1. Introduction

Characterizing atmospheric aerosols is a burgeoning endeavor pursued for monitoring potentially harmful airborne particles from standoff distances. Laser-induced breakdown spectroscopy (LIBS) is a technique capable of rapid quantitative elemental and isotopic analysis of aerosols by measuring emission derived from a laser-produced plasma (LPP) containing analyte particles [1]. The robust capabilities of LIBS have been leveraged in the past to detect radiological materials in nuclear applications where it is desirable to avoid prolonged exposure to ionizing radiation [2–4]. With advancements in fission reactors and ongoing efforts to mitigate the effects of potential nuclear release events, an interest in applying LIBS in the detection and characterization of radiological aerosols has emerged for real-time monitoring and atmospheric plume tracking [5].

Traditionally, LIBS of aerosols uses ns lasers with pulse energies on the order of hundreds of mJ to maximize the size of the LPP as a result of plasma shielding [6], where the longer pulse duration and higher pulse energy significantly heat and expand the plasma. This enlarges the sampling volume of particle-laden air, which benefits signal-to-noise ratios and reduces particle size matrix effects [7–9]. Due to the success in utilizing fs pulses in techniques such as laser-ablation inductively-coupled mass spectrometry (LA-ICP-MS) [10] and double-pulse LIBS [11], the application of fs pulses for aerosol LIBS measurements has also attracted attention. It has been reported that the use of fs pulses reduces observed matrix effects associated with aerosol LIBS measurements and offers comparable performance to ns LIBS under dilute particle loads and short focusing conditions [12,13].

For fs pulses above the critical power threshold of $P_\text {cr} \approx 10$ GW in the air, nonlinear self-focusing begins to overcome diffraction resulting in self-guided filaments capable of propagating over extended distances – as long as several kilometers provided there is sufficient laser energy to sustain the filament [14–16]. Through mechanisms such as energy reservoir regeneration [17–19] and fog-clearing hysteresis [20–22], fs laser filaments have been demonstrated to be tolerant to instabilities from atmospheric turbulence and attenuation in aerosolized environments, making them promising for standoff characterization of airborne particles. While filaments can form spontaneously from collimated laser beams of sufficient peak power, they can also be produced within confined laboratory spaces using an external focusing lens by forcing early filamentation [23–25]. External focusing affects the filament length, diameter, and electron density, having implications on aerosol measurements which are highly dependent on both plasma geometry and collisional plasma-particle energy transfer by free electrons [1,26,27].

Aerosol measurements with filaments were performed using a 1-m lens under dilute particle loads; however, due to the relatively low rate of filament interaction with particles in the aerosol plume (i.e., sampling rate), it was necessary to implement single-shot conditional analysis to obtain spectra of sufficient quality [12,28]. The side collection optics observes only a small fraction of the total filament length that interacts with aerosols, and thus the low sampling probability was attributed to side collection. Several groups performed similar measurements up to 70 m using near-on-axis light collection at saturated aerosol concentrations but suffered from the light collection efficiency being limited by the inverse-squared law at longer distances [29–31]. It is evident from these previous efforts that the main challenges associated with filament-based aerosol sensing are the combined effect of relatively low emission yield and inefficient light collection at desirable standoff distances [12,32].

In this study, we investigate the emissions from bulk aerosols excited by externally focused filaments generated using external 400-mm and 750-mm focal length lenses. The effects of pulse energy and repetition rate on the emission profile from a Sr aerosol are characterized using time-resolved plasma images of the filament and compared to the $\text {N}_2$ fluorescence profile. The results indicate that aerosol emissions are highly sensitive to the pulse energy and repetition rate as significant restructuring is observed in the emission profile. Axial profiles of the filament emission, temperature, and electron density are constructed using on-axis and side-collected aerosol emission spectra, and changes to self-absorption behavior are examined using curves of growth under different aerosol concentrations to study self-absorption. On-axis collection of bulk aerosol emissions is shown to result in higher self-absorption as emissions are back-propagated through the excited plasma column, resulting in over-estimated plasma temperatures and densities using Boltzmann plots and Stark broadening extraction methods, respectively, when compared with filaments profiled using side collection.

