Abstract

We investigate the formation, propagation, and interaction of femtosecond laser-induced flows of compressed air at a water/air interface by recording the transient reflectivity of shockwaves. Subsonic fronts of compressed air and weak shockwaves can be hard to detect due to their inherently subtle change of refractive index. Therefore, we study these weak flows by looking at the interaction dynamics of two and four shockwaves simultaneously produced at adjacent locations. An analytic model is used to retrieve the velocity and position of the shockwave from the experimental results. The use of multi-spot excitation opens up a versatile method to further investigate and understand the physical mechanisms contributing to photomechanical tissue damage during femtosecond-laser-based surgery and to study the fluid dynamics of complex systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Today, ultrashort laser pulses are used in a vast variety of scientific fields that extends from basic research in physics, chemistry, and biology to medical and technological applications [14]. The ultrafast and spatially deterministic nature of the energy deposition of femtosecond (fs) laser pulses when interacting with solid and liquid targets is one of their outstanding advantages [57]. Thus, they are a very attractive tool to simulataneously locally modify and dynamically study the chemical and optical properties of the target with high spatial and temporal resolution. The application for material removal via fs-laser ablation has been thoroughly investigated for more than two decades [79].

Laser-induced breakdown inside liquid targets has also been studied due to its tremendous potential in ophthalmic and non-invasive surgery [1,1013]. The laser-liquid interaction dynamics inside bulk water has been studied using time-resolved microscopy techniques in transmission mode (shadowgraphy), upon irradiation with femtosecond, picosecond, and nanosecond laser pulses [3,1417]. The interaction of ultrashort laser pulses with water triggers a chain of physical processes that are very well separated through the different timescales, mainly due to the ultrafast energy deposition [6,9]. During the first hundreds of femtoseconds, the laser triggers the generation of a dense electron plasma, mediated by multiphoton and avalanche ionization [18,19]. On the timescale of tens of picoseconds after irradiation, the energy is transferred from the electrons to the molecules, which leads to evaporation of the irradiated water volume. Subsequently, the water vapor explosively expands from hundreds of picoseconds to nanoseconds. This expansion gradually decelerates due to the pressure equilibration with the surrounding medium. In bulk, a cavitation bubble and a shockwave are launched. At a water/gas interface, the laser-induced water vapor expands and generates a shockwave in the surrounding gas atmosphere. In the microsecond time-regime, this leads to surface waves and mechanical deformation of the surrounding water surface [14,16].

The visualization of laser-induced shockwaves in gases and liquids provides information about the gas flow and about the energy released during the expansion [2022]. Yet, it is extremely challenging to properly image weak shocks or subsonic fronts of compressed gas due to the low refractive index change caused by the expanding front.

In this Letter, we demonstrate the use of simultaneous multiple laser-excitation locations at a water/air interface in order to investigate flow velocities in a regime where shockwaves would not occur with a single excitation beam. To that end, we use a simple, robust, and low-cost beam shaping technique that employs Fresnel bi-prisms. We combine it with a pump and probe imaging layout that allows us to study the interaction of the shocks dynamically, thus providing information about their expansion speed and location.

Our sample consists of a beaker with 25 mL of mili-Q demineralized water, placed inside a sealed container; see Fig. 1(a). We designed the sealed container so that a microscope objective is hermetically attached to it by using an elastic rubber band and vacuum-grade o-rings. The water vapor pressure is saturated with the air inside the container at room temperature. In this way, the water surface remains in focus during the irradiation experiments.

 figure: Fig. 1.

Fig. 1. (a) Scheme of the experimental setup. (b) Transient reflectivity images of a variety of shocks. Note that all the images were acquired at a delay of 10 ns using a fluence of 18J/cm2, except for single beam illumination, which was recorded at a 4 ns delay time using a fluence of 22J/cm2.

