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. 2024 Apr 3;78(6):579–590. doi: 10.1177/00037028241240782

Effect of Femtosecond Ultraviolet and Infrared Laser Wavelength on Plasma Characteristics of Metals, Ceramics and Glass Samples Using Femtosecond Laser-Induced Breakdown Spectroscopy

Gytis Zaremba 1, Domas Paipulas 1, Virgilijus Vaičaitis 1, Ona Balachninaite 1,
PMCID: PMC11977832  PMID: 38567880

Abstract

In this work, we present studies on the effect of laser wavelengths on the laser-induced plasma characterization using a femtosecond (fs) ytterbium-doped potassium-gadolinium tungstate (Yb:KGW) laser. Plasma plumes of copper, steel, ceramics, and glass samples were induced using a multiple shot of 200 fs laser pulses with 1030 nm and 343 nm wavelengths at fixed laser fluence ( 10.5J/cm2 ) and analyzed using the laser-induced breakdown spectroscopy (LIBS) technique. Time-resolved fs-LIBS measurements were performed on the same set of samples and under the same experimental conditions. For the calculation of plasma parameters, the set of spectral lines of Cu(I) (for copper sample), Fe(I) (for steel sample), and Ca(I), K(I) (for glass and ceramics samples) were observed. The plasma electron temperature and density were evaluated from the Boltzmann plots and Stark-broadening profiles of the plasma spectral lines, assuming the local thermodynamic equilibrium condition. Time-resolved plasma temperature and electron density for fs-LIBS using ultraviolet (UV) and infrared (IR) laser wavelengths were analyzed and no significant dependence on fs laser wavelength was observed for any of the samples. However, for all samples the signal-to-noise ratio (SNR) significantly increased using UV laser radiation: copper ( 100% ), steel ( 300% ), glass ( 400% ), and ceramics ( 40% ). Therefore, by using a fs UV laser wavelength for laser-induced breakdown spectroscopy experiments, for certain materials the SNR and at the same time the limit of detection can be significantly enhanced.

Keywords: Plasma emission, femtosecond laser-induced breakdown spectroscopy, fs-LIBS, femtosecond ultraviolet and infrared LIBS, optical emission spectroscopy, plasma plume, electron density, plasma temperature

Introduction

Laser-induced breakdown spectroscopy (LIBS) is a versatile tool widely used for the elemental analysis of various materials, both in situ and in the laboratory.1,2 The use of ultrashort femtosecond (fs) pulses for LIBS has many advantages compared to long pulses. One of them is the reduced heat-affected zone, which is proportional to the square root of the pulse duration.3,4 Other advantages of fs-LIBS are reduced optical continuum emission, generation of colder plasma, less susceptibility to sampling matrix and elemental fractional effects, non-gated detection, better spatial and depth resolution, lower ablation threshold, and better repeatability.2,5 Fs laser pulses are perfect for remote or stand-off detection because they can form filaments and are able to deliver high energies over long distances. They have been used in remote atmospheric sensing and pollution detection,6,7 analysis of chemical and biological agents, 8 cultural heritage monitoring, 9 metal analysis, 10 and the detection of explosives,11,12 etc.13,14

An important parameter of LIBS is the laser wavelength used for plasma generation on the sample surface. The dependence of laser-induced plasma parameters on wavelength has been studied before, but mainly using nanosecond laser pulses. Most of the studies presented below used nanosecond laser pulses.

Diaz et al. 15 found that the main parameters of LIBS (plasma temperature and electron density) were almost the same for both 1064 and 355 nm wavelengths of the neodymium-doped yttrium aluminum garnet (Nd:YAG) laser using 56 mJ pulse energy on gold- and silver-bearing minerals, but the repeatability of measurements increased by 50% with 355 nm wavelength. There were also other studies that have observed better repeatability with the shorter laser wavelengths.1618

Amoruso et al. 19 evaluated absorption mechanisms in aluminum laser-ablated plasmas, and found that, at the visible laser wavelength (532 nm) of the Nd:YAG laser, in the first stages of the laser–vapor interaction, ionization is mainly caused by an inverse bremsstrahlung process due to electron scattering by neutrals and subsequent collisional ionization, whereas in the ultraviolet (UV), photoionization of excited species plays the most important role. In both cases, the plasma acts as a shield for the laser radiation, thus absorbing a part of the laser pulse. 20 However, shorter pulses (on the order of picoseconds rather than nanoseconds) have been reported to be more effective in ablating the mass, probably because plasma shielding does not have such a strong effect at shorter pulses. 21

