reaches the spinodal limit, due to large density fluctuations, the liquid metal explosively converts to vapor bubbles and droplets of material that are ejected to the surroundings.36 

However, the laser intensity regime above 10 11 W / cm 2, where the process of ablation is mainly driven by phase explosion, remains largely unexplored in terms of understanding the correlation between the size of the ablated crater with the physical properties of the plasma, such as density, temperature, and plume size. In this article, we investigate the correlation between the ablation crater size and the plasma density by ablating a 6.3 μ m thick Al foil using a 9 ns laser pulse, with laser intensities from 6.3 × 10 11 to 3.6 × 10 12 W / cm 2 (fluence: 5.6 to 32.4 × 10 3 J / cm 2). Laser ablation of micron-scale foils has industrial applications in laser scribing of solar cells and laser cutting in the packaging industry, which frequently require mass removal from metallic and semiconductor layers with a thickness of less than 10 μ m.42,43 Microscope images of the ablation crater show a logarithmic increase in the crater size with increasing laser intensity. The measurement of plasma density via the width of Al I (396.2 nm) emission revealed that the ablation crater diameter and plasma electron density exhibited a strong linear correlation [Pearson correlation coefficient (r) = 0.97]. The linear correlation between the crater size and the plasma density holds significant implications for optimizing elemental analysis and assessing the minimally destructive nature of LIBS analysis. To understand the physical origin of this observation, the plasma temperature, indicating the plasma energy, was calculated using electron-neutral Al Bremsstrahlung emission ranging from 512 to 700 nm. It is found that increasing laser intensity decreases the fraction of laser energy converted to plasma energy. As a result, the percentage of laser energy used for Al ablation is increased. This supports the logarithmic increase in the ablation crater size with the laser intensity and the linear correlation between the crater size and the plasma density.

The experimental setup is depicted schematically in Fig. 1(a). Experiments were performed in air using the fundamental wavelength (1064 nm) of a Spectra-Physics QuantaRay Q-switched Nd:YAG laser. The laser was focused using a 20 cm focal length lens, creating a diffraction-limited focal spot diameter of 37  μm. The laser pulse has a pulse length of 9 ns. The laser energy was varied during the experiment from 30.6 to 174.7 mJ with 2.4% energy stability, resulting in laser intensities of 6.3 × 10 11 to 3.6 × 10 12 W / cm 2 (fluence: 5.6–32.4 × 10 3 J / cm 2). The laser energy was varied by adjusting the flash lamp energy. Changing the flash lamp energy alters the laser energy without affecting the beam profile.

FIG. 1.

(a) A schematic diagram of the experimental setup. (b) Al foil after laser ablation with craters spaced by 1 mm.

FIG. 1.

(a) A schematic diagram of the experimental setup. (b) Al foil after laser ablation with craters spaced by 1 mm.

Close modal

Aluminum (Al) foil of 6.3 μ m thickness was used as the target material. The foil was composed of 99.35% Al and trace amounts of copper, iron, silicon, magnesium, and zinc. We chose the 6.3 μ m Al foil for single-shot laser ablation based on literature results in which a 2 - 3 μ m crater depth per pulse in a phase explosion regime was reported.35 The root-mean-squared (RMS) surface roughness of the Al foil was measured to be 0.2 ± 0.02 μ m using a Zygo Optical Profilometer. Compared to the 1 mm Rayleigh length of our focusing geometry and the 1.064  μ m laser wavelength, the roughness of foil can be considered to be negligible.

The Al foil was mounted on a motorized translation stage using a 3D-printed holder. During the experiment, the stage was moved by 1 mm in the x axis after each laser shot. After nine shots in the x axis, a 1 mm step was taken in the y axis. In Fig. 1(b), the x and y axes are perpendicular to the laser propagation axis ( z). The image of the Al foil in Fig. 1(b) shows a grid pattern of craters with a 1 mm step formed by a single laser shot.

Plasma emission spectroscopy was performed to determine the temperature and density of the laser-produced plasmas. An optical fiber was placed at a 45 ° angle to capture plasma emission and was coupled to a Czerny–Turner CCD spectrometer (Thorlabs CCS200) with a spectral range of 380–900 nm and a spectral resolution of 0.4 nm at 532 nm. The plasma spectrum was acquired for each laser shot with an integration time of 1 ms. A total of 525 spectra were collected, with 105 spectra acquired for each laser intensity. Additionally, 105 background spectra were collected without a laser pulse. The spectrometer’s wavelengths were calibrated using a mercury (Hg) lamp, and the spectrometer’s detection response curve for intensity correction was calculated using a tungsten halogen lamp.