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The optical system is based on a pump and probe microscopy layout in a collinear configuration; see Fig. 1(a). We use a laser amplifier (Hurricane, Spectra-Physics) that provides 150 fs laser pulses at 800 nm with a repetition rate of 1 kHz. We select a single laser pulse using a mechanical shutter (Thorlabs SH05), which is split into the pump and probe pulses using a polarizing beam splitter (PBS). The pump is sent to a Fresnel bi-prism that splits the beam into two equally energetic and independently collimated sub-beams that propagate at a slightly different angle; see Fig. 1(a). This angle depends on the glass and geometry of the bi-prism (Newlight Photonics, N-BK7 179°). The shaped pump beam passes through an objective (Nikon CFI60, 100×, NA=0.8) that tightly focuses it at the water/air interface at two adjacent locations with an approximate separation of ho=14μm. We have estimated a negligible pump pulse broadening of 20 fs, which is due to the group delay dispersion induced in the PBS, the bi-prism, and the microscope objective. The frequency of the probe beam is doubled (λ=400nm) using a beta barium borate crystal [BBO in Fig. 1(a)]. Afterwards, a lens is used to focus the probe beam at the back focal plane of the microscope objective, resulting in wide field illumination at the water/air interface. We make sure that the pump beam is tightly focused at the water/air interface, while imaging the surface using the probe beam (depth of focus <800nm). The relative time delay between the probe and the pump pulses is controlled using a motorized delay line (Newport Co.), and an additional detour [not shown in Fig. 1(a)] in the pump beam is added in order to achieve the zero delay. As shown in Fig. 1(a), the two pumps and the probe beams are spatially recombined in a first pellicle beam splitter (Thorlabs, BP145B1) and sent to the objective. The light reflected at the laser-excited water/air interface is collected by the objective. A second pellicle beam splitter reflects the collected light towards a bandpass filter (400±10nm) and a tube lens (TL) that creates an image of the irradiated water surface at the chip of an electron multiplying CCD camera (Andor, Ixon 885).

In this way, we record the transient reflectivity of the water surface for several time delays. Figure 1(b) shows examples of the irradiation geometries we can typically generate using a combination of Fresnel bi-prisms. These show circles of reduced reflectivity with a bright rim, which we attribute to the laser-induced water vapor and to the contact discontinuity between the vapor and the compressed air at the edge, respectively. The image of the single excitation spot illustrates the formation of a dim shockwave with a diameter of 20 μm, when using a high laser fluence of 22J/cm2. The use of lower excitation fluences results in shockwaves with an even poorer optical contrast, which has two possible explanations. (1) This can merely be due to the absence of a shockwave when the water vapor initially expands at a subsonic velocity (vr<vs, with vs being the speed of sound in air). (2) The resultant density change across the shock induces a negligible refractive index change when the vapor expansion is supersonic, but near the speed of the sound of air (vrvs). In either case, we can generate a strong elongated shock by using two adjacent irradiation beams, as shown in the right column of Fig. 1(b), showing that the relative flow between the spots greatly overcomes the speed of sound, thus producing a large optical contrast. Moreover, we can detune the energy balance between the excitation laser pulses to bend the initially flat shockwave into a parabola-shaped shock. The energy balance between the two spots can be achieved by shifting the position of the bi-prism axis with respect to the center of the pump beam. We can also generate more complex geometries by using two crossed Fresnel bi-prims, resulting in the formation of three and four irradiation locations that lead to several elongated shocks.

Figure 2 presents the evolution of the transient reflectivity of the laser-induced vaporization at two adjacent locations from 1 ps to 10 ns. Initially, we observe a high increase of the reflectivity coefficient at 1 ps that achieves an absolute value of Rmax=0.2, which is 10 times higher than the reflectivity of unexcited water. We attribute the reflectivity increase to a laser-induced dense and hot electron plasma. This increment is of the same order as the reflectivity observed during fs-laser ablation of transparent solid materials with similar electronic properties [9,23]. Subsequently, we observe a reflectivity decrease that we link to the evaporation onset. From hundreds of picoseconds to a few nanoseconds, Fig. 2 shows the rapid expansion of the water vapor, which gradually slows down due to the pressure equilibration and due to air swept up at the contact discontinuity. This results in two individual fronts of compressed air propelled at each adjacent location. When they collide, the relative flow speed is high enough to cause a sharp straight shock. The collision onset at this particular laser fluence is observed at 3 ns after laser excitation. Afterwards, as the fronts of the compressed air radially expand, the resultant elongated shockwave grows in length. From the dynamics of the elongated shock, we can pinpoint the location and calculate the velocity of the weak shocks and subsonic fronts of compressed air.

 figure: Fig. 2.

Fig. 2. Fs-laser-induced electron plasma, vapor expansion, and shockwave formation during a double excitation experiment.

