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Abstract
Studies of high-power ultrashort laser pulse interaction with matter are not only of fundamental scientific interest, but are also highly relevant to applications in the domain of remote sensing. Here, we investigate the effect of laser wavelength on coupling of femtosecond laser filaments to solid targets. Three central wavelengths have been used to produce filaments: 0.4, 0.8, and 2.0 µm. We find that, unlike the case of conventional tight focusing, use of shorter wavelengths does not necessarily produce more efficient ablation. This is explained by increased multi-photon absorption arising in near-UV filamentation. Investigations of filament-induced plasma dynamics and its thermodynamic parameters provide the foundation for unveiling the interplay between wavelength-dependent filament ablation mechanisms. In this way, strategies to increase the sensitivity of material detection via this technique may be better understood, thereby improving the analytical performance in this class of applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Self-focusing of intense ultrafast laser pulses leading to optical filamentation continues to stimulate research interest since the discovery of this phenomenon about two decades ago [1]. The ability to extend the filament propagation length to distances as long as kilometers [2] has opened remarkable prospects for its use in remote sensing based on inducing fluorescence by broadband supercontinuum [3, 4] or by direct filament ablation [5], also referred to as remote laser induced-(R-LIBS) or filament-induced breakdown spectroscopy (FIBS). With steady advances in ultrafast laser technology, the interest in application of laser filamentation can be expected to increase.
The standard practice for extending filament propagation length is to increase the laser peak power to many multiples of critical power (Pcr) [6, 7], the minimum peak power which can cause self-focusing. When the longer laser wavelengths are used, the pulse propagates as a long, single filament at higher peak powers [8]. Previous work by Gruetzner et al. [9] suggests empirical wavelength-cubed scaling law for the power to support filamentation in the mid-IR regime. In contrast, Pcr for UV-based filaments is a small fraction of that for the mid-IR, resulting in the onset of self-focusing at lower powers [10, 11]. When any of these filaments is used to produce ablation, efficient filament-solid coupling is vital. Compared to traditional tight focusing of femtosecond or nanosecond pulses [12, 13], filament ablation is characterized by a lower mass removal rate. This directly impacts the intensity and dynamics of emission signals emitted from the plasma, therefore significantly affecting analytical capabilities. While filament ablation experiments at 0.8 µm have been performed extensively in the past [14–19], the characteristics of filament-induced ablation plasmas produced with near-UV and mid-IR (0.4- and 2.0-µm, respectively) laser radiation is lacking in the literature.
Therefore, the objective of this work is to determine the experimental conditions that favor the most efficient filament-solid coupling at various filament wavelengths, including near-UV, near-IR, and mid-IR. We present a comparative study of plasma characteristics obtained via filament ablation within those three spectral regimes, which helps to identify their prospects for application in remote sensing.
2. Experimental
The experiments were performed using the λ3 Ti:sapphire laser system at the University of Michigan, which produces up to 17 mJ pulses with ∼0.8 µm center wavelength at a repetition rate of 480 Hz and durations as short as 30 fs [20]. In this study the typical pulse duration was set to ∼50 fs, intensity contrast ratio set according to [21], and the repetition rate was chopped to 80 Hz. All experiments were performed in air. The experimental setup is shown in Fig. 1. Filaments were formed by focusing the 25 mm beam with an enhanced silver coated, 50 mm diameter, 1 m focal length spherical mirror. The copper target was placed at the geometrical focus of the mirror. A rotation stage was used for continuous sample movement during the measurements. Pulses at 0.4-µm wavelength were produced by frequency doubling the fundamental 0.8-µm pulses in a 100-µm-thick β-Ba(BO2)2 crystal. The residual 0.8-µm radiation was removed by means of high-pass dichroic mirror with <0.2% reflectivity for p-polarization at 0.8 µm. The pulse duration of the generated 0.4-µm pulses was calculated [22] to be 41 fs. The 2.0-µm, 43-fs pulses were produced in a non-degenerate optical parametric amplifier (OPA) pumped at 0.8-µm [23]. The Pcr value for 2.0-µm pulse self-focusing was empirically determined in two