Qaisar and Pert 22 investigated the effect of laser wavelength on the ablation process by comparing UV KrF excimer and infrared Nd:YAG lasers. It was discovered that plasma screening is more effective for longer-wavelength lasers, whereas shorter-wavelength lasers are more beneficial for ablation. Other studies confirm these results.16,21,2325 Qaisar and Pert 22 also observed that a longer infrared (IR) wavelength produces a higher temperature but lower density plasma, as compared to shorter UV wavelength-induced plasma. However, Abdellatif and Imam 26 obtained different results, where the UV wavelength of an Nd:YAG laser produced both a higher temperature and higher electron density of the plasma on aluminum, as compared with the IR wavelength.

Kasem et al. 17 established that the use of the UV wavelength of the Nd:YAG laser with 22 mJ pulse energy results in more stable plasma, which gave more realistic elemental results of the archaeological bone plasma than longer IR wavelengths. They also observed that the use of UV laser radiation reduces fractionation effects, which can cause the ratios of the elements in a plume to differ from the stoichiometry of the sample. Other studies confirm these results.27,28 However, Huber et al. 29 concluded that the IR wavelength is better at finding heavy metal impurities in polymer materials.

Fornarini et al. 30 found that, when using Nd:YAG laser radiation in the UV range for LIBS on bronze samples, there is almost no dependence of the plasma parameters on fluence, which was varied from 50 to 250 J/cm 2 , contrary to IR excitation.

Aberkane et al. 31 investigated the influence of a 50 mJ Nd:YAG laser with wavelengths 1064, 532, and 355 nm at 7, 9, and 10 ns pulse durations, respectively, on the relationship between Te and surface hardness of Fe–V–C metallic alloys. They determined that employing an excitation laser in the IR range rather than in the UV range is more efficient for measuring surface hardness using LIBS.

Studies on the effects of an appropriate combination of laser wavelengths and pulse energies on the characterization of generated plasma on a pure copper sample using a single shot picosecond (170 ps) Nd:YAG laser were performed by Fikry et al. 32 It was found that the copper emission line intensities (SNR), plasma temperature, and density show a strong dependence on the laser wavelength and pulse energy. The electron temperature and electron density values gradually increase with the increase of the laser wavelength and pulse fluence. The researchers explained this tendency by the fact that using picosecond pulses enhances the plasma shielding effect, which is due to the inverse Bremsstrahlung being the dominant absorption mechanism, not photoionization. Therefore, most of the laser energy is absorbed by the free electrons of the target, and more energetic electrons are preserved, which causes an increase in the electron temperature and electron density with the increase of the picosecond laser wavelength and pulse energy.

A comparison of mid-infrared (2.05  μ m) and infrared (800 nm) wavelength fs ( 40 fs) pulses using a Ti:sapphire laser for LIBS on copper was carried out by Hartig et al. 5 A pulse energy of 200  μ J was used. They found that the signal-to-noise ratio (SNR) decreases by 40% with the use of a longer mid-IR laser wavelength, compared to IR. The overall line intensity was approximately seven times higher after 800 nm laser ablation. Plasma electron density and temperature are also decreased with the longer 2.05  μ m laser wavelength, and the authors attribute this decrease to the reduced multi-photon ionization efficiency at longer wavelengths, which then results in less effective laser–matter coupling, lower ablation, and plasma density.

The choice of wavelength for LIBS measurements is thought to be more important for longer pulses, closer to the regime of nanoseconds, but in the case of fs-LIBS, the pulse–matter interaction is different, the pulse duration is much shorter than the material heat transfer time, plasma forms after the pulse, eliminating the problem of plasma shielding. However, the dependence on fs UV and IR LIBS has not been extensively studied.

In this work, two different fs laser wavelengths of 1030 and 343 nm were used to determine the effect of wavelength on LIBS parameters. We found that using both IR and UV laser wavelengths results in plasma of roughly the same temperature, electron density, and intensity of spectral lines, but the SNR is significantly increased using UV laser wavelength for plasma generation.