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Figures 3(a) and 3(b) show a transient reflectivity image, upon double pulse irradiation, and its schematic representation. The water vapor front and the air fronts are presented as the black and red circumferences. We define the distance between irradiations as ho, the length of the shock as L(t), and the radius vector r(t) that points at the ends of the flat shock. The angle between r(t) and ho is defined as α(t). We also indicate the radial velocity vector at the intersection of the air fronts as vr and its horizontal and vertical components. To optically detect a stationary flat shockwave, we establish that the condition vl(L/2,t)vs must be fulfilled, where vl is the sum of the vertical components of the air front velocities, originated at the upper (u) and lower (d) laser-excited locations:

vl(L/2,t)=(|vru(t)|cosα(t)+|vrd(t)|cosα(t)),
where the modulus of the velocity of the shock as a function of time satisfies |vru(t)|=|vrd(t)| for equally energetic pump laser pulses. Equation (2) defines the modulus of the radius vector as a function of L(t) and ho and establishes its relation with the Sedov–Taylor expansion model for point blast explosions [24]:
|rs(t)|=ho24+L(t)24|rs(t)|=A(E/ρ)15t25,
where E is the energy carried by the shock, ρ is the density, and A is a proportionality constant that depends on the dimensionality of the system. Figure 3(c) shows the length of the elongated shockwaves as a function of time (blue circles). These values represent the average of the length, along with their standard deviation obtained from several images for each time delay. Using Eq. (2) and the experimental values of L(t), we obtain the radius of the individual shocks as a function of time, which are shown in red in Fig. 3(c). In order to interpolate the r(t) values, we perform a fit using the Sedov–Taylor model presented in Eq. (2); see the red line in Fig. 3(c). The fit provides an estimate of the energy released by the shock equal to 1.8±0.5pJ. Besides, from r(t), we can also calculate the velocity of the compressed air front as a function of time by performing the time derivative
|vr(t)|=|r˙s(t)|.
Figure 3(d) shows the radial velocity and its vertical and horizontal components as a function of time, with which we mean the air flow perpendicular and parallel to the direction defined by the elongated shockwave, as defined in Fig. 3(b). The radial velocity of the air front initially achieves Mach numbers (|vr(t)|/vs) between 2 and 1 for delays shorter than 7.5 ns. The snapshot at 3 ns time delay in Fig. 2 illustrates two very dim shocks that form an eight-shaped reflectivity change. The radii of these shocks agree with the value retrieved from the length of the flat shockwave r(3ns)=8.5μm, which corresponds to a speed of 665 m/s. This confirms that weak shocks with a supersonic speed near the speed of sound are indeed hard to detect upon optical inspection in case of single beam illumination. The vertical component of the front velocity is always larger than vs/2, which indicates that the resultant (two-front) velocity composition fulfils the vl(L/2,t)vs condition. However, its decrease to vlvs/2 at 9 ns is consistent with the fact that the length of the shock remains almost constant for longer time delays. We also obtain a considerable velocity for the horizontal component reaching values near the speed of sound in air. In order to qualitatively investigate the nature of the horizontal flows, we use four excitation irradiation spots in a square configuration.

 figure: Fig. 3.

Fig. 3. (a) Snapshot of the vapor propagation and shock formation at 10 ns time delay. (b) Geometrical scheme during double pulse excitation. (c) Elongated shockwave length and compressed gas front radius as a function of the delay time. (d) Compressed air front radial velocity as a function of time.

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Figure 4 presents the transient reflectivity after laser excitation using a square-pump arrangement. Similar to Fig. 2, we observe a reflectivity increase of 1 ps after laser excitation, which we attribute to a laser-excited electron plasma. Then, for tens of picoseconds, the water vaporizes and explosively expands for the first few nanoseconds. Approximately from 3 ns onwards, the fronts of compressed air propelled from each excitation location start to interact, presenting the characteristic elongated shape found for the two-spot case. Furthermore, as the elongated shocks grow in length, their effect combines, resulting in a spot with higher reflectivity near the center of the square, i.e., a 7 ns snapshot. At 9 ns and 10 ns time delays, the bright spot evolves into a bright cross that is rotated 45° with respect to the bigger cross. This inner cross is consistent with the interaction of the air flows parallel to each individual elongated shock. The square-pump geometry demonstrates that using our method, complex shockwave patterns with more subtle features can be used to investigate the fluid dynamics of laser-induced weak shocks in the micron-scale.

 figure: Fig. 4.

Fig. 4. Femtosecond-laser-induced electron plasma, vapor expansion, and shockwave formation during a quadruple pump experiment.

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In conclusion, we investigate the ultrafast dynamics of fronts of compressed air generated during femtosecond laser ablation of water at a water/air interface. We show that the use of a multiple-excitation beam-based technique opens up a new venue to investigate the nature of weak shockwaves. We appeal to the versatility of our method to create different irradiation geometries that can unravel information about supersonic and subsonic fluid dynamics of fs-laser-induced shocks that would otherwise be untraceable upon optical inspection. This approach can contribute to understand the physical processes involved within a variety of research fields that cover nanophotonics, physics of fluids, biological systems, and laser-based surgery.

Funding

Horizon 2020 Framework Programme (H2020) (703696 ADMEP).

