1. Introduction

The interaction of high peak power laser pulses with micro-scale particles is a very common physical problem that is relevant to a wide range of applications. For example, the propagation of laser beams in the atmosphere involves the interaction of high power or high peak intensity pulses with atmospheric aerosols which can alter the beam energy delivery and its spatial characteristics over long propagation lengths [1–5]. On the other hand, laser-particle interactions have been used as a means to remove contamination particles from a surface through the process so-called dry laser cleaning [6–9]. The ability to remove contamination particles from surfaces was found to strongly depend on the laser parameters [10–13] and the environment [14]. Above certain irradiation conditions, this interaction causes modification of the substrate in the form of either smooth pits [15,16] or larger and more complex formations that are typically undesirable [17] and considered as damage. The modification of the substrate arising from laser-particle interactions has also been explored as a means to imprint on surfaces and membranes micro-patterns with novel properties [18,19]. Similar laser-based methods have been explored for the removal of particles from surfaces in harsh environments such as in nuclear fusion engines [20] or for the decontamination of radioactively contaminated surfaces [21–23].

The physics involved in the interaction of micro-scale particles with laser pulses is also critical in the development of novel materials synthesis and manufacturing processes. Specifically, it has been shown that exposure of metallic or dielectric particles to higher energy laser pulses leads to production of smaller particles, a process that has been proposed for the synthesis of nanoparticles with narrower range of size distributions [24,25]. In additive manufacturing applications, laser beams are commonly used for the melting and fusion of metal particles. It has been proposed that pulses with a temporal duration on the order of 10 ns provide unique traits (arising in part from the lower energy density delivered supporting faster cooling) in the material fusion process [26–28]. Arguably, the combination of laser pulses with particles will find some novel future applications, such as decontamination in harsh environments [15–18] or particle-based laser ablation plasma thrusters [29].

In the field of high power laser systems, contamination of the surface of optical components can adversely affect the performance of the laser and lifetime of its components [30–35]. The presence of either transparent or opaque contaminant particles located on the input or exit surface of optical components can initiate damage via field modulation and intensification or direct ablation of the particle leading to damage of the substrate. This interaction typically results in one or more of the following modifications: a) the formation of craters containing the remnants of exposure to high temperatures, b) modification of a surface layer or coating indicating exposure to plasma, c) cracks indicating exposure to high pressures and d) deposition on the surface of the substrate of a layer of material and/or smaller particles originating from the contaminant particle [32].

The above cited and numerous other studies have investigated, within the scope of each intended application, the effects of the interaction of particles with lasers beams. Efforts to model these interactions were also presented. However, the exact dynamics of these interactions remain unclear and can be very complex (except perhaps when the only mechanism is heating) involving high gradients of pressure, temperature and corresponding thermodynamic material properties, plasma formation and aerodynamic effects. As a result, current models typically involve numerous simplifications. Moreover, experimental measurements of the dynamic processes involved in these interactions are limited [24,25] and contain a rather narrow range of measured parameters. Particle ablation induces a recoil momentum that pushes the particle along the beam. In addition, the formed plasma can interact with the laser pulse while the melted material layer on the particle is ejected and can be the source of secondary contamination or other effects. To the best of our knowledge, these important processes involved in the laser-particle interaction have not been adequately resolved. Consequently, comprehensive dynamic studies of laser-particle interactions over a wide range of excitation conditions with adequate spatial and temporal resolution are required. Such measurements may be designed to be informative and translatable across a wide range of material and irradiation geometries relevant to several applications.

In this work, we investigate the interaction of micro-scale, nominally spherical metallic particles having a range of mass density values with nanosecond laser pulses at 1064- and 355-nm. A specially designed experimental platform allows direct measurements of the particle velocity, the dynamics of the plume and the kinetics of the ejected molten material. Analysis of experimental results demonstrates that the concept of momentum coupling introduced for the exposure of plane metal targets to large-aperture laser beams can be adopted to describe the laser interaction with micro-particles. The results also indicate the important role of laser energy deposition within the formed plasma that affects the energy partitioning and the material modifications to the substrate.

2. Experimental setup

Figure 1 shows a schematic depiction of the dual-axis, time-resolved shadowgraphic microscope system utilized in this work. The basic design and functionality of this imaging system have been described in detail elsewhere [36]. Nominally spherical metallic particles having a diameter on the order of 30 µm were dispersed on the exit (output of the laser beam) surface of 5-cm round, 1-cm thick commercially available fused silica optical windows (referred to as substrate). The substrate was positioned vertically, thus the gravitational force on the particles was parallel to the surface of the substrate. Two microscope systems positioned orthogonal to each other were used to image the area containing the particle a) along the surface of the sample, referred to as transmission view (TV) microscope, and b) normal to the surface, referred to as side view (SV) microscope. Time resolved images were captured using polarized strobe light illumination. The illumination was derived from two probe beams operating at 532 nm, both linearly polarized but having their polarization orientation orthogonal with respect to each other. Each probe pulse had a predetermined temporal separation with respect to the peak of the pump pulse. The two probe beams were first combined and subsequently split to illuminate the particle parallel and orthogonal to the surface of the substrate. In this arrangement, the dual axis microscope could capture the dynamics involved with two transient images and temporal resolution determined by the probe pulse durations. A composite lens system consisting of a 5X zoom and a long working distance objective were used to collect the dual-probe illumination traversing the imaged area. Depending on the desired spatial image resolution (and dimensions of the imaged area) in each experiment, the optical magnification of the objectives used was either 2X, 5X or 10X,corresponding to 10X, 25X or 50X total optical magnification, respectively, and spatial resolution from ~5 μm to ~1 μm. The light collected by the imaging optics was subsequently passed through a 532-nm narrowband filter and separated into its constituent polarization components using a polarizing beam-splitter. With this approach, the images generated by each probe pulse were recorded by separate charge-coupled device (CCD) cameras.

 

Fig. 1 Schematic depiction of the experimental system. Details are provided in the text.

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The pump beam was incident at either 0° or 36° (angle denoted as θ in Fig. 1 inset) with respect to the normal to the sample’s surface. The two pump lasers used were operating at 355 nm (3ω) and 1064 nm (1ω). The particles were exposed to fluences up to about 25 J/cm² and 180 J/cm² using the 3ω and 1ω pump lasers, respectively. Above these upper-limit fluences, breakdown (damage) on the substrate was observed (outside the particle location). As a result, experiments using 3ω pulses were performed over a narrower range of fluences relative to experiments using 1ω laser pulses.

The diameter of the pump beam at the particle location (exit surface of the substrate) was on the order of a few hundred µm, thus significantly larger than the size of the particles. Specifically, the 1ω pump beam profile was approximately circular with 1/e² diameter of about 270 µm and presented a nearly flat-top inner section of about 130 µm in diameter with ~20% local intensity variations around the mean. The 3ω beam profile was elliptical (due to the 36° angle of incidence of the laser beam) having a major axis of about 455 µm and minor axis of about 315 µm. The 3ω beam was nearly flat-top with ~25% local intensity variations around the mean. The particles were positioned in this nearly flat-top section of the beam for the execution of the experiments.