Experimental Setup

The experimental scheme for our LIBS measurements is shown in Figure 1. In our experiment, we used the “Pharos” fs ytterbium-doped potassium-gadolinium tungstate (Yb:KGW) laser (Light Conversion Ltd.) with a pulse duration of 200 fs, average power up to 6 W at 1030 nm and pulse repetition rate of 6 kHz. The fundamental harmonic (1030 nm) was used for IR radiation. For the generation of UV radiation, the fundamental wavelength was first frequency doubled (515 nm), and then the sum frequency generated (343 nm) using nonlinear beta barium borate crystals. High reflectivity mirrors (for 343 nm) M4–M7 were used to filter out the first (1030 nm) and second (515 nm) harmonics, so that only the third harmonic (343 nm) remained. M1–M3 mirrors were used for the first harmonic and M2–M3 mirrors were used only during the IR laser wavelength experiment. The fluence on the sample using both UV and IR laser wavelengths was kept constant at 10.5±1.5J/cm2 . The spot size on the sample surface was 29±2μm with UV and 39±2μm with IR wavelengths. It was measured using a laser beam profile Newport LBP2 camera and Liu’s method (with steel sample used). 33 UV radiation was focused on the sample surface with a 200 mm focal length ultraviolet grade fused silica (UVFS) lens, and IR radiation was focused with 100 mm focal length UVFS lens. The corresponding energies of the fundamental and the third harmonics were chosen to keep the same laser fluences in both cases.

Figure 1.

Figure 1.

Experimental setup for time-resolved fs-LIBS measurements using 343 and 1030 nm wavelengths. M1–M3 are high-reflective mirrors for the first harmonic and M4–M7 are high-reflective mirrors for the third harmonic and high transmittance for the first and second harmonics (used to eliminate IR and visible laser radiation). P1 and P2 are half waveplate and dispersion compensation elements.

Our samples were copper, oxygen-free high thermal conductivity (99.95+% purity) (Goodfellow Cambridge Ltd.); stainless steel, AISI 301 (Goodfellow Cambridge Ltd.); glass (green optical glass filter; Izium); and a ceramics (Diwali light turquoise plate; Luminarc Ltd.). The elemental analysis of the glass and ceramics samples was performed with the wavelength dispersive X-ray fluorescence (WDXRF) method using the wavelength dispersive XRF spectrometer (Axios mAX) with a 4 kW STmax160 X-ray tube with an Rh anode. The composition is shown in Table I. A fresh spot on the sample surface was chosen for each accumulation after 3000 laser shots. The integration time for one spectrum was 0.5 s. Plasma emission was collected by a 400  μ m diameter fiber, which is coupled to a spectrograph (Andor Mechelle model ME5000) built with a gateable intensified charge-coupled device camera (iStar 334T from Andor Technology). Synchronization with the laser was performed using a digital delay generator (AtomTrace, AC-DDG-4 model). The gate time was fixed at 200 ns. All experiments were performed in ambient air (laboratory temperature in the range from 21 to 23 C and humidity <20%). For each experimental set, the spectrograph was wavelength calibrated using a mercury calibration source (HG-2, Ocean Optics), and the relative efficiency correction was performed using a continuous halogen-deuterium lamp (DH-2000-BAL, Ocean Optics). Profilometry was performed using a laser confocal microscope (Olympus OLS5100) with a resolution of 0.012  μ m using the 50 × objective, the wavelength of the laser used was 405 nm, laser light receiving element—photomultiplier.

Table 1.

Elemental composition of ceramics and glass samples, measured using the WDXRF method.

Ceramics sample Glass sample Ceramics sample Glass sample
Element Composition (%) Composition (%) Element Composition (%) Composition (%)
O 41.861 30.527 Cr 0.015 0.133
Na 23.489 14.445 Fe 0.021 0.009
Mg 0.105 0.000 Ni 0.003 0.000
Al 7.340 0.135 Cu 0.177 0.107
Si 22.799 20.068 Rb 0.003 0.000
P 0.077 0.002 Sr 0.057 0.007
S 0.006 0.006 Zr 0.045 0.000
Cl 0.015 0.168 Ba 1.812 0.114
K 0.833 2.446 Ce 0.079 0.000
Ca 1.211 4.592 As 0.000 0.193
Ti 0.054 0.000

