Abstract

When a femtosecond laser pulse propagates through water clouds, optical breakdown can occur once the laser intensity exceeds a certain threshold. This photoionization process, along with the resultant laser-induced plasma, can strongly influence laser communications and laser-induced precipitation. However, the calculation model for the initial evolution of the laser field and its self-generated plasma remain insufficient. Here, we provide a theoretical transient coupling model to investigate the evolution of the laser-induced plasma in the water-cloud droplets, along with the nonlinear absorption occurring during optical breakdown. Agreement is achieved between the experimentally determined breakdown threshold and our calculated prediction. The calculation results indicate that the optical breakdown occurring in a water cloud has a considerable influence on the laser field. It is recommended that the laser intensity does not exceed the breakdown threshold for laser communications. We expect that our findings will also be helpful for weather control.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

2017 (1)

2016 (1)

2015 (1)

N. Linz, S. Freidank, X. X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, “Wavelength dependence of nanosecond infrared laser-induced breakdown in water: Evidence for multiphoton initiation via an intermediate state,” Phys. Rev. B 91, 134114 (2015).
[Crossref]

2014 (3)

2013 (1)

T. V. Liseykina and D. Bauer, “Plasma-formation dynamics in intense laser-droplet interaction,” Phys. Rev. Lett. 110, 145003 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (2)

Y. E. Geints, A. A. Zemlyanov, A. M. Kabanov, E. E. Bykova, D. V. Apeksimov, O. A. Bukin, E. B. Sokolova, S. S. Golik, and A. A. Ilyin, “Angular diagram of broadband emission of millimeter-sized water droplets exposed to gigawatt femtosecond laser pulses,” Appl. Opt. 50, 5291–5298 (2011).
[Crossref] [PubMed]

S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
[Crossref] [PubMed]

2010 (2)

Y. E. Geints, A. M. Kabanov, G. G. Matvienko, V. K. Oshlakov, A. A. Zemlyanov, S. S. Golik, and O. A. Bukin, “Broadband emission spectrum dynamics of large water droplets exposed to intense ultrashort laser radiation,” Opt. Lett. 35, 2717–2719 (2010).
[Crossref] [PubMed]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

2009 (1)

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407 nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
[Crossref]

2008 (1)

A. Vogel, N. Linz, S. Freidank, and G. Paltauf, “Femtosecond-laser-induced nanocavitation in water: implications for optical breakdown threshold and cell surgery,” Phys. Rev. Lett. 100, 038102 (2008).
[Crossref] [PubMed]

2006 (2)

2005 (1)

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

2004 (5)

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[Crossref]

A. Lindinger, J. Hagen, L. D. Socaciu, T. M. Bernhardt, L. Wöste, D. Duft, and T. Leisner, “Time-resolved explosion dynamics of h2o droplets induced by femtosecond laser pulses,” Appl. Opt. 43, 5263–5269 (2004).
[Crossref] [PubMed]

M. Kolesik and J. V. Moloney, “Self-healing femtosecond light filaments,” Opt. Lett. 29, 590–592 (2004).
[Crossref] [PubMed]

S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93, 023901 (2004).
[Crossref] [PubMed]

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light filaments without self-channeling,” Phys. Rev. Lett. 92, 253903 (2004).
[Crossref] [PubMed]

2003 (3)

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215 (2003).
[Crossref]

F. Courvoisier, V. Boutou, C. Favre, S. C. Hill, and J.-P. Wolf, “Plasma formation dynamics within a water microdroplet on femtosecond time scales,” Opt. Lett. 28, 206–208 (2003).
[Crossref] [PubMed]

J. Kasparian, M. Rodríguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbery, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

2002 (1)

C. Favre, V. Boutou, S. C. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. K. Chang, L. Woeste, and J.-P. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett. 89, 035002 (2002).
[Crossref] [PubMed]

2001 (1)

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470 (2001).
[Crossref] [PubMed]

2000 (2)

J. Kasparian, R. Sauerbrey, and S. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[Crossref]

P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
[Crossref]

1999 (2)

C. H. Fan, J. Sun, and J. P. Longtin, “Breakdown threshold and localized electron density in water induced by ultrashort laser pulses,” J. Appl. Phys. 53, 2530–2536 (1999).