Three different configurations of the above-described system were used for the execution of the experiments involving two pump lasers and four probe lasers. The parameters of each configuration are summarized in Table 1. In configurations 1 and 2 (see Table 1), the dual 532-nm probe beams were derived from separate lasers and their delay was adjusted via external triggering. In configuration 3, the two probe beams were derived from a single laser using a 50/50 beam splitter, had orthogonal polarization of one arm with respect to the otherand variable optical delay path (up to 6 ns). A set of fast rise-time photodiodes and oscilloscope were used to record the relative temporal delay of the pump and probe pulses at peak intensities for each experimental configuration.

Table 1. The pump and probe laser pulse parameters for various experimental configurations.

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Most of the experiments discussed here employed stainless steel (SS) particles as the model metallic particle system. This choice was in part motivated from the fact that stainless steel particles are largely free from an oxide layer forming (in many metals systems) on the surface that could arguably affect the observed dynamics. The SS particles were roughly spherical in shape with an average diameter of approximately 27 µm. A limited set of experiments were also performed using aluminum (Al) and tungsten (W) particles to study the ejection kinetics of the particles as a function of their mass density. Each measurement involved imaging the dynamic behavior of individual particles that were visualized and down selected before being exposed to the pump laser pulse to have similar diameters and nearly spherical shape. All experiments were performed in ambient laboratory conditions.

3. Experimental results

Figures 2 and 3 capture the main manifestations of the dynamics involved following the pulsed laser irradiation of the metallic particles (here SS) located on the exit surface of a silica substrate. Specifically, the time resolved images shown in Fig. 2 were captured using the SV microscope in configurations 1 (images (a1)-(a4)) and 2 (images (b1)-(b3)). We note that similar in size (~30 μm diameter) and shape (nominally spherical) SS particles were irradiated in each experiment. The laser beam was propagating from right to left, thus illuminating the particle through the transparent silica substrate. Figures 2(a1) and 2(b1) show the SS particle (denoted with numeric 1) attached on the surface of the substrate prior to its exposure to the pump beam. The time resolved image shown in Fig. 2(a2) was acquired using the 180-ps probe beam and allows the visualization of the plume (2) and shockwave (3) formations at 2 ns delay (from the peak of the pump pulse) following irradiation with ~10 J/cm² at 3ω. The plume appears as a dark feature due to reduced transmission of the probe light. The shock front edge is also visible due to the induced diffraction of the probe light. This image (and others acquired at similar delays) shows that the plume expands around the sides of the particle. The shockwave is located ahead of the plume and has expanded along the substrate’s surface about 40 µm from the contact point of the particle with the substrate but only a few µm from the tip of the particle on the opposite side to the contact point. These observations suggest that the plume (and shockwave) emerges from the region near the interface between the metal and the substrate and expands outward before encapsulating the entire particle at a later delay. The dynamics of this mechanism will be discussed in more detail later after taking into consideration additional related experimental observations.

 

Fig. 2 Time-resolved SV images capture the main features observed following the irradiation by a laser pulse of ~30 μm diameter SS particles (1) located at the exit surface of a silica substrate that include the plume (2), the shockwave (3) and the atomized melted material (4). Irradiation conditions: ~10 J/cm² at 3ω for images (a1)-(a4) and ~100 J/cm² at 1ω for images (b1)-(b3). The corresponding image capture delay times are: before exposure for (a1) and (b1), 2 ns for (a2), 100 ns for (a3), (a4) and (b2), and 500 ns for (b3).

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Fig. 3 Time-resolved TV images (after image normalization) captured at (a) 2.5 ns and (b1)-(b2) 39 ns delay times, using ~10 J/cm² at 3ω. The main features observed are the particle (1), the plume (2), the shockwave (3) and the atomized melted material (4).

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The image shown in Fig. 2(a3) was acquired with the second probe pulse at 100 ns delay; the spatial scale of this image is different from all other images in Fig. 2 in order to fully capture the almost uniformly expanding shockwave (3) while the particle (1) is also visible. Figure 2(a4) is a digital zoom in of the image shown in Fig. 2(a3) at the same spatial scale used in Figs. 2(a1)-2(a2). This image demonstrates that in addition to the particle (1) that is separating from the substrate, there is also material visible as a darker feature (4) that is moving faster and around the particle. This material “flowing” around the particle must be associated with the portion of the particle that was melted by the laser beam. The ensuing flow of the plume gases (in air) is propelling the generated droplets of melted material faster than the particle as a result of the relatively smaller droplet size. The same behaviors were consistently observed during our experiments using either the 1ω or the 3ω pump lasers. For example, the image shown in Fig. 2(b2) was obtained using configuration 2 under exposure to 1ω fluence of about 100 J/cm². This image was acquired at about 100 ns delay and shows the particle clearly separated from the substrate while the melted material droplets (4) are traversing around and in front of the particle. Intriguingly, images of the particles captured at later delays demonstrate that regions in front of the particle exhibit reduced transmission of the probe light.

A typical (contrast enhanced) image captured at 500 ns delay while the particle is in flight (the substrate is not visible) is shown in Fig. 2(b3). This behavior suggests that at least part of the melted material forms nano-scale droplets that are captured by the airflow and eventually thrusted in front of the particle. The regions of higher concentration of droplets (atomized material) are visualized in the images as regions (4) of reduced transmission (due to higher scattering by the nano-droplets) of the probe light. The origin of this behavior will be discussed later. The images shown in Fig. 2 were captured using different optical magnifications as follows: 25X for Figs. 2(a1)-2(a4), 50X for Figs. 2(b1)-2(b2) and 10X for Fig. 2(b3). As expected, the optical magnification affects the image resolution and thus the sharpness of the features observed in each image.

The processes discussed above and illustrated by the SV images shown in Fig. 2 are also discernible using the TV microscope where, owing to the different observation geometry, additional information can be gained. Typical examples are shown in Fig. 3 obtained using the experimental configuration 1 upon irradiation with ~10 J/cm² at 3ω. In addition, to enhance the visualization of the transient effects, the time resolved images were normalized by the image prior to laser exposure; this normalization process makes the particle appear as a gray object. Figure 3(a) shows the normalized image captured at ~2.5 ns delay where a SS particle (1) is visible as a gray feature (due to the normalization process). The region outside the particle represents the surface of the substrate. The pump propagation direction is towards the observer (out of the page) at 36° with respect to the normal of the surface from the right hand side. Note that the images shown in Fig. 2 were acquired with the SV microscope which was located on the right hand side of the particle as viewed in Fig. 3(a).

The plume (2), which appears as a dark feature and the shockwave (3) are visualized in Fig. 3(a) and reveal an asymmetric expansion (faster towards the right hand side). This effect can be assigned to the oblique (with respect to the direction of observation) irradiation of the particle by the pump pulse, as discussed above. As a result, a larger section of the right hand side of the particle is exposed to the pump laser, thus generating a larger amount of plume. This in turn causes the generated shockwave to propagate at a higher speed on this (right hand) side of the particle. As the microscope is in focus near the surface of the substrate, the observed shockwave represents a cross section of the 3-dimensionally expanding shockwave near the intersection with the substrate. It must also be noted that although the exposure of the particle to the laser beam leads to the ejection of the particle, the movement of the particle is too small to be perceived in the time resolved images captured at early delays, when the plume is still visible. As the plume expands, the loss of transmission experienced by the probe pulse (strobe light) is decreasing; hence, the image contrast of the plume (to enable its visualization by our microscope system) is diminishing.