Results and Discussion

All plasma spectra were captured with a time gating window of 200 ns with a 50 ns delay step following the first registered plasma spectrum, until plasma emission was not present in the measured spectra at 1.5μs . The plasma spectra of copper at different delay times are shown in Figure 2. The same spectral lines of Cu(I) are observed using both laser wavelengths, there are no spectral lines that would appear induced with only one of the wavelengths. At a 150 ns delay, the use of an IR laser wavelength results in a 20% higher continuum and similar intensity lines. After 250 ns, a UV wavelength induces more intense Cu(I) 510.5, 515.3, and 521.8 nm spectral lines, and approximately the same intensity 570 and 578.2 nm lines. At 450 ns delay, UV laser wavelength-induced plasma produces a more intense signal across the full spectrum and continues to do so until plasma extinction. Spectra of steel at different delays are also shown in Figure 2. A higher ( 400%) continuum is observed when using the IR laser wavelength. Plasma induced with both laser wavelengths displays similar intensity lines up to 750 ns, when the use of the UV laser wavelength results in more intense lines.

Figure 2.

Figure 2.

Comparison between the spectra of the plasma induced by the fs UV laser radiation (343 nm) and those induced by fs IR laser radiation (1030 nm) on copper (top) and steel (bottom) samples at different delay time.

Plasma spectra on ceramics and glass samples are shown in Figure 3. On the Y -axis, the relative differences in intensities can be observed. The use of UV laser wavelength resulted in 20 times higher amplitude of the signal as compared to IR laser wavelength-induced plasma. Most of the visible lines are calcium lines, which were used to calculate plasma temperature. With UV laser wavelength we were able to observe Ba(I) 611.08 nm and Ba(II) 614.17 nm spectral lines, which were not detectable using IR laser wavelength, as shown in Figure 3c. It is important to note that the amount of Ba presented in the glass sample was very low and did not exceed 0.2%. Cr spectral lines were also detected.

Figure 3.

Figure 3.

Comparison between the spectra of the plasma induced by the fs UV laser radiation (343 nm) and those induced by fs IR laser radiation (1030 nm) at 300 ns delay on a ceramics (a) and glass (b), and (c) shows a magnified spectrum region of interest on glass sample.

Plasma temperature and electron density were determined by analyzing Cu(I), Fe(I), Ca(I), and K(I) emission lines, their spectroscopic data were obtained from the National Institute of Standards and Technology (NIST) database 34 and is shown in Tables II to IV. The plasma temperature was calculated using the Boltzmann plot method, 35 under the assumption of local thermodynamic equilibrium (LTE), which was verified through the McWhirter criterion, presented in Eq. 1:

ne1.6×1012Te1/2(ΔE)3cm3 (1)

ΔE (eV) is the highest energy transition for which LTE exists and Te (K) is the plasma temperature. 36 For a neutral plasma with transition energies of 3.2 eV for Fe, 3.8 eV for Cu, 37 and 4.34 eV for K, 38 and temperature of 6000–10 000 K, a plasma with electron density 9×1015cm3 would satisfy this criterion for all samples.

Table II.

Spectroscopic parameters of Cu(I) emission lines used to calculate plasma parameters, taken from the NIST database. 33

Energies (eV) Transitions
Wavelength of Cu I (nm) E i E k Transition probability (g k A ki )(10 7 s 1 ) Upper level Lower level
510.55 1.389 3.817 0.8 3d 10 4p 3d 9 4s 2
515.32 3.786 6.191 24 3d 10 4d 3d 10 4p
521.82 3.817 6.192 45 3d 10 4d 3d 10 4p
570.02 1.642 3.817 0.01 3d 10 4p 3d 9 4s 2
578.21 1.642 3.786 0.33 3d 10 4p 3d 9 4s 2

Table IV.

Spectroscopic parameters of Ca(I) and K(I) emission lines used to calculate plasma parameters on glass and ceramics samples, taken from the NIST database. 33

Energies (eV) Transitions
Wavelength of Ca(I) (nm) E i E k Transition probability (g k A ki )(10 7 s 1 ) Upper level Lower level
527.03 2.526 4.878 25 3p 6 3d4p 3p 6 3d4s
558.88 2.526 4.744 34 3p 6 3d4p 3p 6 3d4s
610.27 1.879 3.910 2.9 3p 6 4s5s 3p 6 4s4p
612.22 1.886 3.910 8.6 3p 6 4s5s 3p 6 4s4p
616.22 1.899 3.910 14 3p 6 4s5s 3p 6 4s4p
Wavelength of K(I) (nm) E i E k Transition probability (g k A ki )(10 7 s 1 ) Upper level Lower level
769.90 0.000 1.610 7.5 3p 6 4p 3p 6 4s

Table III.

