Abstract

High-power lasers can be used to clear a foggy or cloudy atmosphere by exploding and shattering water microdroplets into smaller fragments. The physics of laser–droplet interaction strongly depend on the excitation wavelength and pulse duration, and new techniques with optimized energy requirements that enable lossless long-distance propagation are urgently needed. In this work, a novel and elegant way of water droplet shattering by sub-µJ long-wave infrared ultrashort laser pulses is proposed, making it possible to practically avoid undesirable electron plasma generation in a water droplet and optical breakdown in air. A multiphysics study is performed, which takes into account a hierarchy of physical processes including free carrier plasma kinetics underpinned by a full-vector nonlinear Maxwell solver and the thermomechanical dynamics of pressure waves followed by droplet shattering into smaller fragments described by Navier–Stokes equations. Our results are crucial both for understanding the fundamental nature of water excitation with long-wave infrared radiation and for development of laser applications such as atmospheric communications.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (4)

S. Tochitsky, E. Welch, M. Polyanskiy, I. Pogorelsky, P. Panagiotopoulos, M. Kolesik, E. M. Wright, S. W. Koch, J. V. Moloney, J. Pigeon, and C. Joshi, “Megafilament in air formed by self-guided terawatt long-wavelength infrared laser,” Nat. Photonics 13, 41–46 (2019).
[Crossref]

X.-X. Liang, Z. Zhang, and A. Vogel, “Multi-rate-equation modeling of the energy spectrum of laser-induced conduction band electrons in water,” Opt. Express 27, 4672–4693 (2019).
[Crossref]

C. Zhang, M. Tang, H. Zhang, and J. Lu, “Optical breakdown during femtosecond laser propagation in water cloud,” Opt. Express 27, 8456–8475 (2019).
[Crossref]

T. Paula, S. Adami, and N. A. Adams, “Analysis of the early stages of liquid-water-drop explosion by numerical simulation,” Phys. Rev. Fluids 4, 044003 (2019).
[Crossref]

2018 (4)

A. Rudenko, J.-P. Colombier, and T. E. Itina, “Graphics processing unit-based solution of nonlinear Maxwell’s equations for inhomogeneous dispersive media,” Int. J. Numer. Model. 31, e2215 (2018).
[Crossref]

S. Y. Grigoryev, B. V. Lakatosh, M. S. Krivokorytov, V. V. Zhakhovsky, S. A. Dyachkov, D. K. Ilnitsky, K. P. Migdal, N. A. Inogamov, A. Y. Vinokhodov, V. Kompanets, Y. V. Sidelnikov, V. M. Krivtsun, K. N. Koshelev, and V. V. Medvedev, “Expansion and fragmentation of a liquid-metal droplet by a short laser pulse,” Phys. Rev. Appl. 10, 064009 (2018).
[Crossref]

P. Koukouvinis, N. Kyriazis, and M. Gavaises, “Smoothed particle hydrodynamics simulation of a laser pulse impact onto a liquid metal droplet,” PLoS ONE 13, e0204125 (2018).
[Crossref]

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 (3)

2016 (5)

C. A. Stan, D. Milathianaki, H. Laksmono, R. G. Sierra, T. A. McQueen, M. Messerschmidt, G. J. Williams, J. E. Koglin, T. J. Lane, M. J. Hayes, S. A. H. Guillet, M. Liang, A. L. Aquila, P. R. Willmott, J. S. Robinson, K. L. Gumerlock, S. Botha, K. Nass, I. Schlichting, R. L. Shoeman, H. A. Stone, and S. Boutet, “Liquid explosions induced by X-ray laser pulses,” Nat. Phys. 12, 966–971 (2016).
[Crossref]

N. Linz, S. Freidank, X.-X. Liang, and A. Vogel, “Wavelength dependence of femtosecond laser-induced breakdown in water and implications for laser surgery,” Phys. Rev. B 94, 024113 (2016).
[Crossref]

C. A. Stan, P. R. Willmott, H. A. Stone, J. E. Koglin, M. Liang, A. L. Aquila, J. S. Robinson, K. L. Gumerlock, G. Blaj, R. G. Sierra, S. Boutet, S. A. H. Guillet, R. H. Curtis, S. L. Vetter, H. Loos, J. L. Turner, and F.-J. Decker, “Negative pressures and spallation in water drops subjected to nanosecond shock waves,” J. Phys. Chem. Lett. 7, 2055–2062 (2016).
[Crossref]