Figures 3(b1) and 3(b2) show the same time-resolved image captured by the second probe pulse at about 39 ns delay but displayed in two different magnifications. Figure 3(b1) shows a lower magnification image in order to include the expanding shockwave along with the particle. The expansion of the shockwave (3) remains asymmetric at this delay while the particle is also surrounded by the atomized melted material. This melted material is better visualized (and enhanced by the normalization process) in Fig. 3(b2) which is displayed using the same magnification as in Fig. 3(a). Contrary to the non-symmetric expansion of the plume and shockwave observed in the image captured at 2.5 ns delay (Fig. 3(a)), the atomized melted material is observed expanding symmetrically around the particle at 39 ns delay. This effect will be discussed in more detail in sections 4.2 and 4.3.

The formation of the plume and shockwave exemplified by the images shown in Figs. 2 and 3 are accompanied by the ejection (propulsion) of the particle originally attached on the surface of the substrate. Experiments to study the resulting speed of the particles as a function of the laser fluence and material density were performed using the experimental configuration 2 (1ω pump laser). The speed was estimated by capturing the distance traveled by the same particle at two predetermined delays. These delays were adjusted depending on the speed of the particle in order to allow sufficient traveled distance by the particle (on the order of 500 µm) to obtain an accurate estimate of its speed.

For the case of SS particles, Fig. 4(a) shows the measured (cross symbols) and averaged values (solid circle symbols) of the particle speeds for a set of discrete laser fluences (distributed between the threshold fluence for removal of the particle up to the fluence that would initiate laser induced damage of the substrate) in semi-logarithmic and linear (see inset) scale. The threshold fluence for removal of the SS particles was ~2.5 J/cm² where the particle ejection speeds averaged about 1 m/s. At this fluence, only a small fraction of the particles were ejected with speeds varying between 4 cm/s and 3 m/s. A continuously larger percentage of particles were ejected with increasing exposure fluence until about 14 J/cm² when all SS particles were ejected, however without a significant increase in the ejection speed (average speed of 1.3 m/s, speeds varying between 0.2 m/s and 6 m/s). Upon further increase of the exposure fluence, particle ejection speeds increased rapidly as a function of fluence. The results shown in Fig. 4(a) demonstrate a wide range of measured speeds for each laser fluence. This behavior cannot be attributed only to the varying size of the particles measured although larger particles were observed to exhibit, on average, lower ejection speeds compared to the smaller particles. Also, it cannot be fully attributed to the pulse to pulse variation of the laser energy. Possible underlying mechanisms will be discussed in section 5.

 

Fig. 4 (a) The measured (cross symbols) and averaged values (solid circle symbols) of the ejection speeds of stainless steel (SS) particles as a function of the 1ω laser fluence in semi-logarithmic and linear (inset) scale. (b) The average speed of stainless steel (SS), Aluminum (Al) and Tungsten (W) particles as a function of the 1ω laser fluence. Particle size ranges for each material are given in the text.

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Similar measurements were performed using Aluminum (Al) and Tungsten (W) particles having an average diameter of 29 µm (between 15 µm and 42 µm) and 33 µm (between 23 µm and 48 µm), respectively. The ejection fluence thresholds for both Al and W were similar to that of SS, however the average ejection speed at fluences below 10 J/cm² was significantly lower than those observed in SS particles. Specifically, the average ejection speed at the ejection threshold was about 10 cm/s and 4 cm/sec for Al and W, respectively. In addition, a wide range of measured particle speeds (at each fluence) was also observed in both Al and W particles, similar to the spread observed for SS particles (see Fig. 4(a)). For clarity, Fig. 4(b) displays only the average speed values for each particle type. Another interesting behavior should be noted in the fluence range for which the probability of ejection is less than 1. Namely, although some of the particles were not removed, it was often the case that their position on the substrate changed following exposure to the pump laser pulse, shifting as much as 15 µm from the original position. This effect may be assigned to the generation of an impulse by the laser pulse which however was not sufficient to overcome the attractive adhesion forces (van der Waals) between the particle and the substrate.

Figure 4(b) demonstrates that the average particle speed varies with the particle mass density (SS:8, Al:2.7, W:19.3 g/cm³). Between Al and W, there is a difference of about one order of magnitude in the mass density and, similarly, in the average particle ejection speeds for fluences above 50 J/cm². This behavior indicates that the speed of the particle is inversely proportional to its density for fixed laser fluence and therefore, the momentum of the particle may be similar for all three types of particles.

Figure 5(a) shows the average particle momentum as a function of laser fluence for the three materials used. The motivation for this analysis arises from the modeling of the recoil momentum transfer under exposure to laser irradiation (ablation) adopted for various applications such as space debris cleaning with lasers as well as laser propulsion [37]. The momentum transfer is due to the ejection of material from the surface (of the particle). Within this physical construct, a key parameter is the coupling coefficient C_m, which represents the ratio of momentum (ΔP) imparted to the target (particle) and the incident laser energy (E), as C_m = ΔP/E. The dependence of the momentum on laser fluence for all particle types becomes linear above 1ω fluence of about 60 J/cm², indicating that the value of C_m (slope) becomes nearly constant. The experimental data in Fig. 5(a) can be re-cast to reveal the dependence of C_m on the laser fluence as shown in Fig. 5(b). The results suggest a similar behavior of Cm vs. fluence, for all particle types. Namely, Cm starts at a value of about 0.1 dyn/W or less at the lowest fluences, then increases and rolls over between 0.6 dyn/W and 1 dyn/W at fluences beyond ~60 J/cm². The underlying mechanism for this behavior will be discussed in more detail in sections 4.3 and 5.

 

Fig. 5 The average (a) particle momentum and (b) momentum coupling coefficient Cm as a function of the 1ω laser fluence for stainless steel (SS), Aluminum (Al) and Tungsten (W) particles.

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Figure 6(a) shows the distance traveled by the generated shockwave at 500 ns delay as a function of the laser fluence. The shockwave was not visible at fluences lower than about 20 J/cm², possibly because its strength was too small to be detected using our system (too small a change in the refractive index of the air). The results show that the shock front position at 500 ns delay monotonically increases with the laser fluence and is about the same for SS and Al, but slightly lower for W particles. The results shown in Fig. 6(a) will be compared to theoretical modeling results discussed in the next section. It must be noted that the observed variation in the measured distance traveled by the shock is smaller to that observed for the ejection speed of the particles. The inset in Fig. 6(a) shows the measured and averaged values of the shock distance traveled for the case of stainless steel (SS) particles. Similar variation was observed for the Al and W particles.

 

Fig. 6 (a) Distance traveled by the shockwave at 500 ns delay and (b) normalized particle kinetic energy (to R⁵) as a function of the 1ω laser fluence for stainless steel (SS), Aluminum (Al) and Tungsten (W) particles. Inset shows the measured and averaged values of the shock distance traveled in stainless steel (SS) particles as smaller and larger solid circle symbols, respectively.

