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The transient changes of free electron density distribution and light field intensity during the interaction between the femtosecond Gaussian laser pulses and millimeter scale water droplets are studied. Based on the nonlinear Maxwell's equations and the ionization rate equation, a transient coupled model is proposed to describe the laser plasma produced in water droplet. The changes of electron density and light field with time are obtained by the finite element method. The calculation results show that the laser induced breakdown threshold in the droplet is about 2 TW/cm2, one quarter of that in a boundaryless water medium under the same condition. We find that the region of plasma generated in the droplet will move along the laser direction at first, however, when the incident laser intensity becomes larger, it will move in the direction opposite to the laser beam propagation and the plasma shielded effect becomes more obvious. The laser beam converged by the droplet focuses outside the droplet, and its power density is five times larger than that of the incident laser. There happen the laser pulse duration compression and waveform distortion at the focus point due to the plasma absorption, and the absorption energy increases with the laser intensity increasing and reaches a saturation finally. We expect the model and calculation results to be able to be used for the study of laser pulse propagation in cloud or rain, the precision control of droplet by laser or eye surgery by laser, and other laser technology applications.
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Keywords:
- laser-induced breakdown /
- interaction between laser and droplet /
- optical field distribution /
- electron density
[1] Gelderblom H, Lhuissier H, Klein A L, Bouwhuis W, Lohse D, Villermaux E, Snoeijer J H 2016 J. Fluid Mech. 794 676
[2] Kurilovich D, Klein A L, Torretti F, Lassise A, Hoekstra R, Ubachs W, Gelderblom H, Versolato O O 2016 Phys. Rev. Appl. 6 014018
[3] Peng X Y, Zhang J, Jin Z, Liang T J, Zhong J Y, Wu H C, Liu Y Q, Wang Z H, Chen Z L, Sheng Z M, Li Y T, Wei Z Y 2004 Acta Phys. Sin. 53 2625 (in Chinese) [彭晓昱, 张杰, 金展, 梁天骄, 仲佳勇, 武慧春, 刘运全, 王兆华, 陈正林, 盛政明, 李玉同, 魏志义 2004 53 2625]
[4] Banine V Y, Koshelev K N, Swinkels G H P M 2011 J. Phys. D: Appl. Phys. 44 253001
[5] Lindinger A, Hagen J, Socaciu L D, Bernhardt T M, Wste L, Duft D, Leisner T 2004 Appl. Opt. 43 5263
[6] Courvoisier F, Boutou V, Favre C, Hill S C, Wolf J 2003 Opt. Lett. 28 206
[7] Geints Y E, Kabanov A M, Matvienko G G, Oshlakov V K, Zemlyanov A A, Golik S S, Bukin O A 2010 Opt. Lett. 35 2717
[8] Klein A L, Visser C W, Bouwhuis W, Lhuissier H, Sun C, Snoeijer J H, Villermaux E, Lohse D, Gelderblom H 2015 Phys. Fluids 27 91106
[9] Wu B 2008 Appl. Phys. Lett. 93 101104
[10] Geissler M, Tempea G, Scrinzi A, Schnrer M, Krausz F, Brabec T 1999 Phys. Rev. Lett. 83 2930
[11] Kolesik M, Wright E M, Moloney J V 2004 Phys. Rev. Lett. 92 253901
[12] Dubietis A, Gaižauskas E, Tamoauskas G, Di Trapani P 2004 Phys. Rev. Lett. 92 253903
[13] Fan C H, Sun J, Longtin J P 2002 J. Appl. Phys. 91 2530
[14] Saxena I, Ehmann K, Jian C 2014 Appl. Opt. 35 8283
[15] Efimenko E S, Malkov Y A, Murzanev A A, Stepanov A N 2014 J. Opt. Soc. Am. B 31 534
[16] Jarnac A, Tamosauskas G, Majus D, Houard A, Mysyrowicz A, Couairon A, Dubietis A 2014 Phys. Rev. A 89 033809
[17] Hong Z F, Zhang Q B, Rezvani S A, Lan P F, Lu P X 2016 Opt. Express 24 4029
[18] Linz N, Freidank S, Liang X, Vogelmann H, Trickl T, Vogel A 2015 Phys. Rev. B 91 621
[19] Noack J, Vogel A 1999 IEEE J. Quant. Electron. 35 1156
[20] Kennedy P K 1995 IEEE J. Quant. Electron. 31 2241
[21] Kennedy P K, Hammer D X, Rockwell B A 1997 Prog. Quant. Electron. 21 155
[22] Zhang C, Lu J, Zhang H C, Shen Z H, Ni X W 2016 IEEE J. Quant. Electron. 52 1
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[1] Gelderblom H, Lhuissier H, Klein A L, Bouwhuis W, Lohse D, Villermaux E, Snoeijer J H 2016 J. Fluid Mech. 794 676
[2] Kurilovich D, Klein A L, Torretti F, Lassise A, Hoekstra R, Ubachs W, Gelderblom H, Versolato O O 2