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Copper plasma generated at different filament-copper interaction points was characterized by spectroscopic, acoustic, and imaging measurements. The longitudinal variation of the filament intensity was qualitatively determined by acoustic measurements in air. The maximum plasma temperature was measured at the location of peak filament intensity, corresponding to the maximum mean electron energy during plasma formation. The highest copper plasma density was measured past the location of the maximum electron density in the filament, where spectral broadening of the filament leads to enhanced ionization. Acoustic measurements in air and on solid target were correlated to reconstructed plasma properties. Optimal line emission is measured near the geometric focus of the lens used to produce the filament.
© 2016 Optical Society of America
1. Introduction
Optical spectroscopic techniques for material analysis that rely on the uses of plasma have been revolutionized by the increases in laser power. Laser-induced breakdown spectroscopy (LIBS), which has been developed shortly after the first demonstration of pulsed nanosecond lasers [1, 2] in the 1960s, has since evolved into a commercially available analytical tool [3]. Nanosecond Q-switched Nd:YAG lasers are the most commonly used lasers for LIBS. LIBS starts with the interaction of a focused high-intensity laser pulse with the surface of a sample material, whereby the intense electromagnetic field in the focal spot forms a micro-plasma on the sample. The detection and spectral analysis of emitted radiation from the excited atomic, ionic, or molecular species within the micro-plasma reveals the elemental composition of the plasma, from which the chemical constituents of the target material can be deduced. LIBS is an optical spectroscopic technique providing rapid chemical analysis without the need for sample preparation. These features, compounded with its relatively low cost and simple experimental setup, have pushed the application boundaries of LIBS from basic research to practical in-field applications in diversified areas [4, 5].
Since LIBS is an all-optical technique, it can in principle be used for remote sample analysis as long as the experimental conditions allow the delivery of the laser pulse to the target surface and the collection of the optical emission by a remote detector. In previous experiments, remote LIBS (R-LIBS) operation by focusing nanosecond pulses at a standoff distance of 8 m have been demonstrated [6].
Extending R-LIBS to even larger standoff distances poses practical challenges. The challenges stem from the implicit requirement imposed on LIBS, which is the delivery of laser pulses at high enough intensity, and thus focused to small enough size, such that they are capable of creating micro-plasmas. The smallest achievable focal spot size w0 is proportional to the f-number of the optical system used (f/# = f/D, where f is the focal length and D is the collimated beam diameter) due to diffraction. As a consequence, prohibitively large diameter optics are required to deliver the laser pulse to a small enough focal spot at large standoff. Delivered focal spot intensity at a distance is further diminished by absorption and wavefront distortion in atmospheric propagation.
In contrast to nanosecond lasers, femtosecond lasers can circumvent this limitation by taking advantage of the complex but favorable nonlinear dynamics of femtosecond laser propagation in air. An initially collimated femtosecond laser pulse self-focuses in air when its power exceeds the critical power Pcr = 3.72λ2/(8πn0n2), where λ is the laser wavelength and n0 and n2 are the linear and non-linear index of refraction, respectively. As the beam self-focuses, it can ionize air molecules, which in turn defocuses the beam. A balance between the self-focusing and plasma defocusing creates intense light filaments with typical intensities of order 1013 W/cm2, capable of propagating over long distances with beam diameters in the range 100–200 μm [7–9]. These unique features of the propagation of high-power femtosecond pulses make them attractive for remote surface ablation and analysis, commonly known as remote filament-induced breakdown spectroscopy (R-FIBS) [10, 11]. Filaments can enable collimated propagation of femtosecond laser pulses of the range of kilometers [8]. Such laser pulses can be produced by laser systems sufficiently small to be mounted on vehicles, with a continued trend of miniaturization, reliability improvements, and reduction of cost. Materials in different states have been analyzed for their composition using the R-FIBS technique. These include the remote detection of NaCl in aqueous solution using R-FIBS at a distance of 16 m [12] and probing of solid metals such as copper at a distance of 90 m, which was limited only by the space available for the experiment [13, 14].
