Introduction

The widely-used spectroscopic analysis method named as laser-induced breakdown spectroscopy (LIBS) involves the use of a high-powered laser beam directed at the surface of a target material [1,2,3]. This laser beam vaporizes, excites, and ionizes the target species, causing the emission of light when the species de-excite or recombine [4]. This emitted light is collected and subjected to spectral analysis to extract valuable information such as elemental identification, quantification, and plasma parameters [5, 6]. The behavior of the plasma is influenced by a range of laser parameters, including incident energy, wavelength, and pulse duration, as well as target material properties [7]. The species appear in the plasma can interact with the incident photons, leading to further heating of the plume, and finally, radiation is emitted from the expanded plasma for an extended duration. By examining the emissions from excited species, it becomes possible to identify the elemental composition of the plasma as it approximately represents the analyte's content [8, 9]. In recent decades, the technique of LIBS has gained recognition as a reliable analytical method across various fields of application. One of its notable advantages is its non-contact, optical nature, which eliminates the need for sample preparation [10]. Numerous areas of application have already been established, such as elemental analysis [11], quality control in steel manufacturing, and characterization of jewelry products [12]. Additionally, LIBS has been utilized in soil studies, thin film deposition, cleaning, preservation of cultural heritage [13] (e.g., cleaning of old papers, wood, and paintings), as well as in situ planetary exploration. Despite the utilization of the LIBS to examine elemental composition of biological samples, limited studies exist on the use of LIBS for investigating plasma produced at human tooth surface. Hence, the present study aimed to look at the correlation between plasma parameters, photon absorption, and laser wavelength, as this information is pivotal in controlling the plasma. Some other plasma parameters (Debye length, number of particles in Debye sphere, and plasma frequency) were considered as well.

Materials and methods

In this experiment, tooth samples are randomly chosen from the Al-Kut Specialized Dental Center in Wasit Governorate, Iraq. All samples were obtained after informed consent of the patients and doctor. These samples are washed in distilled water and stored in numbered sealed pots. Figure 1 depicts a typical LIBS analysis system used to produced plasma, it mainly consists of laser source, collection optics, analysis device, and material target. The information of a laboratory-made arrangement are introduced in Table 1.

Fig. 1
figure 1

Schematic diagram of LIBS setup

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Table 1 Setup details for samples analysis
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Results and discussion

Plasma emission and identification of elements

Emission spectra of laser-produced tooth plasma captured at spectral window of 250–650 nm are shown in Fig. 2 for two different wavelengths (1064 and 532 nm). Beside continuum background, predominated ionic and atomic emission lines have been assigned. The significant major, minor, and trace element observed in the samples were Ca, P, Mg, Si, Sr, Ti, and Cr.

Fig. 2
figure 2

Predominated emission lines are produced by two different wavelengths (1064 and 532 nm)

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According to the NIST database [14], a number of characteristic emission lines for Ca were found in the plasma spectrum. Among of many detected lines, Ca II 396.84 nm and Ca II 422.67 nm will be utilized to both compute plasma parameters (Ne and Te) and to study the plasma dependence on laser irradiance. Figure 3 displays the variation in the intensity of the calcium lines with laser irradiance. As a result of increasing laser ablation rate, the plasma's ability to absorb laser light increases with increased laser irradiation leading to an increase in spectral line intensity. However, one can see an increase in the line emission intensity for both spectral lines Ca II 396.84 and Ca II 422.67 nm with laser wavelength 1064 nm compared to 532 nm at fixed laser energy. Same trend has been concluded by other researchers [15,16,17]. This was explained by the distinctions between optical and thermal characteristics of calcium element in visible (Vis.) and infrared (IR.) laser spectral regions.

Fig. 3
figure 3

Emission peak intensity for Ca II 396.84 nm (circles) and Ca II 422.67 nm (triangle) at 1064 and 532 nm

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Variation of plasma temperature (Te)

Plasma temperature and electron number density are two essential parameters for realizing excitation and ionization activities during plasma production. One of the acceptable methods for determining the electron temperature in the local thermodynamic equilibrium is the Boltzmann plot [15, 18], expressed as follows:

$$\mathrm{ln}\left(\frac{{\lambda }_{ij}{I}_{ij}}{{g}_{i}{A}_{ij}}\right)=-\frac{{E}_{\mathrm{j}}}{{k}_{\mathrm{B}}{T}_{\mathrm{e}}}+\mathrm{ln}\frac{N(T)}{U(T)}$$
(1)

where \({\uplambda }_{ij} {I}_{ij}, {g}_{j}, {A}_{ij},\, \mathrm{and}\, {E}_{j}\) are the wavelength, line intensity, statistical weight, transition probability, and excited level energy. N(T) and U(T) are the plasma number density and the partition function.

A graph in Fig. 4 is plotted concerning excitation energy Ej (in eV) and ln (\({\uplambda }_{ij} {I}_{ij}{/g}_{j}{A}_{ij}\)), Te in kelvin is concluded from the slope (1/kBT) of the linear line. The excitation temperature was 10,549 K for 1064 nm and 10,179  K for 532 nm recorded at laser power density of 1.9 × 109 W/cm2.

Fig. 4
figure 4

Regular Boltzmann plot for Ca II emission lines at 1064 and 532 nm

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We show the variation of the electron temperature with the laser irradiances in Fig. 5, it was found that the Te values increased with increasing laser irradiation. The electron temperature at wavelength of 1064 nm was higher than that recognized at 532 nm due to the change in optical absorption at longer wavelengths [19, 20].