2. Experimental methods

A simplified schematic of the experimental setup used for filament LIBS of aerosols is shown in Fig. 1. A chirped-pulse amplified Ti:sapphire laser (Coherent Astrella USP) was operated with a 35-fs pulse duration and 6.8-mJ maximum pulse energy at a repetition rate of 1 kHz and a central wavelength of 800 nm. For Gaussian-shaped pulses, the peak power was approximately 0.2 TW, which is well in excess of the critical power for self-focusing in the air estimated to be $P_\text {cr} \approx 10$ GW. As a result, multiple filament channels are expected to form given peak powers of $P \approx 20 P_\text {cr}$, the behavior of which may be affected by external focusing conditions [14,15]. Filaments were formed through external focusing using 400-mm (f/15.7) and 750-mm (f/29.5) focal-length BK7 lenses. The lenses were mounted on a 1-m translation stage to adjust the position of the filament relative to the collection optics. For time-resolved spectroscopy, collected filament emission was coupled into a multimode fiber to a Czerny-Turner spectrometer (Princeton Instruments HRS-500) with an emICCD detector (Princeton Instruments PI-MAX4). The use of 1200 gr/mm grating resulted in a resolving power of $\sim$4500 at 435.8 nm (measured with a Hg calibration lamp). All spectra were corrected for the wavelength-dependent instrumental response using an intensity-calibrated deuterium-tungsten lamp (Ocean Optics DH-2000 CAL). For emission spectroscopy, 15,000-shot averages were used with a 2-ns gate delay and 8-ns gate width, where fluctuations in the average integrated intensity from the Sr I 460.7 nm emission remained under 11.5%. Filament plasma emission images were recorded using an emICCD from the side, orthogonal to the beam path. Images were demagnified by $m=0.13$ to capture the entire length of the filament fluorescence within the same window. Fluorescence from the $\text {N}_2$ second positive system and the $\text {N}_2^+$ first negative system was isolated using a 355$\pm$5 nm and a 391$\pm$1.5 nm bandpass filter, respectively. Each $\text {N}_2$ and $\text {N}_2^+$ image was captured using three separately averaged 500-shot on-chip accumulations with a varied gate delay and gate width. Emission from Sr I 460.73 nm was isolated using a 460$\pm$5 nm bandpass filter and imaged using ten separately averaged 1,000-shot on-chip accumulations with a gate delay of 5 ns and a gate width of 50 ns.

 

Fig. 1. Experimental setup for on-axis collection spectroscopy using a pierced parabolic mirror along the beam path axis and side-collection spectroscopy orthogonal to the beam path axis.

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An open-ended chamber was used to allow the passage of freely propagating filaments. To contain aerosols within the chamber close to saturation conditions, a valved exhaust was used to achieve a slight negative pressure by allowing inward airflow. Aerosols were generated using a medical nebulizer (Resperonics SideStream) with an aspiration rate of 0.09 mL/min and a mean aerodynamic droplet diameter of 3.1 µm using a nominal gas flow rate of 6 L/min controlled with a digital mass flow controller (Sierra Instruments SmartTrak 100). Aerosol measurements were performed for Ti and Sr using 10,000 µg/mL and 7,500 µg/mL inductively-coupled plasma (ICP) standard solutions (SPEX CertiPrep), respectively.

For on-axis Ti and Sr aerosol measurements, a 50.8 mm-diameter silver-coated pierced off-axis parabolic (OAP) mirror was used with a 90$^\circ$ off-axis 150-mm focal length, whereas for measurements for $\text {N}_2$ and $\text {N}_2^+$ below 400 nm a UV-enhanced aluminum-coated pierced OAP mirror was used for improved reflectance. The collected light from the mirrors was collimated and focused onto an SMA coupler using a matching 50.8-mm diameter UV-fused silica lens. The aerosol was introduced into the chamber through a tee close to the focal point of the silver-coated mirror, extending the length of the chamber. This increases the distance over which filament-particle interactions take place, as shown in Fig. 1.

For side-collected Ti and Sr aerosol measurements, a 25.4-mm diameter and 35-mm focal length lens in a lens tube with fiber coupling optics was inserted through an open port orthogonal to the filament path in the side of the chamber and sealed. To introduce the aerosol closer to the focal point of the side collection lens similar to the on-axis setup, the aerosol flowed directly into the chamber body, and the tee was removed. The entrance and exit (replacing the tee) were covered with a flanged cover plate that included a small central piercing to allow the filament to pass through while retaining containment. The particle concentration near the focal point of the collection optics was approximately equivalent between on-axis and side collection as the chamber was nearly saturated in both cases through adjustment of the exhaust valve and careful monitoring of flow velocities with an anemometer and eliminating supercontinuum light scattering from leaking particles at the exit. Images of Sr emission were taken with the filament formed in a 25.4-mm diameter quartz tube attached to an entrance Brewster window, placed immediately before the focusing lens to avoid damage. The aerosol is co-propagated with the filament in the tube at 6 L/min, resulting in a 19.7 cm/s flow velocity.