Acknowledgment

The authors are grateful for fruitful discussions with Hanneke Gelderblom, Denise M. Krol, Allard Mosk, and Ingmar Swart. They also are grateful for the technical assistance provided by Paul Jurrius, Cees de Kok, and Dante Killian. Sebastiaan Greveling and Abhilash Thendiyammal are acknowledged for proofreading the manuscript.

REFERENCES

1. A. Vogel and V. Venugopalan, Chem. Rev. 103, 577 (2003). [CrossRef]  

2. R. R. Gattass and E. Mazur, Nat. Photonics 2, 219 (2008). [CrossRef]  

3. C. B. Schaffer, N. Nishimura, E. N. Glezer, A. M.-T. Kim, and E. Mazur, Opt. Express 10, 196 (2002). [CrossRef]  

4. S. S. Harilal, B. E. Brumfield, B. D. Cannon, and M. C. Phillips, Anal. Chem. 88, 2296 (2016). PMID: 26732866. [CrossRef]  

5. H. Zhang, D. M. Krol, J. I. Dijkhuis, and D. van Oosten, Opt. Lett. 38, 5032 (2013). [CrossRef]  

6. B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. Anisimov, Appl. Phys. A 79, 767 (2004). [CrossRef]  

7. D. von der Linde, K. Sokolowski-Tinten, and J. Bialkowski, Appl. Surf. Sci. 109-110, 1 (1997). [CrossRef]  

8. X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997). [CrossRef]  

9. J. Hernandez-Rueda, D. Puerto, J. Siegel, M. Galvan-Sosa, and J. Solis, Appl. Surf. Sci. 258, 9389 (2012). [CrossRef]  

10. F. Courvoisier, V. Boutou, C. Favre, S. C. Hill, and J.-P. Wolf, Opt. Lett. 28, 206 (2003). [CrossRef]  

11. C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, New J. Phys. 14, 075021 (2012). [CrossRef]  

12. N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015). [CrossRef]  

13. T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016). [CrossRef]  

14. B. Strycker, M. Springer, A. Traverso, A. Kolomenskii, G. Kattawar, and A. Sokolov, Opt. Express 21, 23772 (2013). [CrossRef]  

15. R. R. Krueger, J. S. Krasinski, C. Radzewicz, K. G. Stonecipher, and J. J. Rowsey, Cornea 12, 330 (1993). [CrossRef]  

16. I. Apitz and A. Vogel, Appl. Phys. A 81, 329 (2005). [CrossRef]  

17. T. T. Nguyen, R. Tanabe, and Y. Ito, Opt. Laser Technol. 100, 21 (2018). [CrossRef]  

18. B. Rethfeld, Phys. Rev. Lett. 92, 187401 (2004). [CrossRef]  

19. B. Rethfeld, Phys. Rev. B 73, 035101 (2006). [CrossRef]  

20. T. Juhasz, X. H. Hu, L. Turi, and Z. Bor, Lasers Surg. Med. 15, 91 (1994). [CrossRef]  

21. A. Vogel, S. Busch, and U. Parlitz, J. Acoust. Soc. Am. 100, 148 (1996). [CrossRef]  

22. N. Arnold, J. Gruber, and J. Heitz, Appl. Phys. A 69, S87 (1999). [CrossRef]  

23. J. Hernandez-Rueda, J. Siegel, M. Galvan-Sosa, A. R. de la Cruz, M. Garcia-Lechuga, and J. Solis, J. Opt. Soc. Am. B 32, 150 (2015). [CrossRef]  