different ways: (1) by observing the onset of filament fluorescence emission, and (2) by observing a constant beam diameter over a distance of several Rayleigh ranges. Both of those methods yielded the same Pcr within 10%. By ensuring that all three beams propagate along the same optical path, the ablation spot location was kept the same for all three filament wavelengths. In this way, light from the plasma produced by filament ablation is collected from the same location. In the following text, we refer to ablation (copper) plasma as “plasma” and to filament-channel plasma as “filament”. Imaging of the plasma in air (1:1) was performed using an achromatic lens of 50-mm diameter and 75-mm focal length. An image was projected directly onto an intensified CCD camera (iStar 334, Andor). Images presented here were accumulated for 50 laser shots, with 5-ns gate width. For spectroscopic measurements, plasma light was collected with an f/2 collimator (CC52, Andor) and coupled into a 400-µm diameter optical fiber connected to an Echelle spectrograph (ME5000, Andor, slit size: 25×50 µm). The spectra were recorded by an ICCD cooled to −25°C. Gate delay and width were experimentally determined to optimize the atomic emission signal. In order to improve the signal-to-noise ratio, the spectra were accumulated for 150 laser shots. Spectral line intensity is approximated by integrating the area underneath the Voigt spectral profile [24]. The spectroscopic detection system was calibrated with a Hg-Ar lamp (Pen Light, Oriel) and a calibrated radiometric source (DH-2000, Ocean Optics). All spectra were corrected to the transmission function of the detection system.
Fig. 1 Schematic of the setup: OPA - optical parametric amplification system; M - mirror; SM - spherical mirror; DM - dichroic mirror; L - achromatic lens; BBO - β-Ba(BO2)2 crystal; ICCD - intensified CCD; S - spectrograph; C - light collector/collimator.
3. Results and discussion
3.1. Plasma dynamics and morphology
In order to compare the effects of different photon energies on plasma formation and dynamics, we chose values of several Pcr for each wavelength. The relationship between Pcr and laser wavelength (λ) is quadratic [25]:
where n0 is the linear and n2(λ) is the wavelength-dependent nonlinear refractive index. It is worth noting that the Eq. (1) is derived for a cw beam with a perfect Gaussian transverse intensity profile. It should be therefore treated as approximate, since the dispersion of air plays an important role in the arrest of the self-focusing collapse in the case of ultrashort pulses [26]. By restricting the peak power to several Pcr, we avoid introducing stochastic effects of multiple filamentation on plasma formation and morphology in the 0.8-µm, and especially the 0.4-µm case. The nonlinear refractive index varies about 25% between 0.4-µm and 0.8-µm wavelengths, as highlighted by Daigle et al. [30] and Geints et al. [27]. Specifically, it is about 4–5×10−19 cm2 W−1 at 0.4 µm and 3×10−19 cm2 W−1 at 0.8 µm. The nonlinear refractive index reported at 248 nm is 8 × 10−19 cm2 W−1 [28]. The nonlinear refractive index at 2.0 µm is not expected to vary significantly from the values at 0.8 µm, which can be typically found in the literature. The work of Gruetzner et al. [9] shows no change in the nonlinear index between 0.8 µm and 1.55 µm. Thus, the nonlinear refractive index values is expected to vary significantly when moving towards UV compared to the mid-IR range. The effects of various mechanisms that lead to resulting intensity at the geometrical focus for each wavelengths are beyond the scope of this work and deserve special attention in the future studies. Figure 2 shows plasma images taken at different filament wavelengths, peak powers, and delay times (0.6, 3.6, and 6.6 µs). Figure 3 shows the time-dependent axial and radial expansion of the copper plasma. The 0.4- and 0.8-µm plasmas expand more quickly in the axial direction, whereas the 2.0-µm plasma exhibits a high expansion rate in the radial direction. Thus, plasma produced with 2.0-µm filament seems more hemispherical in the early stage, whereas the 0.4 and 0.8-µm plasmas are elongated. The expansion shape and plasma size may reflect the complex interplay between temperature-dependent reflective properties of Cu and filament characteristics. However, we note that the size of the plasma seems to be well correlated with the Pcr, despite the fact that the energy of 2.0-µm pulse is about 3 times higher, and in the case 0.4-µm pulse an order of magnitude smaller than the energy of 0.8-µm pulse.Fig. 2 Normalized plasma emission images produced by 0.4, 0.8, and 2.0 µm filaments at 2 Pcr and 4 Pcr recorded with 5 ns gate width at three different delays (0.6, 3.6, and 6.6 µs) after the incidence of the laser pulse.
