We report generation of femtosecond-laser-induced shockwaves at an air-water interface by millijoule femtosecond laser pulses. We document and discuss the main processes accompanying this phenomenon, including light emission, development of the ablation plume in the air, formation of an ablation cavity, and, subsequently, a bubble developing in water. We also discuss the possibility of remotely controlling the characteristics of laser-induced sound waves in water through linear acoustic superposition of sound waves that results from millijoule femtosecond laser-pulse interaction with an air-water interface, thus opening up the possibility of remote acoustic applications in oceanic and riverine environments.
© 2013 Optical Society of America
The generation of acoustic shockwaves in optically transparent and absorbing liquids via intense laser radiation has been of interest since shortly after the invention of the laser. In 1963, Askar’yan et al. were the first to observe shockwave generation through light absorption and thermal expansion in a liquid . The next year, in 1964, Brewer and Rieckhoff observed shockwaves induced by dielectric breakdown in a liquid . A number of subsequent works investigating the phenomena involved with laser-induced shockwaves in liquids were outlined in a review paper published by Bunkin and Komissarov in 1973 . The next decade saw significantly increased productivity in this area, resulting in two more well-referenced review papers published in 1980 and 1981 [4, 5]. By this time, three main physical mechanisms for shockwave generation by laser radiation in liquids had been identified: linear optical absorption with subsequent bulk thermal expansion, explosive evaporation, and dielectric breakdown and ionization.
At the end of the 1980’s and beginning of the 1990’s, the field had become well-established, and definitive monographs and textbooks were written [6–9]. In the 1990’s, it was realized that shockwaves in liquids had applications in medical surgery and biological tissue ablation, and renewed interest resulted in several works analyzing the generation of shockwaves in water using nanosecond and picosecond laser pulses [10–13] (see  for a list of medically-oriented works). By this time, femtosecond laser systems had come into widespread use, and characterization of femtosecond-laser-induced shockwaves in tissue and water for medical purposes was undertaken. In the 2000’s, research into femtosecond-laser-induced shockwaves continued along these lines [13–20], with applications broadening into cell processing, optical trapping, and fluidic control [18–20]. Reviews of femtosecond laser nanosurgery and shockwave emission by laser-generated bubbles have also been written [21, 22].
Our own interest in femtosecond-laser-induced shockwaves in water stems from the discovery and development of applications involving femtosecond laser filaments . Specifically, we have in mind applications in remote sensing from air-based platforms over oceanic and riverine environments. Femtosecond laser filaments in air are formed from laser pulses having energies on the order of a few millijoules. Several works have sought to characterize the interaction between potentially filament-forming femtosecond laser pulses in air and water-micro-droplets in the atmosphere. Of these, major foci have been the explosion of water micro-droplets by femtosecond laser pulses [24, 25] and plasma formation, transmission, harmonic generation, and white-light generation within the micro-droplet [26–33]. Dynamics of plasmas formed by femtosecond laser pulses incident onto planar water jets have also been studied [34–36]. Shockwaves cannot, however, propagate appreciable distances in micro-droplets or water jets, and so, remarkably, little to no work has been done investigating the acoustic phenomena involved when a femtosecond laser pulse with energy on the order of a few millijoules propagates across an air-water interface separating large volumes of bulk media. This basic science is prerequisite to any remote sensing applications that may be developed from femtosecond laser filaments in air interacting with the surface of a body of water. Previous works investigating laser pulse interaction with air-water interfaces have utilized nanosecond pulses with wavelengths in the mid- to far-infrared [37–48]. Oshemkov et al.  have investigated jet formation at an air-water interface using femtosecond laser pulses in tightly-focused geometry. Acoustical responses were not investigated, however. While many of these works document shockwaves generated from thermal expansion of heated water or explosive evaporation , the shockwaves we have generated using femtosecond laser pulses originate from dielectric breakdown and ionization of water at the air-water interface. This paper is dedicated to reporting and describing the shockwaves generated by femtosecond laser pulses with energies of a few millijoules. Section 2 describes our experimental setup. Section 3 briefly describes the phenomenological context in which the shockwaves occur, while Section 4 focuses on the characteristics of the shockwaves themselves. Section 5 discusses the physics and generating mechanisms responsible for the shockwaves and possible applications. Finally, Section 6 contains our conclusions, and our acknowledgments are listed in Section 7.