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The distance traveled by the shockwave is directly related to the energy deposited during the interaction with the laser pulses. Specifically, assuming for simplicity a simple point explosion, the total energy deposited (E_total) is the sum of the thermal energy (E_thermal) and the kinetic energy (E_kinetic) of the surrounding gas (shock energy). These components (for the ideal case) are about equal E_thermal≈E_kinetic≈ρ₁(R⁵/t²) where ρ₁ is the background fluid density (ambient air in our case) and R(t) the shock radius (at time t). In our case, two additional energy components must be included: the kinetic energy of the particle (E_particle = mv²) and the energy spent to generate the additional components of ejected material (E_ejecta = E_{metal evap} + E_{SiO2 evap} + E_{ejecta kin}). The latter involves the evaporation of metal and substrate material as well as the kinetic energy of the plume and atomized particles generated. The partitioning of energy between these processes is not trivial. However, the experimental results can be used to monitor the change in the amount of energy partitioned to the shockwave (E_thermal≈ρ₁(R⁵/t²)) to that partitioned to the kinetic energy of the particle (mv²) as a function of laser fluence. As ρ₁ (air density) and t (500 ns) are constants, the ratio mv²/R⁵ provides a method to gain insight into the energy partitioning mechanisms (results shown in Fig. 6(b)). This will be discussed in more detail in section 4.3.

As discussed in the previous section, the pump beam was incident at either 0° or 36° on the sample’s surface. Experiments were performed to monitor the direction of ejection of the particles with respect to the surface normal under 3ω irradiation and 36° incident angle. We found that the particle is traversing through air at an intermediate angle of about 20°, between the propagation direction of the laser pulse and the surface normal. This observation suggests that more than one mechanism is involved in the particle ejection process. The origin of this behavior will be discussed in more detail later.

Laser ablation of the particle involves i) ablation of at least part of the particle surface exposed to laser light (depending on laser fluence) and ii) formation of a plasma. It is known that this plasma can interact with the incoming laser pulse during the exposure of the metal to the laser beam [38]. In the experimental geometry utilized in the present work, the particle is attached on the surface of the substrate but the region around the particle is quickly filled with the formed plasma as clearly revealed in the time-resolved image shown in Fig. 2(a2) (taken at 2 ns delay). To better understand this issue, we used the experimental configuration 3 to capture two images of the expanding plume during the pump laser pulse using two orthogonally-polarized, 180-ps probe pulses that were temporally separated by 2.4 ns. This experiment was performed with a 3ω pump laser fluence of about 8 J/cm². From each pair of images of the same ablation event, the instantaneous speed of expansion of the plasma plume along the surface of the substrate was measured as well as the distance traveled (from the point of contact of the particle with the substrate) of the outer boundary of the plasma. The results are shown in Fig. 7. Specifically, Fig. 7(a) shows the speed of the plume during the pump laser pulse (shown with dashed line) as a function of the probe 1 delay. It must be noted that the speed measured represents the average value during the time elapsed between the two probes, thus starting at the probe 1 delay time (shown in Fig. 7(a)) and continuing for 2.4 ns. It is observed that initial speeds (with the onset of plasma formation) are on the order of 10 km/s and decline to about half this value by the end of the laser pulse. This speed profile is highly sensitive to the pump laser fluence and probably to the laser wavelength. The detailed dependence on these parameters has not been investigated as part of this work. However, using a fluence of about 4 J/cm², the measured speed of plasma expansion was on the order of1.5 km/s. These limited results offer evidence of its strong dependence on laser fluence. Figure 7(b) shows the position of the plasma front/boundary along the surface of the substrate as a function of the delay time. It can be appreciated that the volume between the particle surface and the substrate can be rapidly occupied by the generated plasma (15-μm average radius of the particles shown for reference) which can subsequently interact with the pump laser pulse. This interaction can lead to loss of laser energy reaching the particle, additional energy deposition on the plasma that in turn can cause modification of the substrate, modulation of the energy partitioning and other possible effects that will be discussed in more detail in sections 4.3 and 5.

 

Fig. 7 (a) The speed of the plume during the laser pulse and (b) the distance of the outer boundary of the plasma from the contact point of the particle with the substrate as a function of the probe 1 delay (time separation between probe 1 and 2 was 2.4 ns).

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The expansion of the plume at such high speeds exposes the surface of the substrate to the generated plasma during the laser pulse. The plasma near the surface and the interface between the particle and the substrate interacts with the laser pulse and absorbs energy. This localization and continuous “heating” of the plasma causes modification of the substrate and gives rise to the formation of a pit (crater). To better understand this process, we measured the spatial characteristics of the formed pits (using confocal microscopy) as a function of laser fluence. Figure 8(a) shows typical pit profiles (average width and depth at the center of the pit, presumably the contact point) for various laser fluences for the case of SS particles. The average width and depth of the pits as a function of laser fluence are shown in Fig. 8(b).These pits were created by 1ω excitation in the experimental configuration 2. Although the onset for ejection of the particle is at about 2.5 J/cm², the threshold for the formation of a pit was found to be at about 8 J/cm². The depth profile of the pit has a nearly Gaussian shape for fluences up to about 70 J/cm², as observed in the representative profiles of the pits shown in Fig. 8(a). Above this fluence, the profile of the pit becomes more complex up until about 120 J/cm² where classical laser damage of the substrate at the location of the particle (with depths on the order of 10 µm) is observed.

 

Fig. 8 Pit morphology following laser ablation of SS particles: (a) Representative cross-section profiles and (b) average width (along with range of values observed shown by vertical bars) and average depth as a function of 1ω laser fluence.

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The results shown in Fig. 8 demonstrate that both, the pit depth and the pit width increase with laser fluence. A semi-circle having diameter equal to the average size of the SS particles used in the experiments is shown in Fig. 8(a) in order to facilitate direct comparison of their physical dimensions to the width of the formed pit. For lower fluences, the results suggest that the pit is developing only close to the contact point between the particle and the substrate. However, as the fluence increases, the width of the pit at the base (surface of the substrate) increases and, at about 50 J/cm², the average width is about equal to the diameter of the particle. A rapid increase of the width is observed upon further increasing the fluence and reaches about 180 µm at a fluence of 100 J/ cm² (about 6-7 times the diameter of the particle). A very wide range of widths and depths at each laser fluence tested was observed as indicated in Fig. 8(b) by the vertical bars (representing the upper and lower measured values of the pit widths only). This behavior parallels the large variation of the observed speeds of the particles discussed earlier. We attribute this variability to the plasma confinement conditions and the localized plasma density after each exposure. These parameters are governed by the localized shape of the particle near its point of contact with the substrate, the amount of surface area of the particle that is ablated and the size of the contact area (area of complete plasma confinement) at the point of attachment of the particle to the substrate.

Figure 9 exemplifies the strong dependence of the spatial dimensions of the pit on the temporal characteristics of the laser pulse. This set of experiments was performed using a different laser facility that offers flexible temporal profiles of the laser pulse and operates at 3ω. Nominally, spherical aluminum particles positioned on the exit surface of fused silica substrates and having diameter of about 6.5 µm were exposed to laser pulses having tailored temporal profiles. The results shown in Fig. 9 were obtained using two different pulse shapes shown in the inset of Fig. 9. The first pulse shape (denoted as t1) is a temporally “flat-top” pulse having duration of 5 ns. The second pulse shape (denoted as t2 in Fig. 9) was a double pulse where the 5 ns “flat-top” pulse was preceded by a 1.5 ns flat-top pre-pulse with about 10 ns separation between the two pulses. The spatial profiles d1 and d2 of the formed pits shown in Fig. 9 correspond to the pulse shapes t1 and t2, respectively, and represent the average of three profiles that were obtained under fluence of about 7.5 J/cm² (for both pulse shapes). The results indicate that the “flat-top” pulse (t1) created nearly conical pits that are significantly smaller in width (but not depth) to the pits formed using the double pulse profile (t2). The nearly conical shape of the pits formed under “flat-top” pulses was confirmed for larger in diameter (on the order of 30 µm) particles. The results shown in Figs. 8(a) and 9 demonstrate that the shape of the pit is strongly dependent on the temporal characteristics of the pulse, suggesting that etching on the substrate is occurring, at least largely, during the laser pulse. This issue is discussed in more detail in section 5.