3. Results and discussion

3.1 Filament imaging

Time-resolved filament images are presented in Fig. 2 using filters to isolate the $\text {N}_2$ second positive system ($\text {C}^3 \Pi _\text {u} \rightarrow \text {B}^3 \Pi _\text {g}$) (0,1) band and the $\text {N}_2^+$ first negative system ($\text {B}^2 \Sigma _\text {u}^+ \rightarrow \text {X}^2 \Sigma _\text {g}^+$) (0,0) band, where the first and second value in the parenthesis denote the upper and lower electronic states, respectively. It is well-known that $\text {N}_2^+$ is prevalent in air filaments due to the direct laser-induced ionization of an inner valence electron of $\text {N}_2$ through multiphoton or tunnel ionization [33]. Following ionization, electron-ion recombination occurs that forms $\text {N}_2$ through a two-step reaction: (1) $\text {N}_2^+$ + $\text {N}_2 \rightarrow \text {N}_4^+$ and (2) $\text {N}_4^+ + \text {e}^- \rightarrow \text {N}_2$($\text {C}^3 \Pi _\text {u}$) + $\text {N}_2$, where the second positive system results.

 

Fig. 2. Images of $\text {N}_2$ and $\text {N}_2^+$ captured at different delays under (a) 400 mm and (b) 750 mm external focusing conditions and a 3-ns gate width without the aerosol present. The color scale is individually normalized for $\text {N}_2$ and $\text {N}_2^+$ images. The signal intensities based on the integrated signal within the FWHM of the axial and radial profiles of the filaments are shown in (c) for measured gate delays. The pulse propagates from left to right.

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The images are summed vertically and horizontally to yield axial and radial profiles, and the fraction of the images that fall within the FWHM of profiles are integrated to represent the intensities in Fig. 2(c) using a 3-ns gate width such that a 2-ns signal overlap persists as the gate delay is incremented by 1 ns. The (length $\times$ width) of the filaments defined as the profile FWHM is (20 $\times$ 0.85) mm and (39 $\times$ 0.90) mm for the 400-mm and 750-mm lens filament, respectively. This corresponds to a doubling in the luminous filament length with a near doubling of the focal length of the external focusing lens, whereas the diameter of the multi-filament channel is unchanged. The $\text {N}_2^+$ fluorescence is constrained to a shorter FWHM length of 13 mm and 27 mm for the 400-mm and 750-mm lens filaments, respectively, indicating ionized species are constrained to a shorter focal volume. The longer filament formed by the 750-mm lens yields a greater $\text {N}_2$ signal, whereas the shorter filament formed by the 400-mm lens produces a greater $\text {N}_2^+$ signal despite its shorter length. The stronger $\text {N}_2^+$ fluorescence is in agreement with the results reported in Ref. [26], consistent with an increase in electron density through the use of shorter external focusing lenses, which the authors attribute to higher $\text {N}_2 \rightarrow \text {N}_2^+$ + $\text {e}^-$ reaction rates. Given the $\text {N}_2$ emission must result from the aforementioned electron-ion recombination of $\text {N}_2^+$, the more intense $\text {N}_2^+$ fluorescence expected for the 400-mm lens filament should be accompanied by a more intense $\text {N}_2$ fluorescence compared to the 750-mm lens filament, but this is shown not to be the case in Fig. 2(c). This may be due to a competing process – an increase in dissociation rate of $\text {N}_2^+$ through $\text {N}_2^+ \rightarrow \text {N} + \text {N}^+$, which results in stronger atomic gas species emission, previously studied for 50-mm, 300-mm, and 1-m lens filaments [34]. This mechanism would counteract the production of $\text {N}_2$ ($\text {C}^3 \Pi _\text {u}$) molecules, which may be dominant over recombination in the case of the 750-mm lens filament.