2. Experimental setup
Our experimental setup is shown in Fig. 1. The pump laser that is used to generate the shockwaves is a Ti:sapphire-based laser system consisting of an oscillator (Micra, Coherent) and an amplifier (Legend Elite, Coherent: 800 nm center wavelength, 35 fs pulse duration, 1 kHz repetition rate, 4 mJ pulse energy). The pump beam propagates into a tower and is directed downward to the surface of a distilled water sample after passing through a focusing lens with a 100 cm focal length. The surface of the water sample is located 100 cm from the lens. The tower itself may be pivoted such that the angle of incidence θ of the pump beam with respect to the normal of the surface of the water sample can be changed to the desired value. The distance from the surface of the water sample to the lens remains constant at 100 cm. Before entering the tower, the pump beam passes through a waveplate that is rotated to ensure that the pump beam remains p-polarized with respect to the surface of the water sample regardless of the pivoting angle θ of the tower; however, no polarization-dependent phenomena were observed in this experiment. A neutral-density wheel attenuator is utilized to control the energy of the pulses at the water surface. Measurements of pulse energy were taken between the neutral-density wheel attenuator and the first mirror of the tower. All pulse energies and calculated intensities quoted in this work have been corrected for reflection from three mirrors and transmission through the 100 cm focusing lens, yielding the pulse energies and intensities at the water surface.
In order to probe the phenomena induced by the pump pulses, we use the 532 nm output of a frequency-doubled 1064 nm beam from a Precision II 9000 Nd:YAG laser by Continuum. The 532 nm probing pulse has a FWHM duration of 7.8 ns. The probe beam is horizontally incident onto the water sample and is orthogonal to the incident pump beam; after interacting with the water sample, the probe beam is imaged by a 5 cm focal length lens onto the CCD of a Nikon D40 camera from which all objectives have been removed. The timing between the pump pulse, probe pulse, and camera triggering is controlled electronically. In this manner, we are able to observe phenomena that take place on time scales ranging from a few nanoseconds to milliseconds and beyond.
3. Time scale of events
Figure 2 illustrates the phenomena involved when a loosely focused femtosecond laser pulse (35 fs duration, 800 nm central wavelength) with an energy of 1 to 2 mJ interacts with the surface of a sample of water. The time scales of the phenomena span at least 12 orders of magnitude, ranging from the femtosecond to the millisecond. On the femtosecond time scale, the loosely-focused, energetic pulse reaches intensities sufficient to ionize many of the water molecules, creating at the surface a region of dense plasma (see Fig. 2(a)). The plasma then subsequently expands upward from the surface on the picosecond and nanosecond time scales. In the region directly above the surface of the water into which the plasma has expanded, a light signal is emitted from the excited plasma species (Fig. 2(b)). At the same time, acoustic shockwaves in both air and water are generated and expand from the interaction region. Figure 2(c) shows shockwaves in both air and water 490 ns after the pulse has passed. A unique feature of the shockwaves we have generated in water is the presence of two shock fronts. The processes giving rise to these different shock fronts are discussed in the following sections. After about 10 microseconds, a cavity (crater) is formed on the surface of the water that expands downward into the bulk. Figure 2(d) shows one of these cavities at about 20 μs after the pulse has passed. The downward expansion of the cavity continues until about 100 microseconds, when the surface of the water closes above the cavity and forms a bubble. Figure 2(e) shows a bubble at about 200 μs after the initial pulse has passed. The bubble continues to propagate downward into the bulk of the sample for several milliseconds, reaching depths of at least 500 microns, after which it eventually returns to the surface.
The many time scales over which these phenomena span provide for rich opportunity for ongoing research. On the femtosecond time scale (Fig. 2(a)), the mechanisms and dynamics of ionization for these high intensities and their relation to the process of liquid surface ablation remain intriguing areas for additional investigation. On the microsecond time scale, the fluid dynamics responsible for the formation of the cavity at the surface and the subsequent cavity closure and bubble propagation may prove interesting in studies involving fluidic control. Our focus in this paper, however, remains the mechanisms immediately responsible for shockwave generation and their subsequent characteristics as they propagate away from the air-water interface as a result of femtosecond pulse propagation and interaction across the surface. Consequently, the following sections will focus on the picosecond and nanosecond time scales, during which a portion of the water surface is ablated and leads to the formation of the two shock fronts shown in Fig. 2(c).