 

Fig. 9 The spatial profiles (d1 and d2) of pits formed after the removal of Al particles having diameter of ≈6.5 µm under exposure to 3ω pulses with different temporal profiles (t1 and t2, respectively) and total fluence of about 7.5 J/cm². The inset shows the temporal profiles of the laser pulses.

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4. Theoretical considerations

4.1 Material ejection mechanisms

Upon exposure of a material to a laser beam, energy is absorbed and deposited over a layer near the surface of the material with thickness determined by the absorptivity (A) and thermal diffusivity (D) of the material and the pulse duration (τ). For the case of a spherical particle, the energy deposited locally can be described by the product$A(\theta )\cdot F(\theta )$, where θ is the angle of incidence (θ <90°) and F is the laser fluence. Although $A(\theta )$ varies strongly with θ for metals, it can be shown that the product $A(\theta )\cdot F(\theta )$remains fairly constant over a large area of the particle (range of θ’s) exposed to the laser beam (see Fig. 2 in [39]), i.e., an effective, angle-independent absorptivity, $A\approx A(\theta =0)$ can be used. This energy deposition can lead to kinetic energy transfer to the particle and its subsequent ejection from the substrate via two main mechanisms related to a) thermal expansion of the particle and b) formation of plasma. We will discuss these processes in more detail next.

4.1.1 Process a: The thermal expansion mechanism

This process has been described in detail elsewhere [40] and is depicted in Fig. 10(a). Fast heating of the metal particle located on the transparent substrate results in its thermal expansion that pushes the particle surface against the substrate. If the kinetic energy of this expansion exceeds the attachment energy due to the van der Waals forces, the particle will be ejected from the substrate.

 

Fig. 10 Depiction of the key mechanisms of particle ejection (with speed u) following exposure to ns-laser pulses: (a) Thermal expansion; (b) Recoil momentum transfer; (c) Confined plasma pressure; (d) Partially confined plasma. The laser is incident normal to the surface of the substrate and the particle is located on the exit surface.

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An upper estimate for the speed of the ejected particles will be the speed of the thermal expansion:

4.1.2 Plasma formation and associated processes

Plasma formation on the surface of a metal during its exposure to a laser pulse has been considered to be associated with the onset of intensive evaporation [41]. The onset of the evaporation process occurs when the deposited energy in the outer layer reaches a value of ~$H\sqrt{D\tau }$, where H represents the enthalpy required to evaporate the material and $\sqrt{D\tau }$ represents the thermal diffusion depth. Thus, to a first order approximation, $H\sqrt{D\tau }$ has been considered to be associated with the plasma formation threshold [42]. Assuming a flat surface and normal incidence of the laser pulse, the threshold fluence F_t is obtained from:

The ejection of material from the surface will lead to transfer of momentum, thus causing motion of the irradiated particle. However, there are three distinct cases that can be involved within the specific particle-substrate geometry involved in this work (the metal particles are attached and irradiated through a silica surface) and relate to the degree of plasma confinement (either none, partial or complete confinement) within the region of plasma generation. We will further discuss each of these cases next.

4.1.2.1 Process b: Recoil momentum transfer

The process related to the momentum transfer due to the ejection of material from the surface is depicted in Fig. 10(b) and has been studied in detail for applications such as space debris cleaning using lasers as well as laser propulsion [37]. A crucial parameter is the coupling coefficient C_m briefly introduced in Section 3, which represents the ratio of momentum imparted to the target (particle) to the incident laser energy (C_m = ΔP/E). C_m reaches maximum value at excitation conditions just above the plasma formation threshold and has been associated with an optimal intensity $I_{opt}$ described as [41]:

A review of data on the dependence of the maximum value of C_m on laser intensity for different materials has been presented by Phipps et al. [41] where the experimental data from different research groups obtained over a broad range of wavelengths, pulse durations and pulse energies are summarized. These results indicate that the maximum value of C_m does not change significantly between different materials and wavelengths and near maximum can be treated as a constant for a wide range of intensities. Typical values of C_m are 1-10 dyn/W [41].

The recoil momentum is directed normal to the surface at each point and integration of the momentum over the entire surface is required to estimate the speed (and direction of motion) gained by the object. Assuming a spherical object, the estimation of the speed ($u_b$) is presented in [37] as:

4.1.2.2 Process c: Complete plasma confinement

This mechanism is dominated by the pressure applied to the particle as plasma develops in the region where the particle makes contact with the substrate (see Fig. 10(c)). This plasma is confined within the silica-metal interface. To a first approximation, assuming a temporally flat-top pulse, the pressure P at the interface is given by expression [42]:

The confinement conditions exist only within the area of contact with radius a (see Fig. 10(c)); this area can be estimated from the solution of the Hertz problem [43]. The particle is attached to the surface due to van der Waals forces with the adhesion energy per unit area φ (work of adhesion) given by:

4.1.2.3 Process d: Partial plasma confinement

Partial confinement conditions can exist well outside the area of direct contact between the particle and the substrate as depicted in Fig. 10(d). As the gap/separation, s, between the particle and the substrate increases with distance from the point of contact and the speed of expansion of the plasma is in the order of 1-10 µm/ns (see Fig. 7 and associated discussion), the pressure builds up within the volume where s is sufficiently small, similarly to the complete confinement situation in Section 4.1.2.2. The velocity v of the vapor-plasma plume (generated at the particle) expansion is about equal to the ion thermal velocity and therefore, the confinement formation time is $t_{cf}~2s/v$ (the time for the shock to reach the substrate and be reflected back to the surface of the particle). At threshold conditions, plasma is generated near the peak of the pulse (shifting at earlier times with increasing intensity). Subsequently, the confinement formation time t_cf cannot exceed ~1/2 of the pulse duration, τ. Therefore, the maximum value of s is $s_{\max }~v\tau /4$.