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35, 1156–1167 (1999).
[Crossref]

1998 (3)

1997 (1)

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. Hammer, B. Rockwell, and C. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[Crossref]

1996 (1)

A. Vogel, K. Nahen, D. Theisen, and J. Noack, “Plasma formation in water by picosecond and nanosecond nd: Yag laser pulses. i. optical breakdown at threshold and superthreshold irradiance,” IEEE J. Sel. Top. Quantum Electron. 2, 847–860 (1996).
[Crossref]

1995 (1)

P. K. Kennedy, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media. i. theory,” IEEE J. Quantum Electron. 31, 2241–2249 (1995).
[Crossref]

1994 (1)

1993 (1)

A. A. Lushnikov and A. E. Negin, “Aerosols in strong laser beams,” J. Aerosol Sci. 24, 707–735 (1993).
[Crossref]

1990 (1)

1989 (1)

1988 (4)

1987 (1)

1985 (1)

1978 (1)

1967 (1)

S. Twomey, H. Jacobowitz, and H. B. Howell, “Light scattering by cloud layers,” J. Atmos. Sci. 24, 70–79 (1967).
[Crossref]

Ackermann, R.

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

André, Y.-B.

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

J. Kasparian, M. Rodríguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbery, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Apeksimov, D. V.

Armstrong, R. L.

Barbano, E. C.

Bauer, D.

T. V. Liseykina and D. Bauer, “Plasma-formation dynamics in intense laser-droplet interaction,” Phys. Rev. Lett. 110, 145003 (2013).
[Crossref] [PubMed]

Bergé, L.

S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93, 023901 (2004).
[Crossref] [PubMed]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470 (2001).
[Crossref] [PubMed]

Bernhardt, T. M.

Bissonnette, L.

Biswas, A.

Bourayou, R.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[Crossref]

J. Kasparian, M. Rodríguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbery, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Boutou, V.

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215 (2003).
[Crossref]

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A. Vogel, N. Linz, S. Freidank, and G. Paltauf, “Femtosecond-laser-induced nanocavitation in water: implications for optical breakdown threshold and cell surgery,” Phys. Rev. Lett. 100, 038102 (2008).
[Crossref] [PubMed]

Pendleton, J. D.

Peschel, U.

S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93, 023901 (2004).
[Crossref] [PubMed]

Petit, Y.

S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
[Crossref] [PubMed]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Pinnick, R. G.

Pohl, T.

S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
[Crossref] [PubMed]

Prade, B.

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470 (2001).
[Crossref] [PubMed]

Produit, T.

Queißer, M.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

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P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
[Crossref]

Rezvani, S. A.

Rockwell, B.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. Hammer, B. Rockwell, and C. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
[Crossref]

Rodriguez, M.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[Crossref]

P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
[Crossref]

Rodríguez, M.

J. Kasparian, M. Rodríguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbery, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

Rohwetter, P.

S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
[Crossref] [PubMed]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

Ronneberger, F.

P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
[Crossref]

Roy, G.

Salamé, R.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Salmon, E.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[Crossref]

J. Kasparian, M. Rodríguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbery, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215 (2003).
[Crossref]

Sauerbery, R.

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[Crossref]

J. Kasparian, M. Rodríguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbery, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
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Sauerbrey, R.

J. Kasparian, R. Sauerbrey, and S. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
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P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
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Saxena, I.

Schillinger, H.

P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
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Schimmel, G.

Schlie, L. A.

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

Schneider, F.