A CCD camera (Blackfly S USB3) with an optical density filter (OD = 6 at 400–600 nm) was used for time-resolved imaging of the plasma plume. The minimum exposure time of the camera was 10  μ s, and a time step of 10  μ s was used to image the plasma plume dynamics. The resolution of the camera was 111  μ m / pixel. A set of 150 images of the plasma plume was acquired, with 30 images for each laser intensity. After the experiment, the laser-produced craters on an Al foil paper were imaged using a conventional microscope with a resolution of 3  μ m / pixel. A total of 50 microscope images were taken to measure the size of craters, with 10 images captured for each laser intensity. For crater depth measurement, a Zygo Optical Profilometer was used.

In this section, we present the experimental findings of crater size and plasma properties with varying laser intensities. We investigate the relationship between the crater size and the plasma density by measuring the plasma density using Al I (396.2 nm) emission. Then, an estimation of plasma temperature via Bremstrlung emission is given. The influence of plasma temperature on a plasma plume shape is discussed. At last, the percentages of laser energy required for plasma heating and Al foil ablation are computed to investigate the reason for the correlation between the crater size and the plasma density.

The ablation craters on an Al foil for varying laser intensities were imaged using a microscope. Figure 2(a) displays microscope images of the ablation craters at each energy. It is possible to quantitatively discern that as laser energies increased, crater diameters likewise grew. Consistent with the literature,35,36 three distinct zones around the crater were observed. First, the crater was found to reach its maximum depth at the center of the crater. Second, a circular rim formed around the crater was observed due to the resolidification of melted aluminum. Third, an unaffected zone of an Al foil was located beyond the rim. The heat diffusivity of Al is44, 9.7 × 10 5 m 2 s 1. Hence, the heat diffusion length within the 9 ns laser pulse duration is only 0.9 μ m, which is significantly smaller than the focal shot of 37 μ m, establishing thermal confinement. Due to thermal confinement, the surface temperature of the foil reaches a critical temperature ( T c = 8860 K) at the time of peak laser intensity, converting solid Al to dielectric material and ejecting material explosively, generating the deep region of the crater.45 After the laser pulse, the surface temperature rapidly decreases, transforming the dielectric layer into a melting layer at 0.8 T c. Long after the laser pulse, the melted layer solidified, forming a rim around the crater.45 

FIG. 2.

(a) Microscope images of ablation craters on a 6.3  μm Al foil for laser energies ranges from 30.6 to 174.7 mJ. The crater image for 174.7 mJ highlights three distinct zones around the crater. (1) A deep crater in the center of the laser-irradiated zone, (2) a circular rim formed by resolidification of melted aluminum, and (3) an unaffected surface of aluminum foil. (b) Crater depth profile for a laser energy of 165.4 mJ.

FIG. 2.

(a) Microscope images of ablation craters on a 6.3  μm Al foil for laser energies ranges from 30.6 to 174.7 mJ. The crater image for 174.7 mJ highlights three distinct zones around the crater. (1) A deep crater in the center of the laser-irradiated zone, (2) a circular rim formed by resolidification of melted aluminum, and (3) an unaffected surface of aluminum foil. (b) Crater depth profile for a laser energy of 165.4 mJ.

Close modal

The depth of a crater formed by the 165.4 mJ laser, averaged over ten single shots, is plotted in Fig. 2(b). The measured depth was 4.4 ± 0.6 μ m. A resolidified rim around the crater reached 1.5 ± 0.7 μ m above the crater surface. The depth-to-diameter ratio of the crater is 4.4 / 681.2 = 0.006, showing that mass ablation from the surface was greater than mass removal from the depth of the Al foil. This result is consistent with the findings reported in the literature,35,36 in which the authors reported a significantly smaller depth (2–3  μm) compared to hundreds of micrometer crater diameter in the phase explosive ablation.

Changes in the crater diameter with different laser intensities were also studied. An ImageJ macro code was developed to measure the crater size for different laser intensities. In that code, the background subtracted crater images were thresholded and fitted with an elliptical profile to measure the major and minor widths of the craters. As the craters were roughly circular, the crater’s diameter was defined as the average of the major and minor widths. The measured crater’s diameters for five different laser intensities are plotted in Fig. 3.

