Optical breakdown during femtosecond laser propagation in water cloud

Chong Zhang; Mao Tang; Hongchao Zhang; Jian Lu

doi:10.1364/OE.27.008456

Optics Express
Vol. 27,
Issue 6,
pp. 8456-8475
(2019)
•https://doi.org/10.1364/OE.27.008456

Optical breakdown during femtosecond laser propagation in water cloud

Chong Zhang, Mao Tang, Hongchao Zhang, and Jian Lu

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Chong Zhang, Mao Tang, Hongchao Zhang, and Jian Lu, "Optical breakdown during femtosecond laser propagation in water cloud," Opt. Express 27, 8456-8475 (2019)

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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.

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Year
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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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2018 (2)

W. Song, J. Lai, Z. Ghassemlooy, S. Li, P. Zhang, W. Yan, C. Wang, and Z. Li, “Influence of fog on the signal to interference plus noise ratio of the imaging laser radar using a 16-element apd array,” Opt. Express 26, 22030–22045 (2018).
[Crossref] [PubMed]

G. Schimmel, T. Produit, D. Mongin, J. Kasparian, and J.-P. Wolf, “Free space laser telecommunication through fog,” Optica 5, 1338–1341 (2018).
[Crossref]

2017 (1)

T. G. de Souza, E. C. Barbano, S. C. Zilio, and L. Misoguti, “Measurement of nonlinear refractive indices of air, oxygen, and nitrogen in capillary by changing the temporal width of short laser pulses,” J. Opt. Soc. Am. B 34, 2233–2237 (2017).
[Crossref]

2016 (1)

Z. Hong, Q. Zhang, S. A. Rezvani, P. Lan, and P. Lu, “Extending plasma channel of filamentation with a multi-focal-length beam,” Opt. Express 24, 4029–4041 (2016).
[Crossref] [PubMed]

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)

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).
[Crossref]

I. Saxena, K. Ehmann, and J. Cao, “Laser-induced plasma in aqueous media: numerical simulation and experimental validation of spatial and temporal profiles,” Appl. Opt. 53, 8283–8294 (2014).
[Crossref]

E. S. Efimenko, Y. A. Malkov, A. A. Murzanev, and A. N. Stepanov, “Femtosecond laser pulse-induced breakdown of a single water microdroplet,” J. Opt. Soc. Am. B 31, 534–541 (2014).
[Crossref]

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)

J. Ju, J. Liu, C. Wang, H. Sun, W. Wang, X. Ge, C. Li, S. L. Chin, R. Li, and Z. Xu, “Laser-filamentation-induced condensation and snow formation in a cloud chamber,” Opt. Lett. 37, 1214–1216 (2012).
[Crossref] [PubMed]

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)

Y. Hu, Z. Liu, D. Winker, M. Vaughan, V. Noel, L. Bissonnette, G. Roy, and M. McGill, “Simple relation between lidar multiple scattering and depolarization for water clouds,” Opt. Lett. 31, 1809–1811 (2006).
[Crossref] [PubMed]

T.-T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006).
[Crossref] [PubMed]

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)

J. Noack and A. Vogel, “Single-shot spatially resolved characterization of laser-induced shock waves in water,” Appl. Opt. 37, 4092–4099 (1998).
[Crossref]

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).
[Crossref]

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
[Crossref]

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)

Y. E. Geints, A. A. Zemlyanov, and R. L. Armstrong, “Explosive boiling of water droplets irradiated with intense co2-laser radiation: numerical experiments,” Appl. Opt. 33, 5805–5810 (1994).
[Crossref] [PubMed]

1993 (1)

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

1990 (1)

R. G. Pinnick, A. Biswas, R. L. Armstrong, S. G. Jennings, J. D. Pendleton, and G. Fernández, “Micron-sized droplets irradiated with a pulsed co2 laser: measurement of explosion and breakdown thresholds,” Appl. Opt. 29, 918–925 (1990).
[Crossref] [PubMed]

1989 (1)