24. L. I. Sedov, Similarity and Dimensional Methods in Mechanics (CRC Press, 1993).

References

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  1. A. Vogel and V. Venugopalan, Chem. Rev. 103, 577 (2003).
    [Crossref]
  2. R. R. Gattass and E. Mazur, Nat. Photonics 2, 219 (2008).
    [Crossref]
  3. C. B. Schaffer, N. Nishimura, E. N. Glezer, A. M.-T. Kim, and E. Mazur, Opt. Express 10, 196 (2002).
    [Crossref]
  4. S. S. Harilal, B. E. Brumfield, B. D. Cannon, and M. C. Phillips, Anal. Chem. 88, 2296 (2016). PMID: 26732866.
    [Crossref]
  5. H. Zhang, D. M. Krol, J. I. Dijkhuis, and D. van Oosten, Opt. Lett. 38, 5032 (2013).
    [Crossref]
  6. B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. Anisimov, Appl. Phys. A 79, 767 (2004).
    [Crossref]
  7. D. von der Linde, K. Sokolowski-Tinten, and J. Bialkowski, Appl. Surf. Sci. 109-110, 1 (1997).
    [Crossref]
  8. X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
    [Crossref]
  9. J. Hernandez-Rueda, D. Puerto, J. Siegel, M. Galvan-Sosa, and J. Solis, Appl. Surf. Sci. 258, 9389 (2012).
    [Crossref]
  10. F. Courvoisier, V. Boutou, C. Favre, S. C. Hill, and J.-P. Wolf, Opt. Lett. 28, 206 (2003).
    [Crossref]
  11. C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, New J. Phys. 14, 075021 (2012).
    [Crossref]
  12. N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015).
    [Crossref]
  13. T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
    [Crossref]
  14. B. Strycker, M. Springer, A. Traverso, A. Kolomenskii, G. Kattawar, and A. Sokolov, Opt. Express 21, 23772 (2013).
    [Crossref]
  15. R. R. Krueger, J. S. Krasinski, C. Radzewicz, K. G. Stonecipher, and J. J. Rowsey, Cornea 12, 330 (1993).
    [Crossref]
  16. I. Apitz and A. Vogel, Appl. Phys. A 81, 329 (2005).
    [Crossref]
  17. T. T. Nguyen, R. Tanabe, and Y. Ito, Opt. Laser Technol. 100, 21 (2018).
    [Crossref]
  18. B. Rethfeld, Phys. Rev. Lett. 92, 187401 (2004).
    [Crossref]
  19. B. Rethfeld, Phys. Rev. B 73, 035101 (2006).
    [Crossref]
  20. T. Juhasz, X. H. Hu, L. Turi, and Z. Bor, Lasers Surg. Med. 15, 91 (1994).
    [Crossref]
  21. A. Vogel, S. Busch, and U. Parlitz, J. Acoust. Soc. Am. 100, 148 (1996).
    [Crossref]
  22. N. Arnold, J. Gruber, and J. Heitz, Appl. Phys. A 69, S87 (1999).
    [Crossref]
  23. J. Hernandez-Rueda, J. Siegel, M. Galvan-Sosa, A. R. de la Cruz, M. Garcia-Lechuga, and J. Solis, J. Opt. Soc. Am. B 32, 150 (2015).
    [Crossref]
  24. L. I. Sedov, Similarity and Dimensional Methods in Mechanics (CRC Press, 1993).

2018 (1)

T. T. Nguyen, R. Tanabe, and Y. Ito, Opt. Laser Technol. 100, 21 (2018).
[Crossref]

2016 (2)

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
[Crossref]

S. S. Harilal, B. E. Brumfield, B. D. Cannon, and M. C. Phillips, Anal. Chem. 88, 2296 (2016). PMID: 26732866.
[Crossref]

2015 (2)

N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015).
[Crossref]

J. Hernandez-Rueda, J. Siegel, M. Galvan-Sosa, A. R. de la Cruz, M. Garcia-Lechuga, and J. Solis, J. Opt. Soc. Am. B 32, 150 (2015).
[Crossref]

2013 (2)

2012 (2)

J. Hernandez-Rueda, D. Puerto, J. Siegel, M. Galvan-Sosa, and J. Solis, Appl. Surf. Sci. 258, 9389 (2012).
[Crossref]

C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, New J. Phys. 14, 075021 (2012).
[Crossref]

2008 (1)

R. R. Gattass and E. Mazur, Nat. Photonics 2, 219 (2008).
[Crossref]

2006 (1)

B. Rethfeld, Phys. Rev. B 73, 035101 (2006).
[Crossref]

2005 (1)

I. Apitz and A. Vogel, Appl. Phys. A 81, 329 (2005).
[Crossref]

2004 (2)

B. Rethfeld, Phys. Rev. Lett. 92, 187401 (2004).
[Crossref]

B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. Anisimov, Appl. Phys. A 79, 767 (2004).
[Crossref]

2003 (2)

2002 (1)

1999 (1)

N. Arnold, J. Gruber, and J. Heitz, Appl. Phys. A 69, S87 (1999).
[Crossref]

1997 (2)

D. von der Linde, K. Sokolowski-Tinten, and J. Bialkowski, Appl. Surf. Sci. 109-110, 1 (1997).
[Crossref]

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
[Crossref]

1996 (1)

A. Vogel, S. Busch, and U. Parlitz, J. Acoust. Soc. Am. 100, 148 (1996).
[Crossref]

1994 (1)

T. Juhasz, X. H. Hu, L. Turi, and Z. Bor, Lasers Surg. Med. 15, 91 (1994).
[Crossref]

1993 (1)

R. R. Krueger, J. S. Krasinski, C. Radzewicz, K. G. Stonecipher, and J. J. Rowsey, Cornea 12, 330 (1993).
[Crossref]

Anisimov, S.