Previous studies have been focused primarily on generating sufficiently long, stable filaments and using them to conduct proof-of-principle R-FIBS experiments. However, little work has been reported that systematically addresses the effects of filament properties on the R-FIBS signal [15]. Outstanding but important questions remain, such as what is the optimal filament propagation distance as well as filament spatial profile for R-FIBS analysis. Those questions are among the ones that must be addressed fully for the R-FIBS technique to be further improved and used to the practical extent comparable to conventional LIBS. In this work, we study the effect of filament propagation on the characteristics of filament-induced copper plasma. Previous measurements of nitrogen fluorescence in air have revealed the instability of multiple filaments in comparison to single filaments, which was attributed to the inefficient use of the background reservoir energy by the filament [16, 17]. There have also been numerous theoretical as well as experimental studies that addressed the effect of filament propagation in air on the filaments themselves. Initially transform-limited pulses are self-transformed into chirped filaments with highly broadened spectra, spanning around three octaves in frequency [18]. It is not clear a priori how this complex filament propagation dynamics affects the characteristics of optical emission from the plasma produced in interaction of the filament with the target at the terminal point of the filament propagation. To that end, in this work we study and quantify the effects of filament propagation distance on the induced copper plasma as well as its optical emission with spectroscopic, acoustic, and imaging diagnostics. We show that the filament intensity can be qualitatively related to the measured filament acoustic emission. We find that the maximum plasma temperature is obtained at the location of maximum filament free electron density and intensity, where the ponderomotive energy is the highest. However, the highest plasma density is present after the filament has propagated past the location of its maximum intensity. Spectroscopic measurements of representative line emission from a copper target reveal that the maximum intensity of line emission and the associated maximum signal-to-background ratio (SBR) is also obtained past the location of maximum filament intensity. These observations are explained by considering the ponderomotive energy and the known spectral effects that occur in filament propagation.
2. Experimental setup
A schematic diagram of the experimental setup is shown in Fig. 1. We used an ultrafast Ti:sapphire based chirped-pulse amplification laser system (Amplitude Technologies Trident) that can deliver ∼16 mJ energy with pulse durations as short as ∼38 fs at a repetition rate of 10 Hz. In our experiments the laser pulse duration was set to 53 fs and the laser energy was attenuated to 3.5 mJ using a half-wave plate and thin-film polarizers installed before the pulse compressor.
The collimated laser beam was 20 mm in diameter at full-width half-maximum and was loosely focused with a 25.4 mm diameter, f = 4 m plano-convex lens to create laboratory-scale filaments. The intensity profile of the beam was imaged on burn paper at multiple positions along the propagation distance of the filament to verify that single filamentation occurred for the pulse duration and energy used in this work.
A cylindrical copper metal sample (CO2 laser mirror), 25.4 mm in diameter and 6.35 mm thick, was used as the target. Controlled and remote sample translation was achieved by mounting the copper sample to a stainless steel sample holder that was also attached to a computer-operated three-axis translation stage. Sample translations in steps of 500 μm provided fresh spots on the target for ablation by the light filaments after every laser shot. Optical emission from the filament-induced plasma was integrated over 20 laser shots for every filament propagation distance used. The filament propagation distance, z (the distance between the lens and the copper sample), was varied by sliding the lens mounted on two aligned 1-meter long optical rails. The circular face of the cylindrical sample was aligned perpendicular to the filament propagation direction with a pinhole placed in front of the sample.