S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
[Crossref] [PubMed]

Scholz, A.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
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M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: The software package opac,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
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S. Skupin, L. Bergé, U. Peschel, and F. Lederer, “Interaction of femtosecond light filaments with obscurants in aerosols,” Phys. Rev. Lett. 93, 023901 (2004).
[Crossref] [PubMed]

Socaciu, L. D.

Sokolova, E. B.

Song, W.

Stecklum, B.

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
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Stein, B.

P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
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Stelmaszczyk, K.

S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
[Crossref] [PubMed]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
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Stepanov, A. N.

Sun, H.

Sun, J.

C. H. Fan, J. Sun, and J. P. Longtin, “Breakdown threshold and localized electron density in water induced by ultrashort laser pulses,” J. Appl. Phys. 53, 2530–2536 (1999).

Tamosauskas, G.

A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, “Whole life cycle of femtosecond ultraviolet filaments in water,” Phys. Rev. A 89, 033809 (2014).
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A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light filaments without self-channeling,” Phys. Rev. Lett. 92, 253903 (2004).
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A. Vogel, K. Nahen, D. Theisen, and J. Noack, “Plasma formation in water by picosecond and nanosecond nd: Yag laser pulses. i. optical breakdown at threshold and superthreshold irradiance,” IEEE J. Sel. Top. Quantum Electron. 2, 847–860 (1996).
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Thompson, C.

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. Hammer, B. Rockwell, and C. Thompson, “Theory and simulation on the threshold of water breakdown induced by focused ultrashort laser pulses,” IEEE J. Quantum Electron. 33, 127–137 (1997).
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Ting, A.

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407 nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
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A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light filaments without self-channeling,” Phys. Rev. Lett. 92, 253903 (2004).
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S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470 (2001).
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Varma, S.

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407 nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
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Vaughan, O. H.

Vogel, A.

N. Linz, S. Freidank, X. X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, “Wavelength dependence of nanosecond infrared laser-induced breakdown in water: Evidence for multiphoton initiation via an intermediate state,” Phys. Rev. B 91, 134114 (2015).
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S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
[Crossref] [PubMed]

A. Vogel, N. Linz, S. Freidank, and G. Paltauf, “Femtosecond-laser-induced nanocavitation in water: implications for optical breakdown threshold and cell surgery,” Phys. Rev. Lett. 100, 038102 (2008).
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J. Noack and A. Vogel, “Single-shot spatially resolved characterization of laser-induced shock waves in water,” Appl. Opt. 37, 4092–4099 (1998).
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A. Vogel, K. Nahen, D. Theisen, and J. Noack, “Plasma formation in water by picosecond and nanosecond nd: Yag laser pulses. i. optical breakdown at threshold and superthreshold irradiance,” IEEE J. Sel. Top. Quantum Electron. 2, 847–860 (1996).
[Crossref]

Vogelmann, H.

N. Linz, S. Freidank, X. X. Liang, H. Vogelmann, T. Trickl, and A. Vogel, “Wavelength dependence of nanosecond infrared laser-induced breakdown in water: Evidence for multiphoton initiation via an intermediate state,” Phys. Rev. B 91, 134114 (2015).
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Waite, D.

P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
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Wang, C.

Wang, W.

Weber, K.

S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
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Wedekind, C.

P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
[Crossref]

Wilkes, Z. W.

Z. W. Wilkes, S. Varma, Y.-H. Chen, H. M. Milchberg, T. G. Jones, and A. Ting, “Direct measurements of the nonlinear index of refraction of water at 815 and 407 nm using single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 94, 211102 (2009).
[Crossref]

Wille, H.

J. Kasparian, M. Rodríguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbery, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref] [PubMed]

P. Rairoux, H. Schillinger, S. Niedermeier, M. Rodriguez, F. Ronneberger, R. Sauerbrey, B. Stein, D. Waite, C. Wedekind, H. Wille, L. Wöste, and C. Ziener, “Remote sensing of the atmosphere using ultrashort laser pulses,” Appl. Phys. B 71, 573–580 (2000).
[Crossref]

Winker, D.

Winn, W.