FIG. 3.

Measured crater diameter as a function of laser energies (top scale: intensity). The red line represents the fitted logarithmic equation [Eq. (1)].

FIG. 3.

Measured crater diameter as a function of laser energies (top scale: intensity). The red line represents the fitted logarithmic equation [Eq. (1)].

Close modal
The crater diameter was found to increase with laser intensity. An expression relating the average diameter of the ablation crater to the Gaussian energy profile of the laser pulse is defined as46,
D = a × w 2 ln ( E / E 0 ) ,
(1)
where a is a proportionality factor, w = 18.5 μ m is the beam spot radius of the laser, E is the laser energy, and E 0 is a fitting parameter. In Fig. 3, this expression is fit to the experimentally determined crater diameter (red line), with a = 18.9 ± 1.3 and E 0 = 22.5 ± 2.2 mJ. Equation (1) is frequently used to determine the focal spot size or the threshold energy required for the ablation.46 In contrast, the proportionality factor a = 1 and E 0 was defined as the threshold energy for ablation in the study by Liu.46 This is valid for laser intensities below 10 10 W / cm 2 where vaporization predominates over phase explosion.36 Notably, we found that the ablation crater diameter remained consistent with the logarithmic equation of laser energy in the phase explosion regime, except with different values of a and E 0.
From the emitted plasma spectrum, the plasma density can be estimated to investigate its relationship with surface mass ablation. In collisional plasmas, Stark broadening width can be used to determine the plasma density according to the following equation:10,
Δ λ s = 2 × w e ( n e 10 16 ) ,
(2)
where w e is the electron impact width and n e is the plasma electron density in cm 3. The plasma density calculation using Eq. (2) is valid under the assumption of optically thin plasma. Self-absorption in optically thick plasma causes intensity reversal and modifies the emission linewidth.47 In this study, the metastable state of Al I (396.2 nm) was used to determine the plasma density, where I indicates a neutral atom and II indicates a singly ionized atom. No intensity reversal of the Al I (396.2 nm) was observed [see Fig. 4(a)] within the range of investigated laser intensities. Therefore, the optically thin plasma assumption for Al I (396.2 nm) emission is reasonable for plasma density measurement.
FIG. 4.

(a) Plasma emission spectra from 390 to 404 nm. The three emission peaks of Al I (394.4 nm, 396.2 nm) and N II (399.5 nm) are fitted with a Voigt profile to calculate the FWHM of the emission. (b) Measured plasma density using FWHM of Al I (396.2 nm) shows a linear positive correlation with crater diameter.

FIG. 4.

(a) Plasma emission spectra from 390 to 404 nm. The three emission peaks of Al I (394.4 nm, 396.2 nm) and N II (399.5 nm) are fitted with a Voigt profile to calculate the FWHM of the emission. (b) Measured plasma density using FWHM of Al I (396.2 nm) shows a linear positive correlation with crater diameter.

Close modal

In addition to Stark broadening, Doppler, resonance, and Van der Waals (VdW) broadening can all contribute to the linewidth of atomic emissions in weakly ionized plasma at ambient air pressure.48,49 The cited articles49,50 provide details on calculating the linewidth for each broadening process. The resonance broadening for Al I (396.2 nm) emission can be insignificant, as resonance broadening predominantly affects singlet p orbital transitions.51 To determine the maximum linewidth of Al I (396.2 nm) due to Doppler and VdW broadening, we assumed that the neutral atom temperature equals the electron temperature ( T n = T e). This assumption is valid under the assumption of the local thermodynamic equilibrium (LTE), which is validated by plasma density and temperature measurements in this work. At T n = 0.5–2 eV, the Doppler broadening width of Al I (396.2 nm) emission is 0.004 to 0.008 nm, which can be considered to be insignificant.

VdW broadening calculation requires the value of the ground state neutral atom density. We used the following equation to compute the neutral atom density: n a = ρ × N A m, where n a ( cm 3 ) is the neutral atom density in the ground state, N A = 6.02 × 10 23 atoms / mol is the Avogadro number, m = 26.98 g / mol is the molar mass of Al, and ρ = 2.7 g / cm 3 is the density of Al at normal ambient pressure and temperature. The calculated n a = 6 × 10 22 cm 3 is the upper limit of plasma’s neutral Al atom density. Material ejected as droplets36 should be subtracted from the calculated n a. However, we could not quantify the number of neutral atoms that were ejected as droplets in the current study. Neglecting droplet formation and assuming a maximum value of n a = 6 × 10 22 cm 3, the calculated linewidth of VdW broadening is 0.22–0.33 nm for T n = 0.5 to 2 eV. Since our spectrometer cannot resolve the modest dependence of VdW broadening on T n, here, we consider a constant 0.3 nm linewidth for VdW broadening.