A 25.4 mm diameter, f = 55 mm lens imaged the light emitted from the filament-induced copper plasma onto the collection end of a fiber bundle. The angle between the optical axis of the lens and the normal to the sample surface was fixed to 45°. The 1-meter long fiber bundle is composed of 19 fibers, each with 200 μm diameter and numerical aperture of 0.22. The collection end of the fiber was arranged in a close-pack round configuration for optimal light collection from the sample. The other end of the fiber, which is arranged in a linear configuration (∼4.2 mm in length), was coupled to the entrance slit of a Czerny-Turner spectrometer. The spectrometer (f = 550 mm, Horiba Jobin Yvon iHR550) uses a 1800 mm−1 grating at a blaze wavelength of 400 nm and is coupled to an intensified charge-coupled device (ICCD) camera (Andor iStar 334T).
Acoustics measurements of sound/ultrasound generated near/in the ablated copper target as well as sound emanating from air as the plasma propagates freely, were also conducted to better understand the dependence of plasma characteristics as well as its emission on the location along the filament where it impinges on the target. By removing the copper target from the beam path, the length of the propagating filament was obtained by detecting the acoustic shock wave produced as the filament propagates in air. In [19], Yu et al. provide a detailed description on the use of acoustic diagnostics for filament length measurement can be found. In our setup, a sensitive microphone (PCB Piezotronics 378A13), installed inside a shielding tube together with its preamplifier, was employed to detect filament-induced acoustic signal. The microphone was staged on a ruled optical rail that enabled the measurement of filaments as long as 2.5 m. The lock-in rail carrier ensured the distance of the microphone from filament axis was constant during microphone translation. The shielding tube, a cylinder 12.7 mm in diameter and 89 mm long, was placed at a distance of 1 cm from the filament propagation axis, restricting the directly measured filament length to 15.6 mm. Acoustic signal as a function of propagation distance of the filament was then obtained by sliding the microphone on the rail in steps of 2 cm. The acoustic signal from the microphone was interfaced to an amplifier (Stanford Research Systems SRS560).
After measuring the filament length, the copper target was placed back in the path of the propagating filament. The microphone used to measure filament length was then moved closer to the ablating target at a distance of 5 cm and at an angle of 45° with respect to normal to the target surface. The amplitude of acoustic signal generated as the laser ablates a solid target has been shown to be proportional to the amount of ablated mass, which in turn is proportional to the fluence of the ablating laser pulse [20–22]. We extend the use of the acoustic diagnostic technique to measure the amount of mass ablated in filament-target interaction. To detect the ultrasound propagating into the ablating target, a transducer was attached to the back face of the copper sample. In [23], Davies et al. has discussed the mechanism of ultrasound production by high-power laser pulses incident on solids and its properties. Briefly, an impulsive force due to the sample ablation as well as the force exerted on the sample due to the expanding plasma are transmitted into the sample, inducing the vibration and generating ultrasound, which is detected by the transducer attached to the back face of the copper sample. Hence, the acoustic signal detected by the transducer captures both the effect of filament plasma expansion and the target material ablation. In contrast, the acoustic signal detected by the microphone in air at 5 cm from the sample represents the amplitude of the shock wave generated when air molecules are heated by energy exchange with the high temperature plasma.
Spatially integrated spectra of the optical emission from the filament-induced plasma were measured with the spectrometer equipped with a gated ICCD detector. The spatial profile of the time integrated optical emission from the plasma was obtained by another, non-gated CCD detector. One quantity of interest is the total ablated mass, which is expected to be proportional to the amount of absorbed filament energy. However, time-delayed and gated spectroscopic measurements of a dynamically evolving plasma cannot be used to directly measure the amount of ablated mass. To make the measurement of the ablated mass, a non-gated CCD is used to integrate optical emission from the plasma over a long time (1 ms).