B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. Anisimov, Appl. Phys. A 79, 767 (2004).
[Crossref]

Apitz, I.

I. Apitz and A. Vogel, Appl. Phys. A 81, 329 (2005).
[Crossref]

Arnold, N.

N. Arnold, J. Gruber, and J. Heitz, Appl. Phys. A 69, S87 (1999).
[Crossref]

Balling, P.

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
[Crossref]

Baumert, T.

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
[Crossref]

C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, New J. Phys. 14, 075021 (2012).
[Crossref]

Bialkowski, J.

D. von der Linde, K. Sokolowski-Tinten, and J. Bialkowski, Appl. Surf. Sci. 109-110, 1 (1997).
[Crossref]

Bor, Z.

T. Juhasz, X. H. Hu, L. Turi, and Z. Bor, Lasers Surg. Med. 15, 91 (1994).
[Crossref]

Boutou, V.

Brumfield, B. E.

S. S. Harilal, B. E. Brumfield, B. D. Cannon, and M. C. Phillips, Anal. Chem. 88, 2296 (2016). PMID: 26732866.
[Crossref]

Busch, S.

A. Vogel, S. Busch, and U. Parlitz, J. Acoust. Soc. Am. 100, 148 (1996).
[Crossref]

Cannon, B. D.

S. S. Harilal, B. E. Brumfield, B. D. Cannon, and M. C. Phillips, Anal. Chem. 88, 2296 (2016). PMID: 26732866.
[Crossref]

Courvoisier, F.

de la Cruz, A. R.

Dijkhuis, J. I.

Du, D.

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
[Crossref]

Favre, C.

Freidank, S.

N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015).
[Crossref]

Galvan-Sosa, M.

J. Hernandez-Rueda, J. Siegel, M. Galvan-Sosa, A. R. de la Cruz, M. Garcia-Lechuga, and J. Solis, J. Opt. Soc. Am. B 32, 150 (2015).
[Crossref]

J. Hernandez-Rueda, D. Puerto, J. Siegel, M. Galvan-Sosa, and J. Solis, Appl. Surf. Sci. 258, 9389 (2012).
[Crossref]

Garcia-Lechuga, M.

Gattass, R. R.

R. R. Gattass and E. Mazur, Nat. Photonics 2, 219 (2008).
[Crossref]

Glezer, E. N.

Götte, N.

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
[Crossref]

Gruber, J.

N. Arnold, J. Gruber, and J. Heitz, Appl. Phys. A 69, S87 (1999).
[Crossref]

Haahr-Lillevang, L.

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
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Harilal, S. S.

S. S. Harilal, B. E. Brumfield, B. D. Cannon, and M. C. Phillips, Anal. Chem. 88, 2296 (2016). PMID: 26732866.
[Crossref]

Heitz, J.

N. Arnold, J. Gruber, and J. Heitz, Appl. Phys. A 69, S87 (1999).
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Hernandez-Rueda, J.

J. Hernandez-Rueda, J. Siegel, M. Galvan-Sosa, A. R. de la Cruz, M. Garcia-Lechuga, and J. Solis, J. Opt. Soc. Am. B 32, 150 (2015).
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J. Hernandez-Rueda, D. Puerto, J. Siegel, M. Galvan-Sosa, and J. Solis, Appl. Surf. Sci. 258, 9389 (2012).
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Hill, S. C.

Hu, X. H.

T. Juhasz, X. H. Hu, L. Turi, and Z. Bor, Lasers Surg. Med. 15, 91 (1994).
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Ito, Y.

T. T. Nguyen, R. Tanabe, and Y. Ito, Opt. Laser Technol. 100, 21 (2018).
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Jelzow, N.

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
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Juhasz, T.

T. Juhasz, X. H. Hu, L. Turi, and Z. Bor, Lasers Surg. Med. 15, 91 (1994).
[Crossref]

Kattawar, G.

Kim, A. M.-T.

Köhler, J.

C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, New J. Phys. 14, 075021 (2012).
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Kolomenskii, A.

Krasinski, J. S.

R. R. Krueger, J. S. Krasinski, C. Radzewicz, K. G. Stonecipher, and J. J. Rowsey, Cornea 12, 330 (1993).
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Krol, D. M.

Krueger, R. R.

R. R. Krueger, J. S. Krasinski, C. Radzewicz, K. G. Stonecipher, and J. J. Rowsey, Cornea 12, 330 (1993).
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Liang, X.-X.

N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015).
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Linz, N.

N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015).
[Crossref]

Liu, X.

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
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Mazur, E.

Mourou, G.

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
[Crossref]

Nguyen, T. T.