As shown in Fig. 4(a), to measure the width of the Al I (396.2 nm) emission, the emission line was fitted with a Voigt profile. The Voigt profile is a result of the convolution of the Lorentzian profile caused by stark and VdW broadening, as well as the Gaussian profile of instrumental broadening. To take into account the interference from the adjacent emissions of Al I (394.4 nm) and N II (399.5 nm), the sum of three Voigt equations was fitted. The measured linewidth of Al I (396.2 nm) was corrected for the instrumental broadening of 0.4 nm using the equation52 
Δ λ mes = Δ λ s 2 + ( Δ λ s 2 ) 2 + ( Δ λ ins ) 2 ,
(3)
where Δ λ mes, Δ λ s, and Δ λ ins are the measured linewidth, the Stark width, and the instrumental broadening FWHM width, respectively. After the correction of instrumental broadening, the contribution from VdW broadening (0.3 nm) was subtracted to calculate the Stark width of Al I (396.2 nm) emission.

Finally, the plasma density for the five distinct laser intensities was calculated using Eq. (2). As found with the crater size, the plasma density increased logarithmically with laser intensity. In Fig. 4(b), the calculated plasma density is plotted against the measured crater diameters. Pearson’s correlation coefficient (r)53 was calculated from a linear fit to quantify the correlation between the crater diameter and the plasma density. The r values vary from 1 to 1, depending on the linear correlation between two variables, with 1 representing a perfect linear correlation, 0 representing no connection, and 1 indicating a perfect negative correlation. The estimated average electron density showed a strong linear correlation with the crater diameter, r = 0.97, within the 95% confidence interval. The linear correlation between the size of surface craters and the plasma density in the phase explosion regime of Al ablation is of great interest in elemental analysis due to its potential for real-time quantification of mass ablation rates and the minimally distributive nature of LIBS.

We calculated plasma temperature and energy using the continuum emission from Bremsstrahlung to investigate the underlying reason for the linear relationship between the crater size and the plasma density. In laser-produced plasmas, continuum emission originates due to kinetic energy loss of free electrons. Free electrons can lose energy by recombining with ions (recombination radiation) or interacting with the Coulomb field of ions or neutral atoms (Bremsstrahlung emission).54 For weakly ionized plasmas where the ratio of electron and neutral atom density ( n e / n a) is less than 10 4, Bremsstrahlung emission due to electron-neutral atom interaction dominates over electron–ion Bremsstrahlung and recombination radiation in the visible range.55 

In our case, the neutral atom density of Al is n a = 6 × 10 22 cm 3, and the maximum electron density is n e = 3.2 × 10 18 cm 3 at a laser intensity of 3.6 × 10 12 W / cm 2. The ratio of n e / n a 5 × 10 5 indicates that electron-neutral Al Bremsstrahlung emission is the dominating process for visible continuum emission in our studied plasma. We selected plasma emission from 512 to 700 nm (see Fig. 5), as the spectrometer detector had the highest sensitivity (intensity correction factor 4 % ) in that region. According to Planck’s law,54 the continuum of graybody radiation from the hot ( 1 eV) ejected macroparticles is negligible in the selected wavelength region.

FIG. 5.

Plasma emission spectrum (512–700 nm) for 174.7 mJ laser energy. The plasma temperature is calculated by comparing the experimental continuum emission with simulated Bremsstrahlung emission for collision between electron and neutral Al.

FIG. 5.

Plasma emission spectrum (512–700 nm) for 174.7 mJ laser energy. The plasma temperature is calculated by comparing the experimental continuum emission with simulated Bremsstrahlung emission for collision between electron and neutral Al.