4. Characteristics of femtosecond-laser-induced shockwaves at an air-water interface
Figure 3 shows the evolution of shockwaves induced by loosely-focused femtosecond laser pulses (see experimental setup in Fig. 1) in air (top) and water (bottom) at different time delays after the initial passage of the pulse through the air-water interface. The shockwaves in air were generated using pulses with energies and peak on-axis intensities of 2.20 mJ and W/cm2, respectively. The shockwaves in water were generated using pulses with energies and peak on-axis intensities of 2.21 mJ and W/cm2, respectively. The images were obtained by very slightly displacing the 5 cm lens, effectively and very slightlydefocusing the image; in this manner, the phase shifts induced in the 532 nm probe pulse by the pressure differentials in the shockwaves result in light interference and intensity changes at the CCD of the camera. We achieve a magnification of 8.2 at the CCD and a spatial resolution of 1.3 μm.
10 ns after the pump pulse has propagated across the air-water interface, we see the formation of a crater of uniform depth visible just below the water surface, which, at large time scales, develops into the cavity and bubble shown in Figs. 2(d) and 2(e), respectively. Above the surface, the crater is accompanied by a shockwave in air. After 50 ns, the crater has formed a shockwave in water of planar geometry which propagates away from the surface and becomes visible. Behind the main front can be seen additional shockwaves that propagate from the edges of the crater toward the center and axis of symmetry of the crater. Above the surface, the shockwave in air has separated from a region of heated vapor that is visible in the remainder of the pictures. Notable in the air-shockwave is the presence of a lip directly above the position of the initial generation point, which also corresponds to a region of white light emission (shown in Fig. 2(b)) indicative of plasma formation, expansion, and recombination. At 50 ns, the darker area behind the leading shockwave front can be seen that is confined between the leading and trailing shockwaves and travels with them, corresponding to pressure-induced changes in the refractive index. At 90 ns, the first shock front in water continues to propagate, while the trailing fronts, propagating from the edges of the crater toward the axis of symmetry, cross and begin to form cavitation bubbles. This dynamic continues until the trailing shock fronts, having propagated from the edges through the axis of symmetry of the crater, form a roughly hemispherical second shock front behind the first hemispherical shock front. Above the surface, the air-shockwave continues to propagate, followed by an upward-expanding region of heated vapor. At 90 ns, the beginning of the formation of a crown of liquid around the crater can be observed, which subsequently expands outward from the axis of symmetry.
By pivoting the angle of the tower shown in Fig. 1 through an angle θ, we can alter the angle of incidence of the incoming pulse. Figure 4 shows the shockwaves generated in water 490 ns after the pulse has propagated through the air-water interface for incidence angles of 0° (Fig. 4(a)), 30° (Fig. 4(b)), and 45° (Fig. 4(c)). The first shock front exhibits a hemispherical shape that is independent of the incident angle of the pump pulse and propagates away from the surface. The second shock front, however, becomes more parabolic in shape and pointed as the angle of incidence is increased. We note that the initial crater visible just below the surface at small times (10 ns) after the pump pulse has propagated across the air-water interface has a diameter of 205 ± 3 μm, 228 ± 5 μm, and 287 ± 14 μm for incident angles of 0°, 30°, and 45°, respectively. This behavior follows a simple geometric projection of the form , where d is the diameter of the crater, d0 is the crater diameter at 0° incidence, and θ is the angle of incidence. The cavitation bubbles tend to form more in the volume irradiated by the laser beam. Also of interest are the most advanced positions of the second shock front, measured from the unperturbed surface position in the region immediately below the crater in Figs. 4(a)-4(c). These positions are 681 ± 2 μm, 672 ± 2 μm, and 668 ± 2 μm for incident angles of 0°, 30°, and 45°, respectively. These shock front position measurements along the vertical axis form the longer leg of a right triangle, the shorter leg being the crater radius (diameter/2) and the hypotenuse being the distance from the outer edge of the crater to the shock front. The hypotenuse length is an invariant in Figs. 4(a)-4(c), suggesting the second shock front to be the result of a quasi-linear acoustic superposition of waves propagating from the crater edges.