Images of the 750-mm lens filament are taken with (dashed lines) and without (solid lines) the Sr aerosol present, and the signal profile is provided in Fig. 3 for different pulse energies and repetition rates. For the $\text {N}_2$ fluorescence in Fig. 3(d) at a fixed repetition rate of 1 kHz, increasing the pulse energy results in earlier self-focusing as a result of higher beam intensity. The filament is also sustained over a longer distance at higher pulse energies, where most of the added length extends on the side of focus towards the focusing lens as a result of earlier self-focusing. For a fixed pulse energy of 3.9 mJ, changing the repetition rate from 1 kHz to 10 Hz shifts the maximum of the $\text {N}_2$ fluorescence intensity in Fig. 3(c) closer to the focusing lens by 8 mm. The hydrodynamic recovery process of air after filament-induced excitation occurs on an $\sim$ms timescale, comparable to the 1-kHz laser repetition rate, leaving a low air density “hole” in the wake of each passing filament that does not recover to ambient conditions [35]. This low-density air channel sustained at higher repetition rates has been shown to improve air transmission through fog clearing [20–22,36] and to give rise to optical anti-guiding structures as a result of a radial index of refraction gradient corresponding to the change in air density [37,38]. Given the nonlinear index of refraction of air is proportional to air density, the index of refraction is effectively reduced at higher repetition rates resulting in weaker self-focusing and thus shifting the onset of filamentation further away from the focusing lens. While the filament energy depletion rate from photoionization is reduced at lower densities [39], the 1-kHz filament generated in a lower air density channel is shorter than the 10-Hz filament by 8 mm, which may be explained by the higher critical power $P_\text {cr}$ at lower air densities. This yields lower $P/P_\text {cr}$ ratios at higher repetition rates and shorter filaments. Furthermore, by initiating filamentation closer to the geometric focus of the lens, the filament length is reduced by more rapid geometric defocusing. Introducing aerosols consistently depresses the $\text {N}_2$ fluorescence intensity in Fig. 3(c,d) which is not fully understood; however, a possible reason is the added humidity from the aerosolized solution that alters the air composition, where the water concentration is estimated to be 1.5 mg/cm$^3$, yielding supersaturated conditions. Without an aerosol present, the filaments are formed in dry air such that the water content is dramatically different with and without an aerosol present. A similar decrease in $\text {N}_2$ fluorescence intensity was reported in Ref. [40] as the relative humidity was increased, which was attributed to (1) decreased concentrations of $\text {N}_2$ at higher humidity and (2) increased generation of N radicals which consume N atoms and thus inhibit recombinative $\text {N}_2$ fluorescence. Increasing humidity has been shown to increase hydrogenated compounds such as NH and $\text {HNO}_3$ concentrations, where $\text {HNO}_3$ formed through oxidization of $\text {NO}_2$ is a cloud condensation nucleus (CCN) which facilitates filament-induced condensation [41–43]. The $\text {N}_2$ signal for the 1-kHz filament is not as dramatically reduced with aerosols present compared to the 10-Hz and 100-Hz filament, which conceivably results from the lower air density channel also experiencing a lower humidity.

 

Fig. 3. Radially summed images of (a,b) Sr I emission and (c,d) $\text {N}_2$ fluorescence with (dashed lines) and without (solid lines) a Sr aerosol present using a 750-mm (dashed-dot lines indicating geometric focus) lens filament. The pulse energy is fixed at 3.9 mJ for (a,c), and the repetition rate is fixed at 1 kHz for (b,d). A 5-ns gate delay and a 50-ns gate width are used for Sr I images, while a 0-ns gate delay and a 5-ns gate width are used for $\text {N}_2$ images. The pulse propagates from left to right.

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The Sr I 460.73-nm emission is imaged in Fig. 3(a,b) using a 5-ns gate width to limit contributions from the background (solid line) and supercontinuum scattering. The Sr I emission profile is shown to deviate substantially from the $\text {N}_2$ fluorescence profile, which may be partially attributed to differences in ionization and excitation energies between the two species. The emissive length of Sr extends beyond the FWHM length of the $\text {N}_2$ fluorescence profile due to the lower ionization threshold of Sr (5.69 eV) compared to the ionization threshold of $\text {N}_2$ (15.6 eV). However, unlike $\text {N}_2$ fluorescence, the Sr emission is shown to vary substantially with both pulse energy and repetition rate. As the pulse energy is increased in Fig. 3(b), the emission profile broadens substantially and begins to develop several maxima along the filament length. For pulse energies at 3.9 mJ and above, the emissive region near 740 mm is consistently present but appears to saturate, at which point the filament begins to form other emissive regions localized around 760 mm and 720 mm instead. Reducing the repetition rate in Fig. 3(a) results in higher Sr emissions from 1 kHz to 10 Hz and the emissive regions of the filament are once again highly restructured. The reduced Sr signal at higher repetition rates indicates the low air density channel may be depleted of aerosol particles which require lower repetition rates to fully recover. Furthermore, the Sr I emission length is also broader at 10 Hz compared to the higher repetition rates similar to $\text {N}_2$, such that the broadening can partially be attributed simply to a longer filament being generated through earlier self-focusing and a higher ratio of $P/P_\text {cr}$ resulting from denser air. Similar to the trends observed with increasing pulse energies, prominent emissive regions are formed around 720 mm and 760 mm at 10 Hz, whereas the emissive region around 740 mm is saturated.