Close modal
The emissivity of electron-neutral atoms Bremsstrahlung can be defined as follows under the assumption of the Maxwellian distribution of electron energy:55 
ϵ ea = C ea n e n a λ 2 ( 1 k B T e ) 3 2 h ν Q ea ( E ) E 2 × ( 1 hc 2 λ E ) 1 hc λ E e E / k B T e dE ,
(4)
where C ea = ( 4 2 / 3 π 5 / 2 ) ( α h / m e 3 / 2 c ). α is the structure constant, m e is the electron rest mass, h is Planck’s constant, k B is Boltzmann’s constant, T e is the plasma electron temperature, c is the speed of light, λ is the photon wavelength, h ν is photon energy, and E is the electron energy. According to Eq. (4), the shape or spectral distribution of the electron-neutral atom Bremsstrahlung depends on the T e, and the absolute emission intensity depends on the n e. Therefore, by comparing the spectral distribution of experimental continuum emission with numerically calculated ϵ ea, we can estimate T e.

To calculate ϵ ea of electron-neutral Al Bremsstrahlung, the elastic collisional cross section [ Q ea ( E )] needs to be known. We used the cross-sectional data up to 8 eV electron energy published by Gedeon et al.56 As shown in Fig. 5, the numerically simulated electron-neutral Al Bremsstrahlung was compared to experimental continuum emission to estimate T e. The estimated T e for a laser intensity of 3.6 × 10 12 W / cm 2 was 13 474 ± 7 K. The error bar in T e represents the fitting error between the experimental continuum and simulated Bremsstrahlung. This method was repeated for all five laser intensities to determine T e. Calculated T e for different laser intensities is shown in Fig. 6. The uncertainty in the laser intensity was calculated using the measured laser energy fluctuation, and plasma temperature uncertainty represents the spectral variation due to laser energy fluctuations.

FIG. 6.

Estimated plasma temperature for varying laser intensities using electron-neutral Al Bremsstrahlung emission and the Boltzmann ratio of Al I (396.2 nm) and (555.7 nm) emission intensity.

FIG. 6.

Estimated plasma temperature for varying laser intensities using electron-neutral Al Bremsstrahlung emission and the Boltzmann ratio of Al I (396.2 nm) and (555.7 nm) emission intensity.

Close modal
Another common method of plasma temperature measurement is the Boltzmann relationship of atomic or ionic line emission intensity. The emission intensity ratio according to the Boltzmann equation can be defined as follows:24,
I 2 I 1 = g 2 A 2 λ 1 g 1 A 1 λ 2 exp ( E 2 E 1 k B T ex ) ,
(5)
where I is the emission intensity, g is the degeneracy factor, A is the Einstein spontaneous emission coefficient, E is the upper-level energy, λ is the emission wavelength, K B is the Boltzmann constant, and T ex is the excitation temperature. The subscripts 1 and 2 represent two different atomic/ionic lines from similar ionization states. Under the LTE assumption, the excitation temperature equals the plasma electron temperature ( T ex = T e). According to the McWhirter criteria [ n e ( cm 3 ] > 1.6 × 10 16 cm 3),57 the LTE assumption is reasonable for the studied plasmas given the calculated electron density of 10 18 cm 3. To estimate plasma temperature with Eq. (5), the energy separation ( E 2 E 1) between two lines should be greater than k B T ex. We used two Al I emissions (396.2, 555.7 nm), separated by 3.1 eV. The values for g, A, and E were obtained from the NIST atomic database.58 

As shown in Fig. 6, the estimated plasma temperature using the Bremsstrahlung and Boltzmann approach increases nonlinearly with increasing laser intensity. However, the Boltzmann approach underestimates plasma temperature by 1.8 × compared to Bremsstrahlung. This is because Bremsstrahlung emissions appear within a few ns of plasma evolution, whereas atomic lines appear hundreds of ns later.59 De Giacomo et al.59 showed that in laser-produced plasmas, atomic lines are impacted by radiation loss by recombination processes, resulting in an underestimation of T e. To avoid underestimation of T e, the use of an ionic line was recommended for the Boltzmann method.59,60 However, the plasma we investigated had insufficient Al ionic lines with a suitable signal-to-noise ratio. Furthermore, the Bremsstrahlung approach uses the fitting of 950 wavelength points rather than a ratio of two points, which provides statistically higher accuracy for plasma temperature calculation, particularly temperature at earlier stages of plasma evolution. As a result, the remaining calculations in this article used Bremsstrahlung’s estimated plasma temperature.