The characteristic elongated shape of the plasma bulk is most likely the consequence of preferential ionization path left in the wake of the filament column. In other words, remnants of the filament that continue to interact with the target on the ns-timescale after the incidence of the laser pulse have an important role in the copper plasma dynamics. We estimate this interaction time to be on the order of several tens of nanoseconds by observing the fluorescence decay of the 0.8-µm filament (at 5 mJ pulse energy), as shown in Fig. 4(a).
Fig. 4 (a) Time dependence of 0.8 µm filament fluorescence in the 400–750 nm range. Inset shows typical filament image recorded using ICCD; (b) Spatially integrated emission intensity from the plasma produced at three different filament wavelengths at 200-ns delay and 5-ns gate width.
Figure 4(b) shows the spatially integrated emission intensity of the plasma for all three filament wavelengths. The 0.4-µm and 0.8-µm plasmas interestingly show a similar rising trend of intensity, whereas the 2.0-µm plasma exhibits notably lower total emission. This behavior may be attributed to the interplay between energy loss mechanisms in the filament and interaction between the filament and target. The intensity of the filament core reaching up to ~1014 W cm−2 [29] is sufficient to ionize air atoms/molecules. Work by Daigle et al. [30] shows the shorter 0.4-µm wavelength ionizes nitrogen molecules, producing a lower clamped intensity than in the case of 0.8-µm. Furthermore, wavelength- and temperature-dependent reflectivity of metals is known to vary significantly with the laser intensity [31, 32] in this range. In order to further investigate the observed behavior and quantitatively estimate the degree of filament-solid coupling, we performed spatially integrated diagnostics of the filament-produced plasma.
3.2. Plasma diagnostics
Our measurements take advantage of optical emission spectroscopy with the broadband spectral range of the Echelle spectrometer, which enables extracting both excitation temperature and electron density from a single acquired spectrum. Under assumption of local thermodynamic equilibrium (LTE), the population of the linked states follows a Boltzmann distribution, which can be used as a first approximation to determine the excitation temperature and the electron density [33]. Due to limitations in maximum available energy output of OPA and frequency doubling, we perform comparison for all three wavelengths at 2 mJ laser energy, while 0.4-, and 0.8-µm cases were additionally compared at 4 mJ. The filament-induced spectra obtained at all three wavelengths and 2 mJ pulse energy are shown in Fig. 5. All spectra were recorded at 5 ns delay and 500 ns gate width. We note the absence of continuous background emission in all spectra recorded in this work. No significant difference in signal intensity is observed between 0.4- and 0.8-µm ablation, whereas at least threefold relative reduction in intensity of spectral lines originating from the highest-lying levels (4s 4p3P0 − 4s3D5s) compared to lower lying (3d104p − 3d104d) is observed in the 2.0-µm case. In optically thin plasmas the relative intensities (Iul) of the lines emitted from a given excitation state can be used to calculate the excitation temperature (Texc), if the transition probabilities are known (Aul), by the relation:
where Eu and gu are the energy and statistical weight of level u, respectively, U(T) is the atomic species partition function dependent on electron temperature, N is the total density of emitting atoms, λul is the wavelength for the given transition, and k is the Boltzmann constant. Plotting ln(Iulλul/Aulgu) versus Eu provides a straight line with a slope −1/kTexc. Thus, the temperature can be obtained without the need for atomic density or the atomic species partition function. Our temperature estimation relied on Boltzmann plots constructed on the basis of Cu I lines listed in Table 1. Atomic parameters were taken from [35]. The selection of lines ensured upper level energy span of about 4.2 eV.Fig. 5 Filament-induced copper spectra obtained at (a) 0.4 µm, (b) 0.8 µm, and (c) 2.0 µm at 2 mJ pulse energy.