A. Zardecki and J. D. Pendleton, “Hydrodynamics of water droplets irradiated by a pulsed co2 laser,” Appl. Opt. 28, 638–640 (1989).
[Crossref] [PubMed]

1988 (4)

J. C. Carls and J. R. Brock, “Explosive vaporization of single droplets by lasers: comparison of models with experiments,” Opt. Lett. 13, 919–921 (1988).
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[Crossref]

1987 (1)

J.-Z. Zhang, J. K. Lam, C. F. Wood, B.-T. Chu, and R. K. Chang, “Explosive vaporization of a large transparent droplet irradiated by a high intensity laser,” Appl. Opt. 26, 4731–4737 (1987).
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1985 (1)

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1978 (1)

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1967 (1)

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André, Y.-B.

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

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Bykova, E. E.

Cao, J.

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Chen, S.-c.

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Chin, S. L.

Chu, B.-T.

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de Souza, T. G.

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Efimenko, E. S.

E. S. Efimenko, Y. A. Malkov, A. A. Murzanev, and A. N. Stepanov, “Femtosecond laser pulse-induced breakdown of a single water microdroplet,” J. Opt. Soc. Am. B 31, 534–541 (2014).
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Favre, C.

Feng, Q.

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Franco, M.

Freidank, S.

Frey, S.

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Hu, Y.

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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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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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Kennedy, P. K.

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]

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

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Z. Hong, Q. Zhang, S. A. Rezvani, P. Lan, and P. Lu, “Extending plasma channel of filamentation with a multi-focal-length beam,” Opt. Express 24, 4029–4041 (2016).
[Crossref] [PubMed]

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Laux, U.

Lederer, F.

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Linz, N.

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

Liu, J.

Liu, Z.

Longtin, J. P.

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).

Lu, P.

Z. Hong, Q. Zhang, S. A. Rezvani, P. Lan, and P. Lu, “Extending plasma channel of filamentation with a multi-focal-length beam,” Opt. Express 24, 4029–4041 (2016).
[Crossref] [PubMed]

Lu, X.

T.-T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006).
[Crossref] [PubMed]

Lushnikov, A. A.

A. A. Lushnikov and A. E. Negin, “Aerosols in strong laser beams,” J. Aerosol Sci. 24, 707–735 (1993).
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G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a gaussian beam, using a bromwich formulation,” J. Opt. Soc. Am. B 5, 1427–1443 (1988).
[Crossref]

Majus, D.

Malkov, Y. A.

E. S. Efimenko, Y. A. Malkov, A. A. Murzanev, and A. N. Stepanov, “Femtosecond laser pulse-induced breakdown of a single water microdroplet,” J. Opt. Soc. Am. B 31, 534–541 (2014).
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Matvienko, G. G.

McGill, M.

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M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
[Crossref]

Moloney, J. V.

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

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
[Crossref]

Mongin, D.

G. Schimmel, T. Produit, D. Mongin, J. Kasparian, and J.-P. Wolf, “Free space laser telecommunication through fog,” Optica 5, 1338–1341 (2018).
[Crossref]

Murzanev, A. A.

E. S. Efimenko, Y. A. Malkov, A. A. Murzanev, and A. N. Stepanov, “Femtosecond laser pulse-induced breakdown of a single water microdroplet,” J. Opt. Soc. Am. B 31, 534–541 (2014).
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Nahen, K.

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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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Oshlakov, V. K.

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A. Zardecki and J. D. Pendleton, “Hydrodynamics of water droplets irradiated by a pulsed co2 laser,” Appl. Opt. 28, 638–640 (1989).
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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]

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G. Schimmel, T. Produit, D. Mongin, J. Kasparian, and J.-P. Wolf, “Free space laser telecommunication through fog,” Optica 5, 1338–1341 (2018).
[Crossref]

Queißer, M.

Rairoux, P.

Rezvani, S. A.

Z. Hong, Q. Zhang, S. A. Rezvani, P. Lan, and P. Lu, “Extending plasma channel of filamentation with a multi-focal-length beam,” Opt. Express 24, 4029–4041 (2016).
[Crossref] [PubMed]

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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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Saxena, I.