Spectroscopic parameters of Fe(I) emission lines used to calculate plasma parameters, taken from the NIST database.33

Energies (eV) Transitions
Wavelength of Fe I (nm) E i E k Transition probability (g k A ki )(10 7 s 1 ) Upper level Lower level
527.04 1.608 3.960 1.1 3d 6 ( 5 D)4s4p( 3 P ) 3d 7 ( 4 F)4s
537.15 0.958 3.266 0.53 3d 6 ( 5 D)4s4p( 3 P ) 3d 7 ( 4 F)4s
541.09 4.473 6.764 57 3d 7 ( 4 F)4d 3d 7 ( 4 F)4p
542.97 0.958 3.241 0.3 3d 6 ( 5 D)4s4p( 3 P ) 3d 7 ( 4 F)4s
544.69 0.990 3.266 0.27 3d 6 ( 5 D)4s4p( 3 P ) 3d 7 ( 4 F)4s
613.77 2.588 4.608 0.7 3d 7 ( 4 F) 4 p 3d 6 4s 2

Examples of Boltzmann plots obtained using 343 and 1030 nm laser wavelengths on copper, steel, glass, and ceramics samples are shown in Figure 4. The calculated excitation temperature values are the same, within error, for both used wavelengths on all samples investigated. Time-resolved plasma temperature is shown in Figure 5. The temperature on metal samples was in the range of 8000–11 000 K, on the glass sample it was in the vicinity of 4500–8000 K, and on ceramics it was 6000–11 000 K. The temperature uncertainty, according to El-Rabii et al., 39 was expressed as

ΔTT=kTEE|ΔXX| (2)

where

ΔXX=ΔII+ΔII+ΔAA+ΔAA (3)

where A is the Einstein coefficient, I is the intensity of the line, and EE is the difference in upper energy state ( 2.4 eV for Cu, 3.5 eV for Fe, and 1 eV when Ca lines are used on glass and ceramics samples). The uncertainty on copper sample was 11%, on steel sample 5%, on ceramic sample, and on glass sample 28%.

Figure 4.

Figure 4.

Boltzmann plots for the calculation of plasma temperature of Cu(I) (a, b), Fe(I) (c, d), Ca(I) on glass (e, f), and ceramics (g, h) samples.

Figure 5.

Figure 5.

Time-resolved plasma temperature for fs-LIBS on copper (a), steel (b), glass (c), and ceramics (d) samples for 343 nm (UV) and 1030 nm (IR) wavelengths.

Electron density was calculated from the Stark-broadened profile of Cu(I), Fe(I), and K(I) lines using Eq. 4:40

ne=Δλ1/2×10162ω (4)

where ω is the electron impact parameter, ne is the electron density and Δλ(1/2) is the full width half-maximum (FWHM) of the emission profile fitted to a Lorentzian profile. The values of ω were taken from Zmerli et al. 41 for Cu(I) 510.5 nm spectral line, Konjević and Wiese 42 for Fe(I) 541.09 nm line and Lesage 43 for K(I) 769.9 nm line. Electron density as a function of delay for 343 nm and 1030 nm laser wavelengths is shown in Figure 6. The spectra were acquired using a 200 ns gate window and delay in the range of 150–1100 ns for metals and 100–2300 ns for ceramics and glass, which are sufficient for the establishment of LTE and a significant reduction in the intensity of the bremsstrahlung emission. There is no obvious impact of the laser wavelength used on the electron density of the plasma. Electron density on copper was in the range of (11.6)×1018cm3 , on steel it was 8×10152×1016cm3 , on glass and ceramics it was within the range of 8×10151.9×1016cm3 . The uncertainty in the determination of the electron density was 30% on copper sample, 35% on steel sample, and 25% on ceramics and glass samples, taking into account the uncertainties of the FWHM measurement, the electron impact parameter, and the linewidth’s de-convolution to the instrumental width. The possibility of electron density error due to temperature uncertainty was also investigated, but it was found to be negligible.