3. Experimental results and discussion
3.1. Acoustic measurement of filament length
The peak-to-peak voltage of the acoustic signal that is produced by the propagating filament as a function of position along the filament axis with respect to the geometrical focus of the lens is shown in Fig. 2. The filament was generated with a laser energy of 3.5 mJ. It has been shown that the amplitude of the acoustic signal is related to the free electron density in the filament through the ionization of air molecules (oxygen and nitrogen) as the filament propagates in air [19, 24–26]. The ionization regime can be gauged using the Keldysh parameter , where IP is the ionization energy of air and Up[eV] = 9.34 × 10−20(λ [nm])2 × I[W/cm2] is the ponderomotive energy [27]. Here, λ, and I are the wavelength and intensity of the filament, respectively. The multiphoton ionization regime is characterized by γ >> 1, while the strong field tunneling regime is dominant for γ < 1. With the effective ionization energy of air molecules ∼12.0 eV and the expected peak filament intensity of ∼ 1013 W/cm2, the value of γ varies from 3 to 6 over a typical 400–800 nm variation in the filament spectrum [28], corresponding to the multiphoton ionization regime. The laser pulse intensity is related to the ionization in the filament, and the electron density can be inferred from the measured acoustic signal. The measured acoustic signal can be used to qualitatively establish the filament intensity along the propagation distance, as previously reported in [14].
Fig. 2 Peak-to-peak acoustic signal averaged over 100 laser shots as a function of microphone distance from the geometrical focus of the lens (f = 4 m) for 53 fs laser pulses at an energy of 3.5 mJ. The region bounded by the vertical dashed lines indicates the locations at which filament-induced line emission from the copper target was observed.
3.2. Position-dependent line emission and its signal-to-background ratio
The dependence of FIBS emission on the filament propagation distance was obtained by varying the distance along the filament axis at which the filament is incident on the copper target. The spectra were measured with an ICCD time gating window of 1 μs and a delay of 200 ns following the arrival of the laser pulse on the target.
The interaction point was scanned in steps of 10 cm over the length of the filament by moving the f = 4 m lens perpendicular to the surface of the copper target. Representative FIBS spectra measured at several filament-copper interaction points are shown in Fig. 3. The distances given in the figure are measured from the geometrical focus of the lens. Figure 4(a) shows the intensity of Cu I 521.82 nm emission line as a function of filament propagation distance. We start detecting the Cu I 521.82 nm line at a propagation distance of −50 cm (referring to the location before the geometrical focus), where the acoustic signal is 24% of its maximum value. Recent experiments [29] measured an average threshold fluence of 0.55 J/cm2 for copper LIBS emission using an 800 nm, 35 fs transform limited pulse and up to 150 μJ energy per pulse. This corresponds to an average threshold intensity of 1.4 × 1013 W/cm2. Since the energy contained in a filament is a fraction of the total pulse energy (the beam includes both the filament and its associated reservoir) [30], the threshold intensity obtained in [29] can be used to analyze filament-induced emission. Since we started detecting Cu I 521.82 nm emission line at a distance of −50 cm, that interaction point can be considered the point at which the filament intensity reached the threshold intensity. Under this assumption, the filament intensity at that location is set to 1.4 × 1013 W/cm2, and is used as a calibration point to obtain the dependence of the filament intensity on position. The estimated maximum laser energy absorbed that leads to the maximum free electron density and intensity in the filament is located at a position 20 cm away from the geometrical focus of the lens.
As the filament intensity increases over its threshold value, the intensity of the Cu I 521.82 nm emission line increases slowly at first, but then rapidly as the filament propagates farther to the location of maximum intensity. The observed threshold-like behavior of the dependence of emission intensity on propagation distance is consistent with a recent study that observed the nonlinearity of the LIBS signal in the vicinity of the ablation fluence threshold [31]. Near the threshold, only a small region of the filament contributes to the optical emission. In contrast, once the threshold is exceeded, the entire diameter of the filament contributes to optical emission. Although the amount of the free electron density in the filament decreases as it propagates farther from the location of maximum free electron density towards the geometrical focus of the lens, a plateau-like Cu I 521.82 nm emission region is observed. At first this appears inconsistent with previous measurements that showed linear dependence of the intensity of line emission from laser-induced plasma on the intensity of the laser pulse. However, the temporal and spectral characteristics of the filament evolve dynamically as it propagates [28, 32]. At the location of maximum free electron density in the filament, the density of ionized electrons in air is the highest [33]. The generated high density plasma self-steepens the propagating filament, which results in blue-shifted asymmetric spectral broadening [34–36]. Recent work has reported that ablation by fs pulses of longer wavelength (2.05 μm) result in a plasma exhibiting a lower density and temperature compared to the same laser fluence at shorter wavelengths (800 nm), which leads to a reduction in the measured LIBS signal [37]. The reduction in the absorbed energy in the filament is compensated by the overall reduction in the required number of photons needed to ionize air, resulting in a plateau-like emission feature. This is also corroborated with the results shown in Fig. 4(b), where the highest plasma density is obtained near the end of the filament.