Schillinger, H.

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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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Schneider, F.

Scholz, A.

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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).
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E. S. Efimenko, Y. A. Malkov, A. A. Murzanev, and A. N. Stepanov, “Femtosecond laser pulse-induced breakdown of a single water microdroplet,” J. Opt. Soc. Am. B 31, 534–541 (2014).
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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).

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Tamošauskas, G.

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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Theisen, D.

Thompson, C.

Ting, A.

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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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Varma, S.

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Vaughan, O. H.

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Vogel, A.

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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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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Wood, C. F.

Wöste, L.

Wright, E. M.

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
[Crossref]

Xi, T.-T.

T.-T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006).
[Crossref] [PubMed]

Xu, Z.

Yan, W.

Yu, J.

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Zhang, J.

T.-T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006).
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Zhang, P.

Zhang, Q.

Z. Hong, Q. Zhang, S. A. Rezvani, P. Lan, and P. Lu, “Extending plasma channel of filamentation with a multi-focal-length beam,” Opt. Express 24, 4029–4041 (2016).
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Zheng, J.-b.

Ziener, C.

Zilio, S. C.

Zimmer, W.

Appl. Opt. (11)

A. Zardecki and J. D. Pendleton, “Hydrodynamics of water droplets irradiated by a pulsed co2 laser,” Appl. Opt. 28, 638–640 (1989).
[Crossref] [PubMed]

J. Noack and A. Vogel, “Single-shot spatially resolved characterization of laser-induced shock waves in water,” Appl. Opt. 37, 4092–4099 (1998).
[Crossref]

A. Deepak and O. H. Vaughan, “Extinction-sedimentation inversion technique for measuring size distribution of artificial fogs,” Appl. Opt. 17, 374–378 (1978).
[Crossref] [PubMed]

Appl. Phys. B (3)

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]

Appl. Phys. Lett. (2)

Bull. Am. Meteorol. Soc. (1)

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).
[Crossref]

IEEE J. Quantum Electron. (3)

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]

IEEE J. Sel. Top. Quantum Electron. (1)

J. Aerosol Sci. (1)

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

J. Appl. Phys. (1)

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. Atmos. Sci. (1)

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

J. Opt. Soc. Am. B (3)

E. S. Efimenko, Y. A. Malkov, A. A. Murzanev, and A. N. Stepanov, “Femtosecond laser pulse-induced breakdown of a single water microdroplet,” J. Opt. Soc. Am. B 31, 534–541 (2014).
[Crossref]

G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a gaussian beam, using a bromwich formulation,” J. Opt. Soc. Am. B 5, 1427–1443 (1988).
[Crossref]

Nat. Commun. (1)

Nat. Photonics (1)

Opt. Express (2)

Z. Hong, Q. Zhang, S. A. Rezvani, P. Lan, and P. Lu, “Extending plasma channel of filamentation with a multi-focal-length beam,” Opt. Express 24, 4029–4041 (2016).
[Crossref] [PubMed]

Opt. Lett. (8)

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

J. C. Carls and J. R. Brock, “Explosive vaporization of single droplets by lasers: comparison of models with experiments,” Opt. Lett. 13, 919–921 (1988).
[Crossref] [PubMed]

M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
[Crossref]

Optica (1)

G. Schimmel, T. Produit, D. Mongin, J. Kasparian, and J.-P. Wolf, “Free space laser telecommunication through fog,” Optica 5, 1338–1341 (2018).
[Crossref]

Phys. Rev. A (1)

Phys. Rev. B (1)

Phys. Rev. E (1)

Phys. Rev. Lett. (7)

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]

T.-T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006).
[Crossref] [PubMed]

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

Science (1)

Other (2)

D. Deirmendjian, “Electromagnetic scattering on spherical polydispersions,” (RAND Corporation, 1969).

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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).

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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 \times 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.

Download Full Size | PPT Slide | PDF

Fig. 4 FED distributions for incident lasers with different laser intensity I₀: (a)

5 \times 10^{12}

, (b)

1.1 \times 10^{13}

, and (c)

2.5 \times 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.