L. de la Cruz, E. Schubert, D. Mongin, S. Klingebiel, M. Schultze, T. Metzger, K. Michel, J. Kasparian, and J.-P. Wolf, “High repetition rate ultrashort laser cuts a path through fog,” Appl. Phys. Lett. 109, 251105 (2016).
[Crossref]

M. Matthews, F. Pomel, C. Wender, A. Kiselev, D. Duft, J. Kasparian, J.-P. Wolf, and T. Leisner, “Laser vaporization of cirrus-like ice particles with secondary ice multiplication,” Sci. Adv. 2, e1501912 (2016).
[Crossref]

2015 (3)

R. C. Ripley, L. Donahue, and F. Zhang, “Fragmentation of metal particles during heterogeneous explosion,” Shock Waves 25, 151–167 (2015).
[Crossref]

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]

A. L. Klein, W. Bouwhuis, C. W. Visser, H. Lhuissier, C. Sun, J. H. Snoeijer, E. Villermaux, D. Lohse, and H. Gelderblom, “Drop shaping by laser-pulse impact,” Phys. Rev. Appl. 3, 044018 (2015).
[Crossref]

2014 (1)

2012 (1)

A. Mani, “Analysis and optimization of numerical sponge layers as a nonreflective boundary treatment,” J. Comput. Phys. 231, 704–716 (2012).
[Crossref]

2010 (2)

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]

E. P. Silaeva, S. A. Shlenov, and V. P. Kandidov, “Multifilamentation of high-power femtosecond laser pulse in turbulent atmosphere with aerosol,” Appl. Phys. B 101, 393–401 (2010).
[Crossref]

2009 (1)

Y. E. Geints and A. A. Zemlyanov, “Phase explosion of a water drop by a femtosecond laser pulse: I. Dynamics of optical breakdown,” Atmos. Oceanic Opt. 22, 581 (2009).
[Crossref]

2008 (2)

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]

G. M. Petrov and J. Davis, “Interaction of intense ultra-short laser pulses with dielectrics,” J. Phys. B 41, 025601 (2008).
[Crossref]

2007 (2)

2006 (1)

E. Herbert, S. Balibar, and F. Caupin, “Cavitation pressure in water,” Phys. Rev. E 74, 041603 (2006).
[Crossref]

2005 (1)

G. Méjean, J. Kasparian, J. Yu, E. Salmon, S. Frey, J.-P. Wolf, S. Skupin, A. Vinçotte, R. Nuter, S. Champeaux, and L. Bergé, “Multifilamentation transmission through fog,” Phys. Rev. E 72, 026611 (2005).
[Crossref]

2004 (2)

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]

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]

2003 (2)

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]

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]

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]

2000 (1)

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microwave Opt. Technol. Lett. 27, 334–338 (2000).
[Crossref]

1999 (1)

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]

1997 (3)

J. B. Freund, “Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound,” AIAA J. 35, 740 (1997).
[Crossref]

W. Marczak, “Water as a standard in the measurements of speed of sound in liquids,” J. Acoust. Soc. Am. 102, 2776–2779 (1997).
[Crossref]

Q. Feng, J. V. Moloney, A. C. Newell, E. M. Wright, K. Cook, P. K. Kennedy, D. X. Hammer, B. A. Rockwell, and C. R. 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)

1994 (2)

L. A. Gundel, W. H. Benner, and A. D. A. Hansen, “Chemical composition of fog water and interstitial aerosol in Berkeley, California,” Atmos. Environ. 28, 2715–2725 (1994).
[Crossref]

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]

1990 (2)

1988 (2)

1987 (3)

M. Pilch and C. A. Erdman, “Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop,” Int. J. Multiphase Flow 13, 741–757 (1987).
[Crossref]

J. C. Carls and J. R. Brock, “Explosion of a water droplet by pulsed laser heating,” Aerosol Sci. Technol. 7, 79–90 (1987).
[Crossref]

S. C. Davies and J. R. Brock, “Laser evaporation of droplets,” Appl. Opt. 26, 786–793 (1987).
[Crossref]

1985 (1)

1983 (2)

M. C. Fowler, “Effect of a CO2 laser pulse on transmission through fog at visible and IR wavelengths,” Appl. Opt. 22, 2960–2964 (1983).
[Crossref]