T. T. Nguyen, R. Tanabe, and Y. Ito, Opt. Laser Technol. 100, 21 (2018).
[Crossref]

Nishimura, N.

Parlitz, U.

A. Vogel, S. Busch, and U. Parlitz, J. Acoust. Soc. Am. 100, 148 (1996).
[Crossref]

Phillips, M. C.

S. S. Harilal, B. E. Brumfield, B. D. Cannon, and M. C. Phillips, Anal. Chem. 88, 2296 (2016). PMID: 26732866.
[Crossref]

Puerto, D.

J. Hernandez-Rueda, D. Puerto, J. Siegel, M. Galvan-Sosa, and J. Solis, Appl. Surf. Sci. 258, 9389 (2012).
[Crossref]

Radzewicz, C.

R. R. Krueger, J. S. Krasinski, C. Radzewicz, K. G. Stonecipher, and J. J. Rowsey, Cornea 12, 330 (1993).
[Crossref]

Rethfeld, B.

B. Rethfeld, Phys. Rev. B 73, 035101 (2006).
[Crossref]

B. Rethfeld, Phys. Rev. Lett. 92, 187401 (2004).
[Crossref]

B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. Anisimov, Appl. Phys. A 79, 767 (2004).
[Crossref]

Rowsey, J. J.

R. R. Krueger, J. S. Krasinski, C. Radzewicz, K. G. Stonecipher, and J. J. Rowsey, Cornea 12, 330 (1993).
[Crossref]

Sarpe, C.

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
[Crossref]

C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, New J. Phys. 14, 075021 (2012).
[Crossref]

Schaffer, C. B.

Sedov, L. I.

L. I. Sedov, Similarity and Dimensional Methods in Mechanics (CRC Press, 1993).

Senftleben, A.

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
[Crossref]

Siegel, J.

J. Hernandez-Rueda, J. Siegel, M. Galvan-Sosa, A. R. de la Cruz, M. Garcia-Lechuga, and J. Solis, J. Opt. Soc. Am. B 32, 150 (2015).
[Crossref]

J. Hernandez-Rueda, D. Puerto, J. Siegel, M. Galvan-Sosa, and J. Solis, Appl. Surf. Sci. 258, 9389 (2012).
[Crossref]

Sokolov, A.

Sokolowski-Tinten, K.

B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. Anisimov, Appl. Phys. A 79, 767 (2004).
[Crossref]

D. von der Linde, K. Sokolowski-Tinten, and J. Bialkowski, Appl. Surf. Sci. 109-110, 1 (1997).
[Crossref]

Solis, J.

J. Hernandez-Rueda, J. Siegel, M. Galvan-Sosa, A. R. de la Cruz, M. Garcia-Lechuga, and J. Solis, J. Opt. Soc. Am. B 32, 150 (2015).
[Crossref]

J. Hernandez-Rueda, D. Puerto, J. Siegel, M. Galvan-Sosa, and J. Solis, Appl. Surf. Sci. 258, 9389 (2012).
[Crossref]

Springer, M.

Stonecipher, K. G.

R. R. Krueger, J. S. Krasinski, C. Radzewicz, K. G. Stonecipher, and J. J. Rowsey, Cornea 12, 330 (1993).
[Crossref]

Strycker, B.

Tanabe, R.

T. T. Nguyen, R. Tanabe, and Y. Ito, Opt. Laser Technol. 100, 21 (2018).
[Crossref]

Traverso, A.

Trickl, T.

N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015).
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T. Juhasz, X. H. Hu, L. Turi, and Z. Bor, Lasers Surg. Med. 15, 91 (1994).
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van Oosten, D.

Venugopalan, V.

A. Vogel and V. Venugopalan, Chem. Rev. 103, 577 (2003).
[Crossref]

Vogel, A.

N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015).
[Crossref]

I. Apitz and A. Vogel, Appl. Phys. A 81, 329 (2005).
[Crossref]

A. Vogel and V. Venugopalan, Chem. Rev. 103, 577 (2003).
[Crossref]

A. Vogel, S. Busch, and U. Parlitz, J. Acoust. Soc. Am. 100, 148 (1996).
[Crossref]

Vogelmann, H.

N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015).
[Crossref]

von der Linde, D.

B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. Anisimov, Appl. Phys. A 79, 767 (2004).
[Crossref]

D. von der Linde, K. Sokolowski-Tinten, and J. Bialkowski, Appl. Surf. Sci. 109-110, 1 (1997).
[Crossref]

Winkler, T.

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
[Crossref]

C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, New J. Phys. 14, 075021 (2012).
[Crossref]

Wolf, J.-P.

Wollenhaupt, M.

C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, New J. Phys. 14, 075021 (2012).
[Crossref]

Zhang, H.