It was recently demonstrated (using plane targets) that the coupling coefficient is independent from the gap size s for small values of s [44]. Therefore, we can assume that coupling coefficient C_m under partial confinement is about that same as the coupling coefficient for the complete confinement case in Eq. (10). Therefore, the particle velocity can be expressed as:

4.1.3 Estimation of particle velocity

The analytical equations of the particle velocity for each individual mechanism can be used to estimate the strength of the individual mechanisms contributing to the particle ejection discussed above. Let us first consider the case of stainless steel (SS) particles. For the mechanism of ejection via thermal expansion, the parameters for Eq. (3) are β~10⁻⁵ /K, ρC~4 J/cm³K, absorptivity A~0.3. Assuming a fluence of F~1 J/cm² and pulse duration of 10 ns (used in the experiments), the estimated ejection speed $u_a$ is on the order of 20 cm/s (without considering the energy needed to overcome the adhesion forces). For the estimation of the plasma formation threshold, the parameters for Eq. (4) are H~50 kJ/cm³, A ~0.3 and D~0.04 cm²/s, thus resulting in an estimated fluence threshold F_t~3.5 J/cm². To estimate the velocity induced by the recoil momentum transfer mechanism, the parameters for Eq. (6) are ρ = 8 g/cm² and C_m = 3 dyn/W. For 30 µm diameter SS particles (as used in the experiment), the estimated particle speed is $u_b$ (m/s) = 0.57x F(J/cm²) or about 11 m/s for exposure to a laser pulse of 20 J/cm². To evaluate the case of complete plasma confinement, we need to consider the impedance values for Eq. (8) which are Z_SS = 4.6x10⁶ g/cm²s for SS particles and Z_Silica = 1.3x10⁶ g/cm²s for the silica substrate. Consequently, the value of the effective impedance of the metal-glass interface is estimated to be Z~2x10⁶ g/cm²s. Using Eq. (10), the value of the coupling coefficient is $C_m^1$~150 dyn/W for I = 1 GW/cm². This value is about 50 times higher compared to the case with no plasma confinement. Using Eq. (12) and $A\text{'}$~2 eV, we find that the radius of confinement, a, is ~120 nm (for particle radius of 15 µm). In the partial confinement case, a plasma temperature of 0.5 eV or larger is expected and, as a result, the thermal velocity is v~900 m/s ($\text{v}=\sqrt{T/{\text{M}}_{\text{A}}}$, where ${\text{M}}_{\text{A}}$ is the atomic mass of Fe) and s_max ~2.25 µm assuming 10 ns pulses.

The above theoretical considerations and simplified analytical forms of the particle speeds from each specific mechanism will be used to estimate the speed of SS, Al, and W particles having a diameter of 30 µm as a function of laser fluence (1ω, 10 ns). It must be noted that the estimated plasma formation threshold of Al particles is noticeably higher, F_t ~13.5 J/cm² due to its higher thermal conductivity. In addition, the plasma formation threshold estimate for W particles is even higher, with F_t ~18.7 J/cm². The estimated ejection speed values are summarized in Table 2 for different fluences of 4 J/cm² (near the experimentally observed threshold of particle ejections), 20 J/cm², 40 J/cm² and 100 J/cm². The experimentally measured ejection speeds of the particles at these fluences are also provided in Table 2 (last row) to enable comparison with model predictions.

Table 2. Comparison of models with experiment can enable an estimate of the contribution of each mechanism as a function of laser and material parameters.

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Comparison of the modeling with the experimental results shown in Table 2 suggests that for lower fluences (near threshold of particle ejection) the measured speed is comparable to that provided by process (a) (thermal expansion mechanism in Fig. 10). It must be noted that the estimated values do not take into consideration the energy needed to detach the particle from the surface (overcome the van der Waals forces). This can explain the lower measured speed compared to the corresponding estimated speeds. For fluences above 20 J/cm² (except for W particles at 20 J/cm²), the estimated speeds from process (b) (recoil momentum mechanism in Fig. 10) appear to be very similar to the experimentally measured values. However, experimental evidence using 3ω pulses are strongly suggestive that process (d) also provides a significant contribution (at least at shorter laser wavelengths). The confinement effect is expected to be strongly dependent on the surface roughness and particle shape at the point of contact with the substrate. In addition, the confinement geometry changes during the laser pulse as the particle starts moving away from the surface (even for a fraction of a micron), thus enabling lateral flow of the plasma. These pre-existing and transient plasma confinement conditions affect the induced particle speed. We suggest in the next section that this mechanism can explain the big dispersion in the measured speeds and pit depths at each fluence setting. The presence of plasma confinement conditions was recently demonstrated elsewhere [45] by investigating the plasma emission characteristics under identical experimental conditions.

4.2 Plume and atomized material flow

Figure 2 shows the generation of the plume but also the presence of a “spray” of small droplets formed by the liquefied (by the laser pulse) near surface layer of the particles. Figure 2 demonstrates that part of the spray is directed around the particle (Fig. 2(a4)) and later in front of the particle (Fig. 2(b2)). This behavior can be understood based on the above discussion regarding the main mechanisms governing the motion of the particle. The initial evaporation and melting of the particle will generate a plume and gas flow orthogonal to the surface of the particle, thus towards the substrate. This gas is subsequently deflected by the surface and starts propagating around and away from the particle. This behavior is captured in the time resolved image in Fig. 2(a2) and partially quantified by the results shown in Figs. 7(a)-7(b). The gaseous plume flows around the particle with a speed that is about two orders of magnitude higher than the speed of the particle. This behavior is depicted in Fig. 11(a). The superheated gaseous plume (a mixture of evaporated metal, substrate silica and ambient air) flowing around the particle captures some of the generated liquid droplets which, due to their small size, are completely confined within the gas flow. This eventually brings at least some of these liquid droplets in front of the particle as depicted in Fig. 11(b) and shown in the time resolved image of Fig. 2(b3). However, images of the substrate after the ejection of the particle as well as other experimental evidence presented elsewhere [32,35] indicate that some of these droplets are ejected toward the surface of the substrate, thus causing its contamination. We propose that principal mechanisms responsible for this complex dynamicsare the following. First, larger droplets maintain their trajectory in the presence of gas flow more efficiently than smaller droplets. Therefore, the larger droplets produced by the melted layer of metal in the particle can reach the substrate. Second, it was recently shown that laser superheating of materials leads to liquid droplet ejection that continues for a relatively long period of time, on the order of 1 µs until a thermodynamically stable liquid is reached [46]. It is therefore likely that the droplets reaching the substrate were ejected later during the volume boiling process when the gas flow was also reduced or even reversed [47]. Conversely, the droplets trapped in the airflow were ejected early in the process when the speed of the gas flow was high.

 

Fig. 11 Schematic depiction of (a) the initial expansion of the plume and (b) the subsequent trapping in the flow of the atomized melted material layer based on the experimental observations shown in Figs. 2 and 3.

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4.3 Interaction of the laser pulse with the plume

The results shown in Figs. 7(a)-7(b) (speed and position of the plasma as a function of the delay time) demonstrate that the plasma rapidly expands in the volume between the particle surface and the substrate early during the laser pulse. Consequently, the later part of the laser pulse interacts with this plasma to induce a secondary heating (energy deposition). On the other hand, the laser energy absorbed by the plasma is inhibited from reaching the metal particle, thus effectively reducing the energy deposition on the particle.

The absorptivity of the ionized plume has a strong dependence on the laser wavelength. In particular, it is known that the critical plasma density at 1ω is about one order of magnitude lower than at 3ω ($n_{cr}={10}^{21}/{\lambda }^2$, where λ is the wavelength in µm). Even for 3ω, this density is smaller than the particle solid density. As the plume expands from the particle during the laser pulse, its density varies and can be higher than n_cr, especially in the confined and partially confined plasma regions. Therefore, there is a separation distance L between the laser absorption zone in the plasma and the ablation surface (solid surface) after the onset of plume expansion. Within the steady state plane ideal plasma model, the distance L which separates the target ablation surface from the absorption front near the critical density surface (where laser energy is absorbed via inverse bremsstrahlung) is $L~I^{4/3}{\lambda }^{14/3}$ [48] and rapidly increases with increasing laser wavelength. Specifically, this distance (L) is 170 times smaller at 3ω than for 1ω laser light.