The exact mechanism driving the axial distribution of emission regions remains unclear. The aerosols are co-propagated with the filament at a flow rate of 19.7 cm/s such that turbulence effects are negligible [19]. The low flow rate of aerosols implies that within the period of a 1-kHz pulse train (1 ms), the particles travel $\sim$0.2 mm, such that it would require $\sim$200 pulses (0.2 s) for any given particle to traverse the entire length of a 40-mm long filament. Thus at higher repetition rates, it is possible that the thermophysical property of the particles is being altered through previous interactions with the filament, corresponding to asymmetric changes in emission behavior as newer particles are introduced from the trailing edge of the filament (left side in Fig. 3) which have yet to interact with the plasma. Aerosol clearing by filament-induced shockwaves and air density gradients can also result in localized regions in the filament where aerosols are depleted, consistent with the strong dependence of the emission profile on the repetition rate and pulse energy [20–22]. The depleted region would closely correspond to where the shockwave is the strongest near the maximum observed for the $\text {N}_2$ fluorescence [44]. By depleting this region of the filament of aerosols, the uniformity in both the particle concentration and velocity profile would be disturbed which may cause several emission minima and maxima to be formed.

3.2 Emission spectroscopy on bulk aerosols

Spectra of $\text {N}_2$ and Sr were collected using 6.8-mJ pulses at a 1-kHz repetition rate for both on-axis and side collection at positions where the $\text {N}_2$ fluorescence was measured to be at its strongest and are presented for comparison in Fig. 4. Using on-axis collection, it is generally seen that the $\text {N}_2$ and $\text {N}_2^+$ spectra yield similar trends to the $\text {N}_2$ and $\text {N}_2^+$ fluorescence recorded through imaging in Fig. 2(c), where the 400-mm lens filament results in a stronger $\text {N}_2^+$ emission intensity compared to the 750-mm filament case, and the 750-mm lens filament results in a stronger $\text {N}_2$ emission intensity compared to the 400-mm filament case. The image intensity in Fig. 2(c) is the spatially integrated intensity bound to the FWHM of the filament dimension; this is similar to the on-axis collection which collects light along the length of the filament to give an axially integrated quantity, thus resulting in similar $\text {N}_2$ and $\text {N}_2^+$ fluorescence trends to imaging. Conversely, side collection spatially constrains light collection to an equal sectional length of the filament for both 400 mm and 750 mm cases, limited by the numerical aperture of the lens. Within an equivalent length of the filament observed using side collection, the 400 mm achieves higher fluorescence and emission signals for both $\text {N}_2$ and Sr, respectively. This is mainly attributed to two reasons: (1) for the implemented light collection schemes, filaments formed using shorter external focusing conditions gradually favor the higher numerical aperture of the side lens (NA = 0.36) to that of the OAP mirror (NA = 0.17) as the emitting species are closely restricted near the focal point of the collection lens; (2) short-focused filaments achieve higher ionization levels that generally results in higher emissions following recombination. These two reasons are considered interdependent as higher ionization levels are achieved using shorter focusing lenses, and shorter focusing lenses result in shorter filaments. Ionized species are restricted to an even shorter focal volume compared to neutral species, resulting in a higher light collection efficiency for $\text {N}_2^+$ and Sr II in Fig. 4(b,d) using side collection for the shorter focused filament.

 

Fig. 4. Time-resolved fluorescence spectra for (a) $\text {N}_2$ second positive (0,1) band and (b) $\text {N}_2^+$ first negative (0,0) band using a 0-ns gate delay and 5-ns gate width. Aerosol emission spectra are shown for (c) Sr I 460.73 nm and (d) Sr II 407.77 nm using a 20-ns gate delay and 80-ns gate width. Each spectrum is measured where $\text {N}_2$ signal is at a maximum using 6.8-mJ pulses at a 1-kHz repetition rate.