N. B. Vargaftik, B. N. Volkov, and L. D. Voljak, “International tables of the surface tension of water,” J. Phys. Chem. Ref. Data 12, 817–820 (1983).
[Crossref]

1982 (1)

R. J. Speedy, “Stability-limit conjecture. an interpretation of the properties of water,” J. Phys. Chem. 86, 982–991 (1982).
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Figures (5)

Fig. 1.
Fig. 1. Projections of energy distribution inside a water microdroplet of $ R = 10\,\,\unicode{x00B5}{\rm m} $ irradiated by a $ \lambda = 10\,\,\unicode{x00B5}{\rm m} $ infrared laser wavelength with intensity $ I{ = 10^{15}}\;{\rm W}/{{\rm m}^2} $. $ \vec k $ indicates the laser propagation direction along the $ Z $ axis, while $ \vec E $ defines the linear polarization along the $ X $ axis.
Fig. 2.
Fig. 2. (a) and (c) Maximum electron density distributions inside the water droplet. (b) and (d) Temporal dynamics of absorbed energy deposition for pulses with equal fluence (a) intensity $ I{ = 10^{15}}\;{\rm W}/{{\rm m}^2} $ and (b) pulse duration $ \tau = 3\;{\rm ps} $ and (c) $ I = 2 \cdot {10^{16}}\;{\rm W}/{{\rm m}^2} $ and (d) pulse duration $ \tau = 150\;{\rm fs} $. “Linear” stands for joule heating without generated plasma, “AI” indicates the avalanche ionization contribution, and “Total” is the total amount of absorbed energy.
Fig. 3.
Fig. 3. Pressure for densities of interest as a function of temperature from EOS for water. Black dashed–dotted line indicates the cavitation pressure threshold. (0) Black solid curve relates initial heating conditions and maximum pressures attained in the shock wave. (1–3) Green, blue, and red dashed curves correspond to conditions in rarefied regions inside water droplet, which can lead (2–3) or not (1) to phase transition. Arrows relate the initial heating conditions for different laser fluences (0) to degrees of rarefaction inside the droplet (1–3).
Fig. 4.
Fig. 4. (a) Maximum temperature distribution inside $ R = 10\,\,\unicode{x00B5}{\rm m} $ water droplet irradiated by $ \lambda = 10\,\,\unicode{x00B5}{\rm m} $ wavelength with $ I{ = 10^{15}}\;{\rm W}/{{\rm m}^2} $ intensity. (b) Density distribution after $ t = 8\;{\rm ns} $, where the irreversibly affected regions are underlined by black ellipsoids. (c)–(f) Pressure distribution inside the upper part of the water droplet at different time evolution. The dynamics of the pressure wave during propagation inside the water droplet is demonstrated.
Fig. 5.
Fig. 5. (a) Absorbed energy, (b) temperature in the upper part of the droplet, and (c) density in the lower part (5 ns after irradiation) distributions inside $ R = 10\,\,\unicode{x00B5}{\rm m} $ water droplet irradiated by $ \lambda = 10\,\,\unicode{x00B5}{\rm m} $ wavelength with $ I = 5 \cdot {10^{14}}\;{\rm W}/{{\rm m}^2} $ intensity and $ \tau = 3\;{\rm ps} $ pulse duration, containing silica particle of $ R = 4\,\,\unicode{x00B5}{\rm m} $.

Equations (5)

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{ E t = × H ϵ 0 1 ϵ 0 ( J L + J NL ) H t = × E μ 0 J L t = J L ν v + ω v 2 E J NL t = J NL τ e + e 2 N e m e E N e t = w pi ( I ) + N e w ai ( I ) ν rec N e 2 ,
w ai = 4 ln 2 e 2 τ e E 2 3 m e E g ( ω 2 τ e 2 + 1 ) ,
E x ( t , z ) = exp [ 4 ln 2 ( t t 0 ) 2 τ 2 2 i π z / λ + i ω t ] ,
{ ρ C i [ T i t + u T i ] = ( k i T i ) + Q abs ( ρ u ) t + ( u ) ( ρ u ) + ( ρ u ) u = P + μ 2 u + 1 3 μ ( u ) ρ t + ( ρ u ) = 0 ,
P 2 2 ρ c 0 2 + ρ ζ 2 R 2 120 6 σ R + μ ζ ,

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