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
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Woeste, L.

C. Favre, V. Boutou, S. C. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. K. Chang, L. Woeste, and J.-P. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett. 89, 035002 (2002).
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Wolf, J.-P.

G. Schimmel, T. Produit, D. Mongin, J. Kasparian, and J.-P. Wolf, “Free space laser telecommunication through fog,” Optica 5, 1338–1341 (2018).
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S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
[Crossref] [PubMed]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
[Crossref]

F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215 (2003).
[Crossref]

J. Kasparian, M. Rodríguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbery, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
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F. Courvoisier, V. Boutou, C. Favre, S. C. Hill, and J.-P. Wolf, “Plasma formation dynamics within a water microdroplet on femtosecond time scales,” Opt. Lett. 28, 206–208 (2003).
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C. Favre, V. Boutou, S. C. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. K. Chang, L. Woeste, and J.-P. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett. 89, 035002 (2002).
[Crossref] [PubMed]

Wood, C. F.

Wöste, L.

S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Hao, W. Nakaema, A. Vogel, T. Pohl, F. Schneider, J. Kasparian, K. Weber, L. Wöste, and J.-P. Wolf, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2, 456 (2011).
[Crossref] [PubMed]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J.-P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

G. Méchain, G. Méjean, R. Ackermann, P. Rohwetter, Y.-B. André, J. Kasparian, B. Prade, K. Stelmaszczyk, J. Yu, E. Salmon, W. Winn, L. A. Schlie, A. Mysyrowicz, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Propagation of fs tw laser filaments in adverse atmospheric conditions,” Appl. Phys. B 80, 785–789 (2005).
[Crossref]

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M. Rodriguez, R. Bourayou, G. Méjean, J. Kasparian, J. Yu, E. Salmon, A. Scholz, B. Stecklum, J. Eislöffel, U. Laux, A. P. Hatzes, R. Sauerbery, L. Wöste, and J.-P. Wolf, “Kilometer-range nonlinear propagation of femtosecond laser pulses,” Phys. Rev. E 69, 036607 (2004).
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F. Courvoisier, V. Boutou, J. Kasparian, E. Salmon, G. Méjean, J. Yu, and J.-P. Wolf, “Ultraintense light filaments transmitted through clouds,” Appl. Phys. Lett. 83, 213–215 (2003).
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Figures (11)

Fig. 1
Fig. 1 Sketch of femtosecond laser interaction with water cloud with (a) three-dimensional model, (b) xy plane model, and (c) yz plane model. The water clouds are composed of large amounts of droplets and cloud condensation nuclei (CCN).
Fig. 2
Fig. 2 Variation of droplet optical breakdown threshold with droplet radius r. The thresholds for droplets with r > 0.9 μ m are not shown, as those thresholds tend to have a stable value.
Fig. 3
Fig. 3 Time evolutions of laser-induced plasmas while femtosecond laser pulse passes through droplets. The droplet r values are (a)–(c) 4 and (d)–(f) 0.8 μ m. Note that the color map in each figure is different as the color scale represents the relative FED only; i.e., the ratio between the FED anywhere and the maximum FED of each figure. ρ / ρ max. In all figures, the laser intensity I0 is 5 × 10 12 W / cm 2. The above figures show only parts of the calculation regimes. The concrete moments for each figure are 85, 165, 245, 48, 123, and 187 fs.
Fig. 4
Fig. 4 FED distributions for incident lasers with different laser intensity I0: (a) 5 × 10 12, (b) 1.1 × 10 13, and (c) 2.5 × 10 13 W / cm 2. (d)–(f) Corresponding laser field distributions for each intensity I0. The droplet r is 4 μ m. Note that the color map in each figure is different as the color scale represents the relative FED only. The figures show parts of the calculation regimes only. The concrete moments for the three laser intensities are 165, 181, and 139 fs.
Fig. 5
Fig. 5 (a) Droplet energy losses Q and (b) energy losses proportion Q / Q t variation with laser intensity for different droplet radii.
Fig. 6
Fig. 6 (a) Energy losses of droplet Q and (b) energy loss proportions Q / Q t variation with droplet size for different laser intensities.
Fig. 7
Fig. 7 Distribution of FED for two series-connected droplets. For both droplets, r = 4 μ m, and the distance between the two droplet centers is 13 μ m. The laser field propagates from left to right.
Fig. 8
Fig. 8 Probability for two arbitrary droplets aligned by series connection variation with beam length l for different water clouds. The droplet size r in Eq. (10) is selected by the model radius of each cloud. The inset is the sketch of two series-connected droplets.
Fig. 9
Fig. 9 Size distributions for different water clouds and fog.
Fig. 10
Fig. 10 Proportion of the energy losses variation with laser intensity for different water clouds and fog. The energy losses represent the decrease in laser energy after the laser pulse propagates through a cloud of length 1 m.
Fig. 11
Fig. 11 Propagation length L variation with laser intensity for different water clouds and fog. Note that the propagation length of fog should be multiplied by 5.