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To characterize the aerosol emission intensity along the length of the filament, the Sr emission was measured on-axis and from the side while translating the axial position of the 400-mm and 750-mm lens filaments relative to the focal point of the collection optics. The results are shown in Fig. 5. The on-axis emission profile is broadened compared to the side-collected profile as particle emission is collected over a broader region along the filament length, generally improving collection efficiency at the cost of achieving spatially selective emission intensities. The peak in the axial emission profile is shown to generally occur near or slightly before the geometric focus of the external focusing lens due to the added beam convergence from self-focusing. Here, the 750-mm lens filament shows two emission regions similar to those developed in the quartz imaging tube for Fig. 3(a,b) whereas the 400-mm lens filament forms a singly peaked emission profile which was later confirmed using imaging. As in Fig. 4, the on-axis collection is shown to generally improve light collection from filaments for most cases due to the higher light coupling efficiency of particle-derived emission. An exception is the Sr II emission from the 400-mm lens filaments, which again shows better light coupling efficiency from the side in agreement with the previous discussion for Fig. 4(b,d) as ions are restricted to a shorter focal volume. Additionally, anti-guiding structures begin to form in the air at a higher repetition rate, changing the radial index of refraction due to sustained changes in air density [38]. This can further reduce the on-axis light collection efficiency as back-propagating emission light is radially refracted away before reaching the OAP mirror, thus reducing the measured emission intensity. Conversely, emissions propagating towards the side collection lens are not significantly refracted as the emissions travel near-parallel to the index of refraction gradient vector in the radial direction. As a result of these effects, anti-guiding is expected to negatively impact the on-axis collection emission intensity more than the side collection emission intensity.

 

Fig. 5. Axial Sr I – 460.73-nm emission profile measured using on-axis and side collection for (a) $f=400$ mm and (b) $f=750$ mm externally focused filaments using 6.8-mJ pulses at a 1-kHz repetition rate. Similarly, axial Sr II – 407.77 nm emission profile is measured using (c) $f=400$ mm and (d) $f=750$ mm externally focused filaments. The black dashed line represents the focal length of the external focusing lens. The pulse propagates from left to right.

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It is shown in Fig. 5(a,c) that the shorter 400-mm lens filament results in stronger atomic and ionic emission compared to the longer 750-mm lens filament in Fig. 5(b,d), regardless of the light collection scheme. A similar observation was made in Ref. [34], where they found that atomic O and N emissions are more pronounced using 300-mm focused filaments compared to 1-m focused filaments with side-collection, which the authors attributed to the predominant role of strong field ionization effects (e.g. tunnel ionization and multiphoton ionization) at the geometric focus that competes with filamentation. Both observations are in agreement with results reported in Ref. [26], where it was determined that shorter external focusing conditions generally lead to higher plasma densities, which would naturally lead to higher atomic and ionic emission for both aerosol and gas species through subsequent recombination. The authors also noted an increase in the filament diameter by up to 25% when using a 500-mm lens compared to a 1-m lens, which has implications for aerosol measurements as it is accepted that emission strengths are directly proportional to the size of the plasma which readily interacts with nearby particles under similar plasma conditions [1,7,28]. However, in this case, both filaments have similar FWHM diameters such that the observed increase in side-collected emission from the 400-mm lens filament can only be attributed to differences in plasma conditions induced by external focusing, not the volume of the filament plasma. This is further supported by observing changes to the Sr II and Sr I emission ratios between the two filaments using side collection. The Sr II intensity is double that of Sr I at its peak (ratio of 2) when using a 400-mm lens but is a factor of 5 lower (ratio of 0.2) when using a 750-mm lens, which is inexplicable without changes to either the plasma temperature or density.

The filament plasma density is determined using the Stark broadening method for the Sr I 460.73 nm line and Sr II 407.77 nm line [45]. Assuming negligible contributions from ion broadening, the electron density is expressed as