Previous studies20,61 have shown that the shape of the plasma plume can provide insight into the laser-plasma coupling process. At peak laser intensity, the plasma produced and the plume expand at a supersonic speed, following the Taylor–Sedov point blast equation.62 During this expansion, the plasma plume can absorb energy from the remaining tail of the nanosecond laser pulse via inverse Bremsstrahlung, resulting in an ellipsoidal shape. At a time greater than 1 μ s, plasma plume expansion significantly slows down and retains its ellipsoidal shape.61 As a result, the shape of the plume at a time much later than the laser pulse could provide information about the laser-plasma coupling process. For this reason, we studied the correlation between increasing plasma temperature and the shape of the plasma plume at a much later time of 30 μ s.

In this study, we defined the arrival time of laser pulse as t = 0, and plasma plumes were imaged for four different delays ranging from 30 to 60 μ s with a 10 μ s step, as illustrated in Fig. 7.

FIG. 7.

Images of plasma plumes with a time step of 10  μ s. The height and width of the plasma plume are calculated from a Gaussian fitting.

FIG. 7.

Images of plasma plumes with a time step of 10  μ s. The height and width of the plasma plume are calculated from a Gaussian fitting.

Close modal

The shape of plasma was ellipsoidal with a major (height) and minor axis (width). The height and width of the plasma plume for each time were calculated using a Gaussian fitting. Then, the aspect ratio, defined as the ratio of width and height of the plume, was determined. The measured aspect ratio of the plume is plotted as a function of plasma temperature in Fig. 8(a). From this figure, it is observed that the overall aspect ratio of the plasma plume is negatively correlated (r = 0.76) with plasma temperature for all delays. The negative correlation between the aspect ratio of the plasma plume and the plasma temperature implies that plasma is elongated in the laser propagation axis and becomes more ellipsoidal as the plasma temperature increases.

FIG. 8.

(a) The aspect ratio (width/height) of the plasma plume is negatively correlated with the plasma temperature. (b) The hydrodynamic length of plasma is plotted for different plasma temperatures.

FIG. 8.

(a) The aspect ratio (width/height) of the plasma plume is negatively correlated with the plasma temperature. (b) The hydrodynamic length of plasma is plotted for different plasma temperatures.

Close modal

To explain the origin of the negative correlation between the aspect ratio of the plasma plume and plasma temperature, the hydrodynamic length of plasma was calculated using the measured plasma temperature. The plasma hydrodynamic length is defined as the expanded length of plasma within the time scale of the laser pulse. Mathematically, plasma hydrodynamic length = v p τ, where v p = γ k B T e / M is the plasma expansion velocity, τ is the laser pulse duration, and M is the atomic mass of Al and adiabatic constant γ = 5 / 3, considering three degrees of freedom.

The calculated plasma hydrodynamic length is plotted in Fig. 8(b). From this result, we can observe that the plasma hydrodynamic length increases with increased laser intensity. Therefore, as the laser intensity increased, plasma heating increased due to higher laser energy absorption by plasma through the inverse Bremsstrahlung process. The associated increase in the plasma temperature leads to the creation of higher energetic plasma species along the laser propagation axis and, thus, increased expansion along that axis,20,61 creating more ellipsoidal (lower aspect ratio) plumes at higher intensities.

Increasing laser-plasma coupling with increasing laser intensity can be perplexing with the fact that Al ablation was increased with increasing laser intensity, leading to a strong linear correlation between the crater size and the plasma density. To understand these findings, the percentage of laser energy converted to plasma energy via plasma heating is calculated. The plasma energy can be expressed as E P = γ N a k B T e, where N a is the total number of atoms within the focal volume. The calculated plasma energy ( E P) was divided by the laser energy ( E L) to estimate the percentage of laser energy used for plasma heating ( E p / E L).

According to Fig. 9(a), the E p / E L decreases exponentially with increasing laser intensity. The energy used for Al ablation can be defined as E Al = E L E R E P, where E R represents the reflected laser energy. E Al represents the total energy required to ablate the Al, including direct laser ablation and enhanced ablation due to increased recoil pressure of plasma plumes on the melted Al surface.30,36 The reflectance of the Al foil is required for calculating E Al, which is dependent on the foil surface roughness and temperature. The measured surface roughness was 0.2 ± 0.02 μ m 2, which is significantly smaller than the Rayleigh length (1 mm) and the laser wavelength (1.064  μ m); hence, the influence of roughness can be reasonably neglected. The numerical simulation of Al ablation by Gragossian et al.45 demonstrated that the reflectivity remains nearly constant until a surface temperature of 0.9 T c. At 0.9 T c, the reflectance stepwise decreases to 68%. However, this rapid change occurs after the peak laser intensity when an opaque Al metal transforms into a transparent dielectric.45 Since most laser energy absorption occurs within the peak laser pulse, a constant 95% reflectivity of Al can be reasonably assumed for the calculation of E Al.63,64 However, this assumption may underestimate the ablation energy without a detailed numerical simulation. Nonetheless, the constant reflectivity assumption can reasonably explain the ablation crater variations with the laser intensity observed in this work.