Fig. 4 (a) Normalized peak spectral intensity (filled circle) and SBR (filled square) of Cu I 521.82 nm emission line. (b) Propagation distance dependent temperature (filled circle) and density (filled square). For the −10 cm position, the density was calculated using the 521.82 nm emission line, due to omission of the 510.55 nm emission in the measurement at this filament propagation distance. (c) Acoustic signal detected with a microphone placed 5 cm away from the copper target (filled circle) and acoustic vibration signal detected with a transducer attached to the back face of the copper target (filled square). The lines are to guide the eye.
Central to the interpretation of FIBS experiments and enhancing the detection performance in FIBS is the understanding and quantification of the background, i.e. the optical emission from the plasma coincident with characteristic, discrete (bound-bound) atomic or ionic line emission. The continuum optical emission due to free-bound recombination, free-free bremsstrahlung in the sample plasma, and the filament itself are the expected backgrounds several μs after the ablation takes place, and they are partially overlapped with the discrete signal spectrum. Therefore, the detection of discrete optical emission from a sample is ultimately limited by the intensity of the background. The background due to the filament itself can be significantly reduced by temporal gating of the light collection. However, the filament undergoes complex spatiotemporal evolution that dynamically affects its spectral and temporal characteristics. This spatiotemporal dynamics in turn affects the spectral and temporal characteristics of optical emission from filament-induced plasmas. Consequently, the SBR of the optical emission from filament-induced plasmas is expected to vary throughout the length of the filament, and a detailed study of the effects of filament propagation on the SBR of the filament-induced optical emission is required to determine the optimal filament-target interaction point.
The dependence of SBR of the Cu I 521.82 nm emission line on filament propagation distance is shown in Fig. 4(a). SBR was calculated with SBR = Iline/IB, where Iline is spectral amplitude of the Cu I 521.82 nm emission line, and IB is the constant background intensity obtained by a linear fit near the foot of the discrete emission line. The most striking feature in Fig. 4(a) is the observation of FIBS emission with high SBR near the threshold intensity, where relatively low intensity Cu I 521.82 nm line is observed. The persistence of SBR into the threshold regime can be understood in terms of the propagation distance dependent temperature and density variations of the plasma shown in Fig. 4(b). In comparison to the falling edge of filament intensity (propagation distance −20 cm to 10 cm), lower density plasma is obtained during the rising edge of the filament intensity (propagation distance of −50 cm to −20 cm). The lower plasma density results in a lower bremsstrahlung emission and the persistence of SBR, as can be seen from Fig. 4(a).
3.3. Propagation distance-resolved temperature and density measurements of the copper plasma
The observed Cu I lines at 427.51, 458.69, 465.11, 510.55, 515.32, 521.82 were used to obtain the filament-induced plasma temperature. The Boltzmann plot method was used to calculate the plasma temperature over propagation distances that produced lines with significant SBR values. If the points in Boltzmann plot can be fit by a straight line, the linearity is indicative of Boltzmann distribution of each excited levels, which is an indicator that local thermodynamic equilibrium (LTE) has been established, and the plasma temperature can be extracted from the Boltzmann plot. Figure 4(b) shows the temperature variation of the copper plasma over the propagation distance of the filament. The calculated maximum plasma temperature occurs at a distance of −20 cm and is consistent with the position at which the measured free electron density in the filament is measured, as can be seen from Fig. 2. The calculated temperature varies by about 20% over the filament propagation distance. This can be understood in terms of the measured 83% variation in acoustic signal, which translates to ≈20% variation in free electron density and rate of energy absorption in the filament, as shown in Fig. 2. Overall, the dependence of plasma temperature is dictated by the longitudinal absorbed energy profile of the filament. This can be understood from energy absorption considerations, where the temperature of the plasma is proportional to the amount of energy absorbed by the sample.