Zielinski, B.

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
[Crossref]

Anal. Chem. (1)

S. S. Harilal, B. E. Brumfield, B. D. Cannon, and M. C. Phillips, Anal. Chem. 88, 2296 (2016). PMID: 26732866.
[Crossref]

Appl. Phys. A (3)

B. Rethfeld, K. Sokolowski-Tinten, D. von der Linde, and S. Anisimov, Appl. Phys. A 79, 767 (2004).
[Crossref]

I. Apitz and A. Vogel, Appl. Phys. A 81, 329 (2005).
[Crossref]

N. Arnold, J. Gruber, and J. Heitz, Appl. Phys. A 69, S87 (1999).
[Crossref]

Appl. Surf. Sci. (3)

T. Winkler, C. Sarpe, N. Jelzow, L. Haahr-Lillevang, N. Götte, B. Zielinski, P. Balling, A. Senftleben, and T. Baumert, Appl. Surf. Sci. 374, 235 (2016).
[Crossref]

D. von der Linde, K. Sokolowski-Tinten, and J. Bialkowski, Appl. Surf. Sci. 109-110, 1 (1997).
[Crossref]

J. Hernandez-Rueda, D. Puerto, J. Siegel, M. Galvan-Sosa, and J. Solis, Appl. Surf. Sci. 258, 9389 (2012).
[Crossref]

Chem. Rev. (1)

A. Vogel and V. Venugopalan, Chem. Rev. 103, 577 (2003).
[Crossref]

Cornea (1)

R. R. Krueger, J. S. Krasinski, C. Radzewicz, K. G. Stonecipher, and J. J. Rowsey, Cornea 12, 330 (1993).
[Crossref]

IEEE J. Quantum Electron. (1)

X. Liu, D. Du, and G. Mourou, IEEE J. Quantum Electron. 33, 1706 (1997).
[Crossref]

J. Acoust. Soc. Am. (1)

A. Vogel, S. Busch, and U. Parlitz, J. Acoust. Soc. Am. 100, 148 (1996).
[Crossref]

J. Opt. Soc. Am. B (1)

Lasers Surg. Med. (1)

T. Juhasz, X. H. Hu, L. Turi, and Z. Bor, Lasers Surg. Med. 15, 91 (1994).
[Crossref]

Nat. Photonics (1)

R. R. Gattass and E. Mazur, Nat. Photonics 2, 219 (2008).
[Crossref]

New J. Phys. (1)

C. Sarpe, J. Köhler, T. Winkler, M. Wollenhaupt, and T. Baumert, New J. Phys. 14, 075021 (2012).
[Crossref]

Opt. Express (2)

Opt. Laser Technol. (1)

T. T. Nguyen, R. Tanabe, and Y. Ito, Opt. Laser Technol. 100, 21 (2018).
[Crossref]

Opt. Lett. (2)

Phys. Rev. B (2)

B. Rethfeld, Phys. Rev. B 73, 035101 (2006).
[Crossref]

N. Linz, S. Freidank, X.-X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, Phys. Rev. B 91, 134114 (2015).
[Crossref]

Phys. Rev. Lett. (1)

B. Rethfeld, Phys. Rev. Lett. 92, 187401 (2004).
[Crossref]

Other (1)

L. I. Sedov, Similarity and Dimensional Methods in Mechanics (CRC Press, 1993).

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Figures (4)

Fig. 1.
Fig. 1. (a) Scheme of the experimental setup. (b) Transient reflectivity images of a variety of shocks. Note that all the images were acquired at a delay of 10 ns using a fluence of 18 J / cm 2 , except for single beam illumination, which was recorded at a 4 ns delay time using a fluence of 22 J / cm 2 .
Fig. 2.
Fig. 2. Fs-laser-induced electron plasma, vapor expansion, and shockwave formation during a double excitation experiment.
Fig. 3.
Fig. 3. (a) Snapshot of the vapor propagation and shock formation at 10 ns time delay. (b) Geometrical scheme during double pulse excitation. (c) Elongated shockwave length and compressed gas front radius as a function of the delay time. (d) Compressed air front radial velocity as a function of time.
Fig. 4.
Fig. 4. Femtosecond-laser-induced electron plasma, vapor expansion, and shockwave formation during a quadruple pump experiment.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

v l ( L / 2 , t ) = ( | v r u ( t ) | cos α ( t ) + | v r d ( t ) | cos α ( t ) ) ,
| r s ( t ) | = h o 2 4 + L ( t ) 2 4 | r s ( t ) | = A ( E / ρ ) 1 5 t 2 5 ,
| v r ( t ) | = | r ˙ s ( t ) | .

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