Figure 6.

Figure 6.

Time-resolved electron density for fs-LIBS for UV and IR laser wavelengths using Cu(I) (a) 510.5 nm, Fe(I) (b) 541.1 nm, and K(I) (c, d) spectral lines on copper, steel, glass, and ceramics samples, respectively.

Signal-to-noise ratio (SNR) was also evaluated for both wavelengths used on all samples, i.e., Cu(I) 521.82 nm, Fe(I) 541.09 nm, and Ca(I) 612.22 nm on glass and ceramics samples, and is shown in Figure 7. The use of the UV laser wavelength resulted in significantly higher SNR on all samples: copper ( 100% higher), steel ( 300% higher), glass ( 400% higher), and ceramics ( 40% higher). Plasma lifetime was evaluated by fitting an exponential decay function to the temporal evolution of the integrated intensity of the plasma emission lines and determining the rate of decay τ . The τ coefficient was increased on all samples with the use of the UV laser wavelength. On the glass sample, it was 98±4ns using UV and 74±5)ns using IR laser wavelengths. On the ceramic sample, it was 107±5ns for UV and 88±7ns for IR laser wavelengths. On the copper sample, it was 61±2ns using UV and 37±0.4ns using IR laser wavelengths. On the steel sample, it was 68±4ns using UV and 58±5ns using IR laser wavelengths.

Figure 7.

Figure 7.

Signal-to-noise ratio (SNR) evolution as a function of delay for Cu(I) (a), Fe(I) (b), and Ca(I), (c, d) on copper, steel, glass, and ceramics samples, respectively.

The ablated volume on all samples was investigated using a 3D laser scanning microscope (Olympus OLS5100). On the copper sample, it was (110±6)×103μm3 following UV laser wavelength ablation and (14±1.5)×103μm3 using the IR laser wavelength. On the steel sample, it was (36±3.5)×103μm3 using the UV laser wavelength and (5±1.5)×103μm3 using the IR laser wavelength. On the ceramics sample, the ablation volume was (82±1)×103μm3 using the UV laser wavelength and (70±1.5)×103μm3 using the IR laser wavelength. On the glass sample, it was (76±1)×103μm3 using the UV wavelength and (13±1)×103μm3 using the IR laser wavelength. Different energies were used on different samples, but the fluence was kept constant between the wavelengths. On all samples, the UV wavelength ablated a larger volume of material by approximately eight times on copper and steel samples, by approximately six times on the glass sample and by 20% on the ceramics sample. In our opinion, the main mechanisms leading to the growth of SNR in the UV range are increased multi-photon ionization when plasma is induced by UV radiation, higher nonlinearity, and higher linear absorption of the material in the UV range. Moreover, the lower background in the case of UV laser-induced plasma was observed. Since the main background continuum in LIBS is caused by the Bremsstrahlung radiation, 35 and it is known that inverse Bremsstrahlung absorption is proportional to λ2 , 44 the continuum background is higher for IR laser-induced plasma.

Conclusion

In this work, we investigated the effect of a fs laser wavelength (1030 and 343 nm) at fixed energy fluence on the observed copper, steel, ceramics, and glass plasma parameters using the LIBS technique. The evaluated plasma temperature and electron density did not show any strong dependence on laser wavelength for all the samples and coincided with the limits of error. However, the SNR significantly increased using UV laser radiation for all samples: copper ( 100%), steel ( 300%), glass ( 400%), and ceramics ( 40%). The UV laser wavelength, unlike the IR laser wavelength, allows us to detect the spectral lines of the elements whose concentration in the sample is <0.2% (e.g., Ba and Cr lines in the glass sample). It was evaluated that fs UV laser radiation significantly increased the ablated material volume on all the samples, which, together with the increased multi-photon ionization efficiency and decreased continuum background radiation at shorter wavelengths for the fs pulses, led to an increase in SNR using UV laser radiation. The results obtained confirmed that using fs UV laser wavelength for laser-induced breakdown spectroscopy experiments can significantly enhance SNR and therefore the limit of detection for certain materials.

Footnotes

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding: The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work has received funding from the European Regional Development Fund (project 01.2.2-LMT-K-718-03-0029) under a grant agreement with the Research Council of Lithuania (LMTLT).

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