Calculating the temperature using the Boltzmann plot method implicitly assumes the existence of quasi-LTE among the bound states of radiation that resulted in the emission of the Cu I lines included in the analysis [38]. This assumption is valid as long as the minimum plasma density satisfies the McWhirter criterion for plasma density,
where the electron temperature Te is in the units of K and the energy energy of the transition ΔE is in the units of eV. With the calculated maximum plasma temperature of 0.93 eV and the energy separation of the considered states of ΔE, a plasma with density ≥ 2.2 × 1015 e−/cm−3 would satisfy the minimum set criterion. As can been seen from Fig. 4(b), the McWhirter criterion is met throughout the propagation distance.The Stark broadening of the Cu I 510.55 nm line, together with interpolation of the temperature dependent electron impact width parameters (0.0149 Å at 5,000 K and 0.0193 Å at 10,000 K) obtained from [39], was used to calculate the propagation distance dependent plasma density. Figure 4(b) shows the dependence of the calculated plasma density on the filament propagation distance. The maximum plasma density obtained near the end of the filament propagation is ne = 6.7×1017 cm−3. The most notable feature in Fig. 4(b) is the abrupt increase of the plasma density at the location of maximum free electron density in the filament (propagation distance of −20 cm), whereas the highest density is obtained for a propagation distance of 10 cm. The increased plasma density for longer propagation distances of the filament could be attributed to the spectral broadening of the filament as it propagates. Due to the nonlinear dependence of photo-ionization on the photon energy, the spectrally broadened filament ionizes the sample more effectively, resulting in higher plasma density as the filament propagates.
The variation of the acoustic signal detected by the microphone placed near the ablating copper target is different from that detected by the transducer attached to back face of the target, as can be seen from Fig. 4(b). The variation of the acoustic signal detected by the transducer on propagation distance shows general qualitative similarity with the variation of plasma density, as can be seen upon comparing Figs. 4(b) and 4(c). This is expected, as the ultrasound generated in the target is composed of a higher amplitude ultrasound wave resulting from the recoil of the target during material ablation, which is followed by a lower amplitude wave due to the pressure exerted by the expanding plasma. The variation of the propagation distance of the signal detected by the microphone placed in air also shows similarity with the variation of the plasma temperature. The amplitude of the generated shock wave due to heating and expansion of air molecules by the heated plasma depends on the total number and temperature of the plasma electrons. The convoluted origin the acoustic signal explains the disparity between the temperature and acoustic measurements.
To gain additional insight into the propagation dependent plasma properties, two dimensional cross-sectional images of the light emitted as the three dimensional plasma expands from the copper sample into air were obtained using a CCD camera (Mightex). The images allow the observation of the radial distribution of the plasma emission. Figure 5(a)–5(h) shows the cross sectional images of the filament-induced plasma emission at different filament-copper interaction distances. Depending on the position of the filament-copper interaction point along the filament axis, the plasma expands to different sizes, and the emitted light yield also varies. Consistent with the calculated highest plasma temperature occurring at the location of maximum free electron density in the filament, light yield with highest intensity is observed at that location. Since the images capture a broad spectral range of light emitted from the filament-induced plasma, the integrated detected emission is correlated with the variation of filament intensity on the propagation distance. The maximum light yield is observed at the location of maximum free electron density in the filament, as can be seen by comparing Fig. 5(i) with the acoustic measurement of the filament length shown in Fig. 2. At the location of geometrical focus of the lens, the intensity of the emission is lower. Although the total light yield is the largest at the location of the maximum free electron density in the filament, the maximum intensity in the emission of Cu I 521.82 nm line occurs at the geometrical focus of the lens, which is 20 cm away from the location of maximum free electron density in the filament, as can be seen from Fig. 4(a).