Axial profiles of aerosol-derived electron densities and temperatures are presented in Fig. 6. The electron density profile obtained through side collection shows a peaked profile similar to the axial emission profiles of $\text {N}_2$ in Fig. 3(c,d) and Sr in Fig. 5. A double maxima seen in the emission profile is not present in the electron density profile for the 750-mm lens filament, but the larger error associated with the electron density is unable to resolve finer details observed in the emission profile after error propagation. Similar profiles have been obtained in the past using Cu solid targets [23], atmospheric O [50], and pure Ar [51]. The electron density is shown to be comparable but also higher for Sr I to Sr II in Fig. 6(a). Assuming the filament is in local thermodynamic equilibrium (LTE), the electron density is expected to be similar between Sr I and Sr II based on the Saha equation. In this case, the electron-impact half-width parameter $w$ used is obtained from theoretical calculations for Sr I and measurements in an Ar plasma for Sr II [46,47], and thus discrepancies in the electron density may arise. Unlike the plasma density, the temperature does not show a significant peak in its profile for both filaments, resulting in a uniform plasma temperature of around 7250 K. Derivative to the phenomenon of intensity clamping, “temperature clamping” has been shown to occur for solid Cu targets over roughly a 2 m distance for a 4-m lens filament [23] and $\text {N}_2$ electron temperatures over a 35 mm distance for a 1 m lens filament [50].

 

Fig. 6. Axial profiles of filament (a) electron densities obtained using the Sr I and Sr II emission lines and (b) temperatures obtained using Ti I emission lines. All properties are determined using a 2-ns gate delay and 8-ns gate width. The theoretical ratio between the Sr II and Sr I lines is shown in (c) for a range of electron densities and temperatures of interest. The pulse propagates from left to right.

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Given that electron density is the only plasma parameter that peaks similarly to the emission profile, the population density of emissive species is evidenced to be closely related to the electron density behavior. In the case of fs-pulses, the pulse duration is shorter than all the major relaxation processes including electron-to-lattice energy transfer, heat diffusion, hydrodynamic motion, and free electron collisions, which are all taken to be on the order of 1 ps [6,52]. In the context of laser ablation, the reduced interaction between the laser pulse and free electrons deemphasizes subsequent collisional processes, resulting in lower plasma temperatures that are less dependent on the sample matrix [13,53,54]. Thus, photoionization makes the dominant impact on the filament plasma conditions such that higher peak powers near the geometric focus result in an increase in electron density [26,27,33]. As in the case with $\text {N}_2^+$, the higher ionic Sr II population results in higher Sr II and Sr I emission after deexcitation and recombination. The observed emission profiles in Fig. 5 are supported by theoretical ratios of Sr II 407.77 nm to Sr I 460.73 nm line intensities provided in Fig. 6(c) derived from Saha’s equation for a range of plasma temperatures and electron densities relevant to those shown in Fig. 6(a,b). As previously discussed, the Sr II to Sr I ratio is approximately 2 and 0.2 for the 400-mm and 750-mm lens filaments in Fig. 5, respectively. A reversal in emission intensities between singly-ionized and neutral species typically indicates a dramatic change in plasma conditions which is not captured in the profiles in Fig. 6(a,b), showing different yet comparable plasma temperatures and electron densities. However, given plasma temperatures ranging from 7250 $\pm$ 800 K in Fig. 6(b), it is shown that the Sr II 407.77 nm intensity can be either greater than or less than the Sr I 460.73 nm intensity for electron densities ranging from $0.5 \times 10^{17} \text {cm}^{-3}$ to $2.5 \times 10^{17} \text {cm}^{-3}$ determined in Fig. 6(a) based on Saha’s equation. The theoretical ratios also show that for any given temperature within reasonable error, the ratio of Sr II to Sr I is highly dependent on the electron density such that peaked axial emission profiles and electron density profiles are achievable despite the uniform temperature clamped profile. This is attributed to the relatively low ionization potential of Sr at 5.69 eV compared to other gas species including $\text {N}_2$ at 15.6 eV and $\text {O}_2$ at 12.1 eV. It is also likely that the true temperature for the Sr aerosol is different from the Ti aerosol due to thermophysical differences within the particle matrix which adds uncertainty to this particular analysis [13].

Unlike the side-collected electron density profiles, the on-axis profiles consistently report higher electron densities that gradually increase as the filament is moved further in front of the collection mirror to measure the emissions occurring near the trailing edge of the filament. The temperature is shown to be within error near the geometric focus which begins to increase similar to the on-axis electron density profile. An asymmetric increase in temperature and electron density of this nature is physically inexplicable, and thus are determined to result from self-absorption of emission light that overestimates electron densities and temperatures determined using the Stark broadening method and the Boltzmann plot method, respectively [55,56]. To determine the severity of self-absorption in the measurements, different solution concentrations of Sr are measured to construct curves of growth (COG) that show increasing levels of self-absorption at higher concentrations of analyte species [57–59]. The curves are constructed where the Sr II axial profile peaks in Fig. 5(c,d). An additional COG is constructed for the on-axis case by moving the 400 mm and 750 mm lens filament 1 cm and 2 cm further in front of the pierced mirror, respectively. By creating the filament further away from the OAP mirror, the optical path length traversed by the emitted back-propagating light increases. The results are presented in Fig. 7 for the Sr I 460.73-nm line and the Sr II 407.77-nm line.