Download Full Size | PPT Slide | PDF

Fig. 5 (a) Droplet energy losses Q and (b) energy losses proportion

Q / Q_{t}

variation with laser intensity for different droplet radii.

Download Full Size | PPT Slide | PDF

Fig. 6 (a) Energy losses of droplet Q and (b) energy loss proportions

Q / Q_{t}

variation with droplet size for different laser intensities.

Download Full Size | PPT Slide | PDF

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.

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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.

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Fig. 9 Size distributions for different water clouds and fog.

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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.

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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.

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Tables (3)

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

View Table | View all tables in this article

Table 2 Breakdown thresholds for water and droplet under laser pulses with different pulse durations τ, wavelengths λ, and numerical apertures N.A. Here, I_exp and I_cal denote the experimental and calculated thresholds for water, respectively; and I_droplet 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%.

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Table 3 Calculated scattering coefficients σ_s, corrected scattering coefficients $σ_{s}^{'} = σ_{s} R_{c}$ ( $θ < {1.5}^{\circ}$ ), and absorption coefficients σ_a 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 $I_{0} = 5 \times 10^{12}$ , $1 \times 10^{13}$ , and $2.5 \times 10^{13} W / {cm}^{2}$ , respectively. The units for all the above coefficients are ${km}^{- 1}$ .

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Equations (15)

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\frac{\partial ρ}{\partial t} = (\frac{β_{K}}{K ℏ ω} I^{K} + \frac{σ_{A} I}{V} ρ) (1 - \frac{ρ}{ρ_{n}}) + \nabla \cdot (D \nabla ρ) - g ρ^{2},

\nabla \times \nabla \times E + \frac{1}{c^{2}} \frac{\partial^{2}}{\partial t^{2}} (ε_{r L} E) + μ_{0} (\frac{\partial J}{\partial t} + \frac{\partial^{2} P_{NL}}{\partial t^{2}}) = 0,

ε_{r} = ε_{r L} + 2 n_{0} n_{2} ε_{0} I + i \frac{c n_{0} σ_{c} ρ}{ω} + i \frac{c n_{0} β_{K}}{ω} I^{K - 1} .

\nabla \times \nabla \times E + \frac{1}{c^{2}} \frac{\partial}{\partial t} (ε_{r} \frac{\partial E}{\partial t}) = 0.

\frac{d N}{d r} = N a r^{α} exp [- \frac{α}{γ} {(\frac{r}{r_{0}})}^{γ}],

\begin{matrix} E = E_{0} \sqrt{\frac{w_{0}}{w (x)}} \exp [- 2 \ln 2 \frac{{(t - τ)}^{2}}{τ^{2}} - c_{0} \frac{y^{2}}{w^{2} (x)}] \\ \times \exp [i (ω t - k x - k \frac{y^{2}}{2 R_{w} (x)} + Φ (x))] \cdot {\hat{e}}_{z}, \end{matrix}

\begin{matrix} Q = \underset{V}{∭} d V \int d t (J \cdot E) \\ = π \iint d y d x \cdot y \int d t (J \cdot E), \end{matrix}

Q_{t} = \int I (t) \cdot π r^{2} d t = \frac{1}{2 \sqrt{ln 2}} π^{\frac{3}{2}} r^{2} τ I_{0},

P = 1 - \prod_{i = 1}^{s} (1 - i p),

p = [\frac{r^{2}}{R^{2}} + \frac{1}{R} \int_{r}^{R} \frac{1}{π} arccos (1 - \frac{r^{2}}{2 δ^{2}}) d δ] (\frac{r}{R}),

Q = \int \frac{\partial Q (I_{0}, r)}{\partial r} n (r) d r,

Q (I_{0}, r) ≅ Q (r) + \frac{Q (I_{0}) - Q (I_{0 i})}{R_{0}^{2}} r^{2} .