Figure 5 shows the position of the most advanced disturbance of the shock front (located directly above and below the crater in the surface for shockwaves in air and water, respectively) as a function of time after the pump pulse has passed; the pulses have an angle of incidence of 0°. Each data point is the average of about 10 measurements, each from a separate image corresponding to the same time delay; the uncertainties are smaller than thedata markers. For measurements of shock front position in water, each time step is separated by 10 ns. Measurements were taken of shock fronts generated by pulses of three different energies. In Fig. 5, the red squares show the positions of shock fronts generated by pulses with energies of 2.25 mJ and peak on-axis intensities of W/cm2. The blue circles (mostly hidden by the red squares) denote positions of shock fronts generated by 1.49 mJ and W/cm2 pulses. Finally, the green diamonds mark the positions of shock fronts generated by 0.72 mJ and W/cm2 pulses. For water, the shock front position as a function of time after the initial slightly nonlinear portion shows primarily linear behavior, indicating that the shockwave is weak and propagates as a plane wave, not experiencing divergence and noticeable reduction of amplitude at considered distances. We fit the linear portion of the curves (corresponding to time delays of 70 ns and above) with an uncertainty-weighted algorithm to yield the shock front velocities. This procedure yields shock front velocities of 1511 ± 2 m/s, 1491 ± 2 m/s, and 1428 ± 2 m/s for pulse energies of 2.25 mJ, 1.49 mJ, and 0.72 mJ, respectively (see the first paragraph of Section 5 for a discussion of these velocity values). According to weak shock theory for underwater shockwaves in a liquid , the shock front velocity cs is51], β is the nonlinearity of the liquid (with a value of 3.5 at 20° C in distilled water ), and u is the particle velocity. For weak shock waves, the linear impedance relationEq. (2) into Eq. (1) and solving for the pressure yields for a measured shock front velocity cs of 1511 m/s (see above) a pressure of 14.5 MPa.
Time steps for measurements of shock front position in air were 20 ns; pulse energies and intensities were 2.20 mJ and W/cm2, respectively. The shape of the curve representing shock front position as a function of time indicates that the shockwave in air is a strong shockwave. In order to calculate a lower bound on the initial peak pressure, we use the distance traveled by the shock wave between the first two data points, which is 108 ± 8 μm. Since the data points are separated by 20 ns, this yields a shock front velocity cs of 5400 ± 400 m/s. Utilizing an approach similar to , we calculate the peak pressure through the Rankine-Hugoniot expression for air:53]), and P0 is the undisturbed air pressure (101 kPa). This yields a lower limit for the initial peak pressure of 29 MPa.
Figure 6 shows the measured positions of the first and second shock fronts 490 ns after the pump pulse has passed as a function of the pulse energy and peak on-axis intensity. The first shock front is denoted by black circles, while the second shock front is denoted by black triangles; each data point is an average of the measurements of about 10 separate images. The uncertainties in the figure are the size of the data markers. Above a pulse energy and peak on-axis intensity of 1.03 mJ and W/cm2, respectively, the shock front positions after 490 ns remain almost independent of pulse energy, i.e. constant. This indicates that there is no significant increase in shockwave peak pressure with increasing pulse energy. It is possible that there may be some shielding effect as pulse energy is increased . Below this threshold energy and peak on-axis intensity value, however, the first and second shock fronts converge with reducing pulse energy until they form a single shock front at a pulse energy and intensity of 0.55 mJ and W/cm2, respectively. This may be due to the fact that the width of the crater just below the surface also decreases below this threshold value, finally becoming unobservable below a pulse energy of 0.55 mJ. Below pulse energies of 0.55 mJ, no shock fronts were detected with our experimental setup. The red line in Fig. 6, corresponding to a pulse energy of 1.03 mJ, indicates the energy and intensity value below which no light emission from plasma is observed (see Fig. 2(b)). This corresponds to the threshold value of pulse energy and intensity below which the first and second shock fronts begin to converge into a single front. A pulse energy of 0.55 mJ may correspond with an ablation threshold for strong evaporation, while a pulse energy of 1.03 mJ may correspond to dielectric breakdown [55, 56]. However, more rigorous study of this question is beyond the scope of this paper.