FIG. 9.

Plasma energy ( E P) is calculated from the estimated plasma temperature. The fraction of laser energy converted to plasma energy ( E p / E L) decreases with increasing laser energy. (b) Under the assumption of reflectivity of the Al constant (95%) over varying laser energies, the fraction of laser energy used for Al ablation ( E p / E L) increases with increasing laser energy.

FIG. 9.

Plasma energy ( E P) is calculated from the estimated plasma temperature. The fraction of laser energy converted to plasma energy ( E p / E L) decreases with increasing laser energy. (b) Under the assumption of reflectivity of the Al constant (95%) over varying laser energies, the fraction of laser energy used for Al ablation ( E p / E L) increases with increasing laser energy.

Close modal

From Fig. 9(b), we can observe that the percentage of E Al / E L increases logarithmically with increasing laser intensity. The logarithmic increase of E Al / E L supports the experimental observation of a logarithmically increasing crater size with increasing laser intensity. Increasing E Al / E L with the laser intensity also implies that the mass ablation rate increases with laser intensity. These findings are in agreement with the observed increase in the plasma density and support the strong linear correlation between the crater size and the plasma density.

The correlation between the ablation crater size and plasma properties was investigated in the phase explosion regime of Al foil ablation by varying the laser intensity of a nanosecond laser from 6.3 × 10 11 to 3.6 × 10 12 W / cm 2. The measured crater size from microscopic images was found to increase logarithmically with laser intensity. To investigate the connection between the crater size and the plasma density, the density of plasma was measured using the linewidth of Al I (396.2 nm) emission. The plasma density was linearly correlated with the crater diameter, with an r of 0.97.

To explain the fundamental reason of the linearity between the crater size and the plasma density, the plasma temperature was determined using Bremsstrahlung emission from 512 to 700 nm. The plasma temperature increased with laser intensity and correlated negatively with the plasma plume’s aspect ratio. The negative correlation between the plume aspect ratio and the plasma temperature resulted from plasma heating by laser energy absorption, which increased the hydrodynamic length. The plasma temperature was used to compute the percentage of laser energy used for plasma heating ( E p / E L) and Al ablation ( E Al / E L). The calculated E Al / E L increased with laser intensity, as did the crater size, supporting an increase in mass ablation as the laser intensity increased. The higher mass ablation is identified as the primary reason for the linear correlation between the crater size and the plasma density. The linear connection between the surface ablated crater size and the plasma density has important implications for optimizing LIBS elemental analysis and real-time assessment of the minimally destructive nature of LIBS.

The findings of the investigation imply that the logarithmic rise of ablation efficiency ( E Al / E L) results in the logarithmic increase of the crater size with the laser intensity. Enhanced ablation efficiency in the phase explosion regime for the 0.63–3.61 × 10 12 W / cm 2 laser intensity leads to forming a significantly larger crater diameter than its depth, resulting in a linear correlation between the crater size and the plasma density. In future work, time-resolved plasma temperature measurement for plasma energy calculation ( E p) and numerical simulation using dynamic reflectivity of Al as a function of time-resolved temperature for estimating E Al will be beneficial for a better understanding of the linear correlation between the crater size and the plasma density.

This work was supported by Alberta Innovates through the Smart Food and Agriculture Digitization Challenge (Agreement No. 202100740) the Alberta Innovates Graduate Student Scholarship (Awarded to Shubho Mohajan), and the Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN-2021-04373). This research was undertaken, in part, thanks to funding from the Canada Research Chairs Program.

The authors have no conflicts to disclose.

Shubho Mohajan: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Resources (equal); Software (lead); Validation (equal); Visualization (lead); Writing – original draft (lead). Nicholas F. Beier: Conceptualization (equal); Data curation (equal); Investigation (supporting); Methodology (equal); Resources (equal); Software (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Amina E. Hussein: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Funding acquisition (lead); Investigation (lead); Methodology (equal); Project administration (lead); Resources (lead); Supervision (lead); Validation (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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