Fig. 5
figure 5

Evaluation of the electron temperature at different laser irradiances

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Variation of electron number density

By using Saha–Boltzmann expression given by Eq. (2) [15], electron density Ne is established via the intensity ratio of two spectral lines of the same element (calcium) having different ionization stages

$${N}_{\mathrm{e}}=6.04*{10}^{24}{(T)}^{3/2}{\left(\frac{I\lambda }{gA}\right)}_{\mathrm{ion}}{\left(\frac{gA}{I\lambda }\right)}_{\mathrm{atom}}\times \mathrm{exp}\left[-\frac{({V}^{+}+{E}_{ion}-{E}_{\mathrm{atom}})}{{K}_{\mathrm{B}}T}\right]$$
(2)

where I is the integrated emission intensity of the ion or atom, Ne is the electron density (cm−3), gA is the product of the statistical weight and Einstein coefficient for spontaneous emission of the upper level (s-1), λ is the wavelength (nm), Eion is the excitation energy (upper level) of the ionic line (J), and Eatom is the excitation energy (upper level) of the atomic line (J).

Figure 6 displays the fluctuation in electron number densities as observed at both wavelengths at various Nd:YAG laser irradiances. There is a gradual increase in the values of Ne with the increasing of laser irradiance. Also, at the same pulse energy, the value of Ne formed at 532 nm is more than its corresponding value formed at 1064 nm. This was caused by increased multi-photon ionization and light matter coupling at shorter wavelengths [21].

Fig. 6
figure 6

Evaluation of Ne as a function of laser irradiance for wavelengths of 1064 (squares) and 532 nm (circles)

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Calculation of other plasma parameters

With the purpose of getting better understanding of plasma properties, other characteristic parameters such as Debye length (λD), number of particles in Debye sphere (ND), and plasma frequency (ωp) are obtained. The length of Debye is the distance at which an individual particle influences another charged particle carrying a reverse charge is inversely proportional to Ne and directly to square root of the electron temperature Te, according to [22].

$${\lambda }_{\mathrm{D}}={\left(\frac{{\varepsilon }_{0}{k}_{\mathrm{B}}{T}_{\mathrm{e}}}{{N}_{\mathrm{e}}{e}^{2}}\right)}^{0.5}$$
(3)

The variation of Debye length at various laser irradiation levels is displayed by Fig. 7. The calculated range of λD was 6.29–4.13 × 10–8 cm for 1064 nm and 4.6–3.26 × 10–8 cm for 532 nm. For both wavelengths, as more light being absorbed by the material, λD contracted as the laser energy increased. Since λD illustrates the shielding length, the self-focusing of laser beams will improve on condition that λD is less than the diameter of laser beam.

Fig. 7
figure 7

Variation of λD for 1064 (squares) and 532 nm (circles) wavelengths at different laser irradiances

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In addition, Debye number can be obtained from \({N}_{\mathrm{D}}=\frac{4\pi }{3}{\lambda }_{D}^{3}{N}_{\mathrm{e}}.\) Due to the direct relationship between ND and λD, their reaction to variation of laser irritation will be identical. Figure 8 shows the variation of ND at different laser irradiances, the calculated range of ND was 0.13–0.2 for 1064 nm and 0.09–0.14 for 532 nm.

Fig. 8
figure 8

Evaluation of Debye number for 1064 nm (squares) and 532 nm (circles) wavelengths at different laser irradiances

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Moreover, plasma frequency (\({\omega }_{\mathrm{p}}\)) was evaluated by [1, 23]:

$${\omega }_{\mathrm{p}}=8.98 \times {10}^{3} \times {{N}_{\mathrm{e}}}^{1/2} \mathrm{Hz}$$
(4)

According to Eq. (4), plasma frequencies are directly proportional to (Ne)0.5, and their results are reliable on electron density. Figure 9 shows plasma frequency (\({\omega }_{\mathrm{p}})\) at various laser irradiances. As higher laser irradiance produces relatively more plasma species, the values of \({\omega }_{\mathrm{p}}\) improved with the increase in irradiance. Furthermore, in laser–plasma interaction, light may be transmitted, scattered, and /or absorbed. As soon as the frequency of the incident laser (\({\omega }_{\mathrm{L}})\) is higher than \({\omega }_{\mathrm{p}}\), laser light could be reflected [22, 24], the maximum frequency of plasma calculated using Eq. (4) at laser irradiance of 9.9 × 109 w/cm2 were 2.33, 2.79 × 1012 Hz for 1064 nm and 532 nm. Taking into account, the frequencies for Nd:YAG laser are equal to 2.8, 5.64 × 1014 Hz for 1064 nm and 532 nm, these two values are larger than the values of\({ \omega }_{p}\). Consequently, the losing energy by reflection is negligible.

Fig. 9
figure 9

Evaluation of plasma frequency for both 1064 (squares) and 532 nm (circles) at different laser irradiances

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Conclusion

The significant properties of plasma produced at the tooth surface were examined. Pulsed Nd:YAG laser with irradiance ranging from 1.9 to 9.9 × 109 W/cm2. Optical emission analysis has been used to deduce several characteristic emission lines of Ca. The effect of laser irradiance and wavelength was evaluated, it was observed that teeth plasma parameters (electron temperature and number density) are remarkably enhanced at all laser irradiances, their maximum values are attributed to developing maximum ablation rate, plasma temperatures are highest in the case of λ = 1064 nm. Furthermore, similar behavior of increasing plasma frequency, Debye length, and number as a function of laser irradiance was also described.