For irradiation of the particle with 3ω pulses, the absorption zone in the plasma remains very close to the particle surface for the entire duration of the pulse. Consequently, the results of the plane target experiments [41] represent a good approximation to describe the particle ablation case. Under 1ω irradiation, the separation between the laser absorption zone in the plasma and the particle surface rapidly increases with time (as the plasma expands during the laser pulse) leading to a distance that can be comparable with the particle size. As a result, the laser energy reaching the particle and consequently, the efficiency of momentum transfer to the particle decreases in comparison with the 3ω case. Instead, because the plasma motion is three dimensional and its size can expand beyond the size of the particle during the laser pulse, laser energy is transferred in the lateral plasma flow, thus favoring energy partitioning towards increased plasma and shock energy instead of kinetic energy of the particle. This mechanism supports a higher efficiency in transferring kinetic energy to the particle with 3ω light compared to 1ω. This predicted behavior was investigated by comparing the speed of particle ejection under exposure to 1ω vs. 3ω pulses. The results (not shown here) demonstrated that the ejection speed of the particles under 3ω irradiation is at least 3X or higher than that under 1ω irradiation for similar laser fluences and pulse characteristics.

The larger amount of laser energy reaching the particle after traversing through the plasma under 3ω irradiation is also affecting the amount of liquid material produced after exposure of the particle to the laser pulse. This predicted behavior is captured by the time resolved images shown in Fig. 2(a4) and Fig. 2(b2), both acquired at about 100 ns delay under about 10 J/cm², 3ω and about 100 J/cm², 1ω laser fluence, respectively. The generated liquid material is observed to flow around the particle (as discussed above) but the images suggest that the amount of liquid material is similar, if not larger for the 3ω pulse, despite the 10X difference in the laser fluence. This qualitative example supports the potentially important role of the absorption of laser light by the plasma in this secondary energy deposition process.

Another manifestation of the role of laser energy absorption by the plasma in the dynamics of particle ejection is captured by the TV images showing the expansion of the plume and the melted material for the case of excitation with 3ω pulses shown in Figs. 3(a)-3(b). Due to the 36° angle of incidence of the laser beam with respect to the surface of the substrate, the plume expansion is stronger on the right hand side (see Fig. 3(a)) of the particle, as a larger fraction of this side of the particle is illuminated by the laser beam. On the other hand, the discharge of the liquid material around the particle observed at 39 ns delay (see Fig. 3(b1)-3(b2)) is symmetric around the particle. As discussed earlier, the motion of the liquid material is due to the aerodynamics (gas flow around the particle). We postulate that this behavior indicates that after the initial non-symmetrical plasma expansion and shock generation, the heating of the plasma generates a more symmetric gas flow which leads to the symmetric flow around the particle of the atomized liquid material. It is worth noting in the typical example shown in Fig. 3(b1) that, although the shock continues to propagate in a nonsymmetrical fashion (travels longer distance on the right hand side), the motion of the liquid material is symmetric, suggesting that this symmetry was achieved after the initial launch of the shockwave.

The secondary plasma heating is also affecting the energy partitioning. This issue was in part examined through the analysis presented in Fig. 6. In particular, Fig. 6(a) shows that the distance traveled by the shockwave at 500 ns delay is approximately the same for SS and Al particles but somewhat lower for W particles. Since the distance traveled is related to the energy deposited (as discussed in the previous sections), we conclude that the energy allocated to the shock is about the same for SS and Al particles but somewhat lower for W particles. This may be related to the higher plasma formation threshold for W. On the other hand, Fig. 6(b) represents (in relative terms) the ratio of energy apportioned to the kinetic energy of the particle vs. shock energy. The latter is related to the heating of the background gas. Therefore, the secondary heating to the plume by the laser beam adds to this component, and is expected to monotonically increase as the fluence increases since the density of the generated plume (and therefore, energy deposited via secondary heating) increases while the fraction of the laser beam reaching the particle decreases. This mechanism may be responsible for the decline observed in the mv²/R⁵ ratio (kinetic energy of the particle compared to shock energy) for fluences above 60 J/cm² in Fig. 6(b). Specifically, as the fluence increases, the density of the generated plume increases and subsequently causes increased absorption in the plume and reduction of the fraction of laser light reaching the particle (thus reduced fraction of energy partitioned to kinetic energy of the particle). On the other hand, for fluences lower than about 60 J/cm², the increase in the energy ratio (mv²/R⁵) as a function of fluence can be assigned to the fact that a larger portion of the surface of the particle reaches the ablation threshold, thus increasing the amount of material removed and acquired recoil momentum. This behavior suggests that the maximum ablation area of the particle is reached at about 60 J/cm². This fluence also corresponds to the value where C_m reaches its asymptotic limit with increasing fluence (see Fig. 5(b)).

5. Discussion

As discussed in the introduction section, the objective of this work is to understand and quantify the relative strength of the mechanisms involved in the interaction of metallic particles with laser beams. The experimental framework adopted in this work involving the use of a spherical particle attached on the exit surface of a silica substrate provides a simple model to help simplify the analysis of the experimental results. Specifically, the use of spherical particles allows for a simple geometry that can facilitate quantitative interpretation of the experimental results using modeling tools. In addition, such spherical particles are widely available for various materials and sizes. Also, the use of a substrate for the attachment of the particles enables repeated measurement under identical experimental conditions. Furthermore, the attached particle on the exit surface is released (ejected) after exposure to the laser pulse allowing for quantification of the acquired kinetic properties. However, this experimental construct creates a confined plasma condition (between the particle and the substrate) that introduces additional processes and energy loss mechanisms. Although the adopted experimental model may be ideal for certain applications, for the general case it can be considered as an acceptable compromise considering the drawbacks of other approaches such as using a free falling particle experimental approach where it would be very difficult to perform controlled experiments under identical excitation conditions. This work aims to help achieve a deeper understanding of the governing mechanisms which in turn can enable expansion of the findings of this work to describe the general case of arbitrarily shaped metal particle interacting with laser beams over a wide range of excitation parameters. We will examine next a number of these underlying mechanisms and how they affect the interaction of the particle with the laser pulse to complement the evaluation of specific mechanics discussed in section 4.

For fluences at the threshold of particle ejection, on the order 2-8 J/cm², a characteristically different ejection threshold speed for each type of particle is observed in the results shown in Fig. 4(b). Specifically, while the average ejection threshold speed for SS particles is about 1 m/s, the corresponding average speeds for Al and W particles are about 15 cm/s and 5 cm/s, respectively. Based on the particle mass density or particle size, there is clearly no apparent correlation. However, we qualitatively observed that the SS particles were more strongly attached on the surface while the W particles exhibited the weakest attachment. This conclusion emerges from the observation that, after each single-shot exposure of a particle to a higher (than threshold) fluence, particles outside the area exposed to the laser beam were also removed, presumably due to their interaction with the resulting shockwave. During the experiments we observed that the rate and distance where particles were removed after each such exposure was clearly larger for W particles than for SS particles, while the behavior of Al particles was intermediate. This qualitative behavior correlates with the ejection threshold speed of the particles. While the modeling suggested that the thermal expansion mechanism dominates the particle ejection at the lowest fluences, the force generated must overcome the van der Walls and potentially other binding forces. Based on the observed behavior discussed above, these binding forces are strongest for SS particles and weakest for W particles. Consequently, a smaller force (which corresponds to a smaller thermally induced speed) is required to release the W (and Al) particles compared to SS particles.