We point out that, in Fig. 5, the curve corresponding to the shock front position as a function of time for pump pulses with energies of 0.72 mJ yields a shock front velocity of 1428 m/s, which is slower than the observed velocity of sound in water of 1494 m/s at a room temperature of 24° C . This discrepancy is most likely a systematic error resulting from the slight defocusing of the 5 cm imaging lens shown in Fig. 1. After a slight defocusing, the object plane no longer contains the axis of symmetry of the crater formed beneath the surface; since we image a two-dimensional slice of a three dimensional shock front, measurements of shock front position are slightly less than the actual values. A sound velocity of 1428 m/s is within 4.5% of the accepted value. Since the generated shockwaves are weak (as evidenced by the linear behavior of the shock front position as a function of time), it is reasonable to conclude that the shock front generated by pulses with 0.72 mJ energy propagates with a velocity very close to the speed of sound. It is therefore reasonable to conclude that the measured quantities retrieved from our images are systematically 4% to 5% less than their actual values. The qualitative and comparative relationships within and between data sets, however, remain accurate.
The shockwaves we have documented are generated at the air-water interface at or just below the surface. The data in Fig. 3 show that the shockwaves originate from a crater that is already clearly visible 10 ns after the pump pulse has propagated across the interface. Moreover, the fact that the first shock front remains independent of the incident angle of pulse as shown in Fig. 4 further supports the conclusion that the shockwaves are inherently due to a surface effect which involves the crater. The origin of the crater is most likely optical breakdown at the surface accompanied by ablation and spallation as a result of dense plasma formation and subsequent expansion into the air above the surface . Since the ablation layer (crater) is of the same thickness across the laser beam cross-section, one can conclude that the transfer of the energy to the liquid should be limited after reaching some threshold. The creation of free electrons leads to a reduction of the refractive index n according to , where ωpl is the plasma frequency, ω is the frequency of radiation, and n0 is the refractive index of the undisturbed medium . Thus, when the concentration of electrons reaches some critical value, n < 0 and the laser radiation is reflected. In our experiment, the plasma densities may begin to approach this value. Our pulse intensity is high enough to ionize the medium and result in the formation of a dense plasma. Strong dissociation of water can also be expected [58, 59]. After ionization, electrons experience oscillating motion in the field of the laser pulse and acquire ponderomotive energy on the order of tens of eV for the laser pulse energies used. The interaction process results in significant deposition of the laser pulse energy in the water surface layer. The hot electron gas exchanges energy with ions and molecules, which results in a high temperature and pressure of the medium in the interaction region. Thus, on this same time scale a strongly non-equilibrium state of an overheated and ionized gas is produced. Subsequently, thermalization, expansion, and cooling down of this plasma occurs, which takes place on the ps-ns time scale. The abruptly produced high pressure pushes the liquid, giving rise to a shock wave in liquid; on the other side it pushes also the gaseous air, forming a shock wave in the air. In view of the much larger density of the liquid, the overheated layer mostly expands above the water surface, forming an evaporation plume. The generation mechanism in water is thus an abrupt pressure increase in the layer of the energy deposition and recoil momentum due to ablation. This picture is supported by the results of Sarpe-Tudoran et al. in . In this work, they observed the electron density at a water surface irradiated by powerful femtosecond laser pulses to be cm−3. They subsequently observed a 20 ps time delay before plasma expansion at a velocity of 5900 m/s. This is consistent with our observations of the shockwave in air after just 10 ns as well as light emission in the region immediately above the crater as shown in Fig. 2(b). Such light emission is consistent with plasma excitation and recombination. It is also consistent with the continuum emission spectrum well-known in laser induced breakdown spectroscopy (LIBS). LIBS analysis of water has been carried out for many years using nanosecond laser pulses in various experimental configurations (see  for a well-referenced review of these techniques). Recently, the mineral composition of seawater has been analyzed using femtosecond LIBS in a time-gated technique , where the light emission was observed for time intervals greater than one nanosecond, corresponding to similar durations of the recombination process and plasma lifetime. Our work supports the utility of femtosecond laser pulses in remotely analyzing water samples based upon dielectric breakdown and plasma formation at a water surface.