 

Fig. 7. COG constructed for the (a) 400-mm lens filament for Sr I, (b) 750-mm lens filament for Sr I, (c) 400-mm lens filament for Sr II, and (d) 750-mm lens filament for Sr II. The lines used are Sr I 460.73 nm and Sr II 407.77 nm with a 2-ns gate delay and 8-ns gate width. Linear regression is fit to the three lowest concentration data points to guide the eye. The position of the filament was translated further from the OAP mirror by 1 cm and 2 cm for the 400-mm and 750-mm lens filaments, respectively for the on-axis (far) case.

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Comparing side-collected COGs, it is apparent that the 400-mm lens filament departs from linearity at lower solution concentrations which indicates self-absorption is more pronounced compared to the 750-mm lens filament. Given self-absorption of any given transition is proportional to the lower energy state population density, these results support that stronger aerosol emission from the 400-mm lens filament is largely due to higher population densities of emissive species as a result of higher ionization rates, most prominently seen for Sr II between Fig. 7(c) and Fig. 7(d). With the exception of Fig. 7(c) for Sr II using the 400-mm lens filament which achieves higher light collection efficiency from the side, switching to an on-axis collection scheme suffers from self-absorption at significantly lower solution concentrations. The electron densities reported for Sr I and Sr II in Fig. 6(a) used a 7500 µg/mL Sr solution that does not show signs of self-absorption using side collection in any of the plots in Fig. 7. However, self-absorption is shown to occur at 7500 µg/mL using on-axis collection either at the peak of the emission profile or when shifted further from the collection mirror as in the case of Fig. 7(d), indicating self-absorption is dependent on the position of the filament relative to the on-axis focal length of the mirror. This confirms that on-axis collection is prone to overestimating the electron density profile in bulk aerosols due to self-absorption which can reasonably be extrapolated to explain the similar trends shared by the on-axis plasma temperature profiles obtained from Ti. In particular, the COG for Sr I 460.73-nm line in Fig. 7(a,b) shows the most obvious signs of self-absorption as it is a singlet resonance transition that returns to the ground state. Given the cold plasma conditions, the population of the ground state is assumed to be high which makes it susceptible to self-absorption. While ionic transitions are comparatively tolerant towards self-absorption in an LPP due to their higher upper and lower state energies [59], Fig. 7(d) for the 750-mm lens filament shows that self-absorption can begin to significantly affect ionic transitions as the filament is moved further in front of the OAP mirror. In comparison, the 400-mm lens filament does not show a significant change in self-absorption behavior by changing the filament position. To explain the observed self-absorption behavior in Fig. 7, self-absorption is formally described for a given wavelength λ by the radiation transfer equation [60]:

4. Conclusions

Bulk aerosol emissions excited by filaments were examined for 400-mm and 750-mm externally focused filaments, and several important considerations are presented for remote aerosol sensing. The emission profile of bulk aerosols was shown to be highly sensitive to the pulse energy and repetition rate of the filament, where for longer filaments, several localized emission regions begin to form along the filament at higher pulse energies and lower repetition rates. The exact mechanism driving this behavior is not yet fully understood, but given dramatic changes in the emission profile at different repetition rates, it is conjectured that perturbations caused by preceding filaments result in a hysteresis effect that does not fully recover to ambient conditions, especially for 100-Hz and 1-kHz filaments. For emission spectroscopy with our experimental configuration, using on-axis collection was shown to improve light collection efficiency for long-focused filaments more than for the short-focused filaments, but the higher ionization efficiency achieved using shorter focusing conditions resulted in higher overall emission intensities, especially for ionic emissions resulting from high upper energy level transitions. On-axis collection was also shown to result in pronounced self-absorption of bulk aerosol emissions, where long-focused filaments experience self-absorption due to longer optical path lengths and short-focused filaments experience self-absorption due to higher excited state population densities. Due to the lack of studies examining the effects of self-absorption for typical filament plasma conditions, applicable correction methods are limited when compared to typical LIBS plasmas, and this remains an important direction for future study.