P_{j} (θ) = \frac{4 π}{β_{s}} \frac{λ^{2}}{4 π^{2}} \int_{r_{1}}^{r_{2}} n (r) i_{j} (θ) d r,

β_{s} = π \int_{r_{1}}^{r_{2}} r^{2} Q_{s} n (r) d r,

R_{c} = 1 - \frac{1}{4 π} \int_{0}^{θ} P_{j} (θ^{'}) sin θ^{'} d θ^{'} .

Parameters	Water	Air
n₀	1.33	1.00
n₂ ( ${cm}^{2} / W$ )	$1.9 \times 10^{- 16}$ [45]	$1.9 \times 10^{- 19}$ [46]
β_K ( ${cm}^{2 K - 1} / W^{K}$ )	$1.05 \times 10^{- 57}$ [38]	$1.27 \times 10^{- 126}$ [35]
K	5	10
V(eV)	6.6 (MPI), 9.5 (AI)[40]	14.6 [47]
D ( $m^{2} / W$ )	$5.57 \times 10^{- 4}$ [37]	0.2995 [37]
τ_c (fs)	1 [38]	350 [47]
g	$2 \times 10^{- 9}$ [38]	$5 \times 10^{- 7}$ [33]
ρ_n	$6.7 \times 10^{22}$ [48]	$2.5 \times 10^{19}$ [47]

τ	λ	N.A.	I_exp	I_cal	I_droplet
[fs]	[nm]		[ $10^{12} W / {cm}^{2}$ ]	[ $10^{12} W / {cm}^{2}$ ]	[ $10^{12} W / {cm}^{2}$ ]
340	520	0.8	2.85 [50]	2.85	1.62
340	520	0.9	3.17 [50]	3.23	1.71
340	1040	0.8	3.37 [50]	3.45	2.10
340	1040	0.9	3.49 [50]	3.88	2.21
240	800	0.8	5.55 [49]	5.25	2.93
240	800	0.9	5.84 [49]	5.75	3.07
340	520	–			0.439
340	1040	–			0.540
240	800	–			0.637

Cloud Category	σ_s	$σ_{s}^{'}$	$σ_{a 5}$	$σ_{a 10}$	$σ_{a 25}$
c. St.	45.0	37.8	0.68	2.12	4.38
m. St.	18.2	14.9	0.34	0.98	2.10
c. Cu.	67.5	57.4	0.97	2.98	6.29
m. Cu.	16.8	13.6	0.39	1.03	2.31
Fog	3.68	2.98	0.08	0.20	0.44

Parameters	Water	Air
n₀	1.33	1.00
n₂ ( ${cm}^{2} / W$ )	$1.9 \times 10^{- 16}$ [45]	$1.9 \times 10^{- 19}$ [46]
β_K ( ${cm}^{2 K - 1} / W^{K}$ )	$1.05 \times 10^{- 57}$ [38]	$1.27 \times 10^{- 126}$ [35]
K	5	10
V(eV)	6.6 (MPI), 9.5 (AI)[40]	14.6 [47]
D ( $m^{2} / W$ )	$5.57 \times 10^{- 4}$ [37]	0.2995 [37]
τ_c (fs)	1 [38]	350 [47]
g	$2 \times 10^{- 9}$ [38]	$5 \times 10^{- 7}$ [33]
ρ_n	$6.7 \times 10^{22}$ [48]	$2.5 \times 10^{19}$ [47]

τ	λ	N.A.	I_exp	I_cal	I_droplet
[fs]	[nm]		[ $10^{12} W / {cm}^{2}$ ]	[ $10^{12} W / {cm}^{2}$ ]	[ $10^{12} W / {cm}^{2}$ ]
340	520	0.8	2.85 [50]	2.85	1.62
340	520	0.9	3.17 [50]	3.23	1.71
340	1040	0.8	3.37 [50]	3.45	2.10
340	1040	0.9	3.49 [50]	3.88	2.21
240	800	0.8	5.55 [49]	5.25	2.93
240	800	0.9	5.84 [49]	5.75	3.07
340	520	–			0.439
340	1040	–			0.540
240	800	–			0.637