Our work also supports the feasibility of remote thrust generation based upon liquid ablation by femtosecond laser pulses [62, 63]. Several works have documented the effects of explosive evaporation at a water surface due to resonant heat deposition using picosecond and nanosecond laser pulses (see  for well-referenced review of these works). These works, however, used light wavelengths in the mid-infrared corresponding to resonances in the water absorption spectrum. Our own pulses, which have a central wavelength of 800 nm, are not centered on a resonance. Nevertheless, the deposition of energy in the liquid is efficient and almost instantaneous due to production of dense plasma. However, this energy deposition can be limited by the screening effect when plasma density exceeds some critical value.
Such an instantaneous planar excitation has significant advantages. On distances smaller than the diffraction length, the leading shockwave front is a plane wave. With propagation distance, it experiences divergence and transforms itself into an expanding hemisphere at larger distances. The observed images of the two tailing wave fronts can be understood from linear sound generation. When a disk-like and almost instantaneous sound source is produced at the surface, the propagating plane wave front of higher pressure arrives first. The wave of high pressure lasts until the sound from the edges of the disk comes to the observation point. This latter corresponds to the tailing front of the pressure wave passing the observation point, and this front has the shape of an expanding half-toroid with its center line coinciding with the edge of the source disk. The change in shape of the second wave front as a function of pulse incident angle as shown in Fig. 4 can also be understood within this framework as was discussed above in Section 4.
As our results show, a loosely-focused femtosecond laser pulse incident upon an air-water interface produces highly reproducible sound waves capable of being linearly superimposed upon one another. When multiple pulses are used, synchronized in both time and space, they can produce arrays of sound sources, generating tailored and directionally-controllable acoustic wave fronts. It may even be possible to remotely control a single sound source and subsequent shockwave propagation direction by exploring the pulse parameters such as spatial intensity distribution (beam mode and beam shaping) and pulse chirp.
The conversion of pulsed laser radiation into acoustic energy has been shown to be more efficient at the intensities corresponding to reaching the optical breakdown threshold [65, 66]. For femtosecond radiation, the interaction with the medium is so fast and ablation is so efficient that no significant heating of the remaining matter occurs. For the same reason, no significant residual stresses are left in the material, and therefore this channel of laser pulse energy distribution (losses) is not so essential for femtosecond as it is for longer pulses. Femtosecond laser pulses therefore offer unique potential for precise control of acoustic waves. Such control may be of practical interest for acoustic generation within tissues; although it has been shown that nanosecond-laser-induced dielectric breakdown results in qualitatively different responses for water and tissue, with compressive acoustic waves in water and compressive/tensile waves in tissue , the possibility for precise control using femtosecond-laser-induced acoustic waves at a surface may be of interest for further research and applications in this area. These properties of femtosecond laser pulses are also important for use in remote sensing applications in oceanic and riverine environments.
We have reported the generation of femtosecond-laser-induced shockwaves at an air-water interface using loosely focused millijoule laser pulses. We have reported the phenomenological context in which the shockwaves are generated as well as the characteristics and generating mechanisms of said shockwaves. We point out that interaction of femtosecond laser pulses with aquatic surfaces may be used to remotely characterize the chemical and mineral composition of waters in oceanic and riverine environments through spectral analysis of the laser-induced breakdown spectroscopy (LIBS) signal generated by the plasma at the water surface. We observed, with femtosecond surface optical breakdown, the generation of weak shockwaves in water and their quasi-linear superposition. Thus, remote control of sound wave pulse shape and propagation direction by superposition of waves produced from spatially and temporally synchronized femtosecond laser pulses interacting with a liquid surface is a feasible possibility. Our results can also be of interest for medical applications dealing with tissue ablation by femtosecond laser pulses and for remote acoustic applications in oceanic and riverine environments.
This work was supported by the The Welch Foundation Grant #A-1547.
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