In addition to the shock propagating in the air, a shock is also launched inside the metal particle. Although the experimental results cannot probe this effect, it was observed that at higher fluences, Al particles would often disintegrate into small fragments after exposure to the laser pulse. The resulting fragments of the original spherical particle (2 or more, largely depending on the laser fluence) were still traveling away from the surface of the substrate, indicating that the breakup event took place after the original particle was ejected from the surface. We attribute this behavior to the shock formed inside the particle, which for the case of Al spherical particles can exceed its mechanical strength. However, for the general case of randomly shaped metal particles, the shape of the particle may support a larger amount of laser energy deposited (larger surface to volume ratio) which will lead to stronger shocks formed inside the particle. This can support breakup of particles of higher strength materials.

As discussed earlier, irradiation of the SS particles with 3ω light incident at 36° with respect to the surface normal demonstrated that the particles are ejected at about 20°. We proposed that more than one mechanism is involved in the particle ejection process. It was also suggested in the theoretical section that the dominant mechanisms transferring momentum to the particle are a) recoil momentum transfer and b) plasma confinement. The former would provide momentum that is along the direction of laser beam propagation while the latter would largely thrust the particle along a direction vertical to the surface of the substrate. What was not considered in the modeling was the secondary heating of the plasma contributing the overall shock formation and gas/vapor flow. Based on the 20° angle of ejection under the experimental conditions used, it can be estimated that the contribution of the recoil momentum mechanism is about 1.25 times that of the plasma induced mechanism (at 3ω).

The formation of the pit is attributed to the interaction of the substrate with the plasma. As the fluence increases, a larger section of the exposed surface of the particle ablates and a larger amount of laser energy is deposited per unit area of the particle leading to increased volume of ablated material. This in turn leads to higher plasma density and temperature while a larger area of the substrate near the point of contact with the particle is exposed to plasma capable of causing removal of material (plasma etching or a similar mechanism). Previous studies have suggested that etching of the substrate takes place during the laser pulse [48,49]. Experiments performed in this work (in part exemplified by the results shown in Figs. 8(a) and 9) also suggest a dependence of the size of the pits on the pulse shape and pulse durations. We therefore conclude that the etching of the material to form the pit is occurring during the laser pulse. The heating of the plasma by the laser beam to maintain its high temperature, although in contact and interacting (losing energy) with the substrate, is critical for sustaining the etching process. As the laser fluence increases, a larger amount of energy is deposited in the plasma while the area where plasma is dense enough to cause etching (etching rate) increases. This is supported by the increased amount of ablated material with increasing laser fluence but also by the increased speed of plume expansion, thus exposing a larger area of the substrate to plasma that is dense enough (during the laser pulse) to support etching. As a result, the width of the pits increases with laser fluence and can become significantly larger that the size of the particle. Furthermore, the presence of a pre-pulse in the experiments depicted in Fig. 9 generates plasma that reaches the surface of the substrate and is subsequently heated by the main pulse. As a result, the etching process may originate not only from the point of contact of the particle with the substrate (which is the case in the absence of the pre-pulse) but from a wider area. This leads to the formation of a pit that is wider but of approximately the same depth to that formed when only the main pulse is present. On the other hand, there is a threshold fluence that can support etching of the substrate, found to be about 8 J/cm² for our 1ω (SS particles) pump experiments.

Although the particles are nominally spherical, some surface irregularities can be discerned even via lowest magnification optical microscopy, i.e. 10X. This can introduce variability in the geometry of irradiation, the area of plasma confinement and the direction of initial expansion of the plume. As a result, the delay time corresponding to the initiation of ablation and plume ejection as well as the spatial distribution of plume density during the laser pulse can significantly vary. These variations can affect the amount of laser energy deposited on the particle and the confined plasma, thus the total energy deposited into the system. The results shown in Fig. 4 demonstrate a wide variability in the measured ejection speed of the particles for same irradiation conditions (fluence). The results shown in Fig. 8 also demonstrate a large variation in the spatial dimensions of the resulting pits under exposure to nominally same laser fluences. We propose these observations are largely due to the initial geometrical conditions of the particle-laser interaction and, to a smaller degree, to the variations in the size of the particles and laser fluence (for each measured particle exposure).

The momentum acquired by a target following laser ablation of a surface region (laser propulsion) has been described (as discussed in the modeling section) in terms of a coupling coefficient C_m, which represents the ratio of momentum transferred to the target to the incident laser energy (C_m = ΔP/E). For the general case, C_m reaches maximum value at excitation condition just above the plasma formation threshold and remains about comparable thereafter. For the case of metallic spherical particles, the plasma formation threshold within the area of the particle exposed to the laser beam varies depending on the position (angle) from the point of contact (incident laser light normal to surface) and polarization of light. With increasing fluence, the area where ablation is initiated also increases, leading to an increase in the effective value of C_m. When the entire area of the particle exposed to the laser beam reaches the ablation threshold, the value of C_m is expected to reach a nearly constant value, as for the general case. The results shown in Fig. 5(b), depicting the experimentally estimated value of C_m as a function of fluence, demonstrate this expected behavior. Specifically, the value of C_m starts at about 0.05 dyn/W and steadily increase to a nearly maximum value (on the order of 1 dyn/W) at about 60 J/cm² while for higher fluences it remains about the same. This value is lower than that measured for flat surfaces, which can be expected from the complex geometry (which reduces the effective energy absorption compared to the ideal case). This value is similar for the three types of metal material used, in agreement with previous studies using flat surfaces [40]. It must be noted that the fluence at which C_m reaches it maximum value coincides with the fluence where the energy partitioning to kinetic energy to the particle compared to the energy for shock formation (shown in Fig. 6(b) and discussed in the previous section) changes its behavior (from increasing to decreasing) is about the same. This suggests a connection between these two observations, and in particular that after the maximum ablation area on the particle is reached, the secondary plasma heating starts to strongly affect the energy partitioning.

In conclusion, the results presented in this work helped develop a better understanding of the major elements of the interaction of ns laser pulses with spherical particles as well as the underlying mechanisms of momentum transfer. The results support that the concept of a coupling coefficient C_m [41] to describe the momentum transfer adopted previously for plane target geometries can also be expanded for the case of small particles. The measured value of C_m for spherical particles is presented to the best of our knowledge for the first time. This description can be very convenient for use in applications where particle acceleration during exposure to a laser beam must be considered. We also examine the ensuing modification of the substrate due to exposure to the plasma generated by the particles and the subsequent secondary deposition of laser energy in the plasma. Such effects are important in applications where structuring of the substrate is important such as via dispersing of metal particles on its surface to generate desired patterns or when such effects are undesirable byproducts of the exposure of particles in laser beams (such as in dry laser cleaning or arising from contamination particles in optical components for high power laser systems) [30–34]. The general description of the processes involved can help translate the findings of this work to related specific settings such as in different irradiation geometry (such as in randomly shaped particles) or using different laser irradiation parameters.