Table 1. Spectral lines used to estimate excitation temperature. Calculation parameters [35]: λul–spectral line wavelength, Aul–transition probability, gu–statistical weight of upper level. El and Eu are the lower and upper level energy, respectively.
Contributions of spectral line broadening mechanisms to the spectral line profiles were considered. Natural, van der Waals and resonance broadening can be safely neglected. Stark broadening is the major broadening contributor in the laser-produced plasmas, being predominantly an effect of electron micro-fields causing level perturbations [34]. Thus, this mechanism provides a link between electron density with the Stark half-width of the atomic spectral line given by:
where a is the electron-impact width parameter, A is the ion-impact parameter, Ne is the electron density, and ND is the number of particles in Debye sphere. By neglecting the contribution of ionic collisions (symmetric line profile), Eq. (3) reduces to the first term, providing reliable determination of electron density in the range of (1014 − 1018) cm−3. The electron density was estimated using 510.55, 515.32 and 521.8 nm Cu I spectral lines and corresponding electron-impact width parameters [36]. The final value of Ne is an average of the values obtained using all three lines. Doppler broadening is characteristic for high temperature plasmas and small mass of the emitters. We estimate Doppler half-width (, λ0 – center wavelength, M – Cu atomic mass) of about 4 pm under our experimental conditions. The Stark half-width was calculated by subtracting instrumental and Doppler contributions from the total half-width. The plasma may be assumed to be in quasi-LTE condition if it satisfies the McWhirter criterion. This is the necessary condition [37], which sets the lower bound on the electron density for LTE as , where ΔE is the largest gap between adjacent upper energy levels.The comparison of Ne and Texc values obtained at all three filament wavelengths is summarized in Table 2. We note the values of electron densities and excitation temperatures lie within experimental uncertainties of one another. Electron density and excitation temperature produced with 2.0-µm filament both appear to be somewhat lower, especially compared to 0.8-µm case. The fact that the emission produced by the 2.0-µm filament is apparently different from the 0.4- and 0.8-µm cases, as shown by Fig. 4(b) and 5, suggests that filament-target coupling efficiency for 2.0-µm is somewhat lower. Specifically, the lower intensities of the higher-lying level transitions (in the range of 400–470 nm in Fig. 5) for the 2.0-µm case indicate reduced excitation in comparison to 0.4- and 0.8-µm. Similarly, weaker 2.0-µm laser-solid coupling compared to the 0.8-µm case was previously reported in the tight focusing (no filament) configuration in [38, 39]. This can be explained by reduced multiphoton ionization efficiency at longer wavelengths, which applies for both tight and loose focusing of ultrashort pulses. However, this reasoning is not sufficient to explain the comparable emission intensity, electron density and excitation temperature obtained at 0.4- and 0.8-µm filament ablation. Therefore, we further investigate temporal evolution of the plasma thermodynamic parameters at 4 mJ pulse energy (Fig. 6). Spectra were measured with 250 ns gate width of the ICCD. Both excitation temperature and electron density of the 0.4-µm plasma appear to be somewhat lower than that of the 0.8-µm plasma. The temperatures in the first microsecond of the plasma lifetime dropped from about 0.9 to 0.6 eV. In the same time interval, the electron density decays by more than an order of magnitude, reaching the lower limit for the existence of LTE state. This signifies the earliest delay times (<500 ns) as more reliable for quantitative considerations. Nonetheless, the measurements at 4 mJ suggest that filament ablation at 0.4 µm is slightly less efficient than at 0.8 µm. This result differs from the conventional tight-focusing ablation, where greater ablation efficiency has been observed when operating at shorter wavelengths [40]. It therefore appears that the effect of laser wavelength on energy deposition and optical penetration depth into solids is different for filament ablation when compared to tight-focusing ablation. For both filament- and tight-focusing ablation, multiphoton and field ionization may contribute to initial (seed) electron generation during resonance absorption [42] by the target surface, followed by collisional ionization. Two ionization mechanisms are usually associated with generation of free electrons in filaments: multiphoton ionization and tunneling ionization. At intensities characteristic for filamentation (1013–1014 Wcm−2), multiphoton ionization is dominant for laser spectrum in the 0.4–0.8 µm range [41]. The molecular oxygen with ∼12 eV ionization potential effectively determines the onset of filamentation. We estimate the threshold intensity needed for filament formation at 0.4 and 0.8 µm using an expression [6]:
where Ncr(λ) is the critical plasma density, σK is the ionization cross section, τp is the laser pulse duration, Natm is the density of neutral molecules at atmospheric pressure, and K is the (integer) number of photons required for multiphoton ionization. At 0.4- and 0.8-µm laser wavelengths, we obtain the threshold intensity values of about 1×1013 and 1.5×1013 Wcm−2, respectively.Fig. 6 Temporal evolution of (a) excitation temperature, and (b) electron density of copper plasma at near-UV and near-IR laser wavelengths and 4 mJ pulse energy. (c) Energy transmission of 0.4- and 0.8-µm filaments.
Table 2. Filament-induced plasma parameters obtained at different wavelengths: λ–central wavelength of the pulse before filamentation, Texc–excitation temperature, Ne–electron density, –LTE limit.
Since tunneling ionization is wavelength independent, clamped intensity limited by multiphoton ionization of the filament core reaching the target surface is the dominant factor determining the efficacy of filament-induced plasma formation. Reduction in the intensity of 0.4-µm compared to 0.8-µm filament is mostly due to increased multiphoton absorption at the shorter wavelength. To estimate the contribution of multiphoton absorption to the energy delivered to the target through the filament, we performed measurements of the laser energy before and after filamentation comparing 0.4- and 0.8-µm, as shown in Fig. 6(c). The shorter wavelength is attenuated more, as expected according to multiphoton ionization rate scaling with IK [6]; this causes a lower clamped intensity. The lower transmission of 0.4-µm filaments with respect to 0.8-µm case agrees with the clamped intensities (1.5 and 5×1013 W cm−2 for 0.4- and 0.8-µm filaments, respectively) reported in [30].
4. Conclusion
In summary, we observed the effects of three different laser wavelengths on filament-induced plasma characteristics. The results of ablation experiments indicate that filament-induced plasma as well as its optical emission characteristics do not differ significantly at near-UV and near-IR laser wavelengths. As the beam propagates in the filamentation regime, it gets attenuated by multiphoton absorption, which is more pronounced at shorter wavelengths. Despite the considerable uncertainties, mid-IR filaments appear to produce colder and less dense plasmas compared to near-UV and near-IR case, similarly to the results of previous studies at 2.0 µm with tight focusing (no filament) geometry. Therefore, they can be considered as viable alternative to conventional 0.8-µm filament ablation if a requirement exists for the use of long, single filaments. In practical applications, the detection of weaker plasma luminosity produced by filament ablation compared to traditional tight focusing will require further improvements in light collection efficiency. On the other hand, the complete absence of continuous plasma emission (regardless of the choice of filament wavelength) due to bremsstrahlung and recombination radiation is advantageous for cold ablation associated with the ultrafast timescales as compared to traditional ns-LIBS. A numerical model that includes filament-intensity distribution, target absorption and plasma formation is necessary to develop a deep understanding of the filament ablation mechanisms. The results presented here are intended to provide benchmark for such modeling efforts. Further experimental work is necessary to correlate the spatially resolved plasma parameters with axial distribution of intensity along the filament.
Funding
Consortium for Verification Technology under U.S. Department of Energy National Nuclear Security Administration (DE-NA0002534); Air Force Office of Scientific Research (FA9550-16-1 and FA9550-0121).
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