Tables (3)

Tables Icon

Table 1 Parameters used in transient coupling model, Eqs. (1), (3), and (4).

Tables Icon

Table 2 Breakdown thresholds for water and droplet under laser pulses with different pulse durations τ, wavelengths λ, and numerical apertures N.A. Here, Iexp and Ical denote the experimental and calculated thresholds for water, respectively; and Idroplet represents the calculated threshold for an additional 4- μ m droplet suspended in the laser field focus area. The last three rows show the calculated threshold for a 4- μ m droplet under the assumption that the laser field corresponds to a plane wave. The thresholds from [49] correspond to a breakdown probability of 1%.

Tables Icon

Table 3 Calculated scattering coefficients σs, corrected scattering coefficients σ s   ' = σ s R c ( θ < 1.5 ), and absorption coefficients σa for different water clouds and fog. Here, σ a 5, σ a 10, and σ a 25 represent the coefficients corresponding to initial laser intensities of I 0 = 5 × 10 12, 1 × 10 13, and 2.5 × 10 13 W / cm 2, respectively. The units for all the above coefficients are km 1.

Equations (15)

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ρ t = ( β K K ω I K + σ A I V ρ ) ( 1 ρ ρ n ) + ( D ρ ) g ρ 2 ,
× × E + 1 c 2 2 t 2 ( ε r L E ) + μ 0 ( J t + 2 P NL t 2 ) = 0 ,
ε r = ε r L + 2 n 0 n 2 ε 0 I + i c n 0 σ c ρ ω + i c n 0 β K ω I K 1 .
× × E + 1 c 2 t ( ε r E t ) = 0.
d N d r = N a r α exp  [ α γ ( r r 0 ) γ ] ,
E = E 0 w 0 w ( x ) exp   [ 2 ln   2 ( t τ ) 2 τ 2 c 0 y 2 w 2 ( x ) ] × exp   [ i ( ω t k x k y 2 2 R w ( x ) + Φ ( x ) ) ] e ^ z ,
Q = V d V d t ( J E ) = π d y d x y d t ( J E ) ,
Q t = I ( t ) π r 2 d t = 1 2 ln  2 π 3 2 r 2 τ I 0 ,
P = 1 i = 1 s ( 1 i p ) ,
p = [ r 2 R 2 + 1 R r R 1 π arccos  ( 1 r 2 2 δ 2 ) d δ ] ( r R ) ,
Q = Q ( I 0 , r ) r n ( r ) d r ,
Q ( I 0 , r ) Q ( r ) + Q ( I 0 ) Q ( I 0 i ) R 0 2 r 2 .
P j ( θ ) = 4 π β s λ 2 4 π 2 r 1 r 2 n ( r ) i j ( θ ) d r ,
β s = π r 1 r 2 r 2 Q s n ( r ) d r ,
R c = 1 1 4 π 0 θ P j ( θ ) sin  θ d θ .

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