Fig. 5 CCD images of light emission as plasma expands for filament-copper interaction points of 50–20cm (a–h). The integrated light yield as function of filament-copper interaction distance is shown in (i). In the images, the propagation direction of the filament is bottom-up and the location of the target is indicated by a white dashed line in (a).
4. Conclusion
In summary, we generated laboratory-scale femtosecond filaments and used them to induce plasma on a copper sample. Spectroscopic, acoustic, and plasma emission imaging diagnostics were used to study filament-propagation distance dependent characteristics of the filament-induced copper plasma. We find that the highest temperature plasma is induced at the location of the maximum filament intensity and can be understood in terms of the the higher ponderomotive energy that produces plasma electrons with highest mean initial energy. However, the highest density plasma is generated near the end of the filament. This is attributed to the spectral broadening of the filament shown in Fig. 6, resulting in more efficient ionization. The filament spectrum broadened by ≈300% from the beginning of the filament to the end of the filament at −120 and 20 cm, respectively. Previous work by Hou et al. in [40] and Weidman et al. in [41], have shown that the optimization of the emission intensity can be attributed to an increase in the ablated mass that occurs near the end of the filament. It has also been shown that the acoustic signal from the expansion of the filament-induced plasma in air is qualitatively correlated with the temperature of the plasma, while the acoustic wave propagating through the ablated solid target is correlated with the density of the plasma. The acoustic signal detected as the filament propagates freely in air is correlated with the integrated light yield from filament-induced copper plasma. Acoustic measurements in air combined with the dependence of multiphoton ionization in air have been used previously to obtain the variation of the amount of absorbed energy and plasma density in filaments along their axis [14, 19, 24, 25, 42]. In this work, we have shown that the combined use of acoustic and spectroscopic measurements could be used to qualitatively relate the intensity profile of a femtosecond filament to the measured acoustic emission.
Spectral intensity of the Cu I 521.82 nm observed along the filament axis is correlated with the temperature and density of the plasma at the corresponding filament-target interaction position. On the basis of those measurements, we find that there is an optimal location where the line emission intensity and signal to background ratio of the Cu I 521.82 nm line are maximized. The optimal location coincides with the geometrical focus of the lens used to focus the femtosecond laser pulse and is past the location of maximum filament intensity. Even though the results are based on specific focusing and target conditions, the existence of an optimal location along the filament indicates that filament-induced plasma as well as its optical emission characteristics are significantly affected by the propagation-distance-dependent temporal and spectral evolution of the filament. While the conclusion made here is drawn based on the studied case of filament-copper interactions, where the filament is obtained under specific pulse and focusing characteristics, the study still provides insights that have a potential to be of general nature. A complete theoretical model that includes filament-assisted multiphoton ionization, plasma formation, and emission is necessary to fully characterize the properties of filament-induced plasma and its optical emission. The results presented here could serve to benchmark and guide such future modeling efforts. Further, additional work is necessary to correlate the measured acoustic emission of the filament to the filament intensity through correlated measurements of the filament intensity and acoustic emission. In [43], Labutin et al. identified that the future potential uses of FIBS will depend on continuing improvements of the understanding of propagation distance effects in filament-target interactions as well as the plasma generation and emission, which this work has partially addressed.
Acknowledgments
This work was funded in part by the Consortium for Verification Technology under Department of Energy National Nuclear Security Administration award number DE-NA0002534 and the U.S. Department of Homeland Security under Grant Award Number, 2012.05 DN-130-NF0001. We would also like to thank Kenneth Ledford of the Acoustics Program at the Pennsylvania State University for his assistance with the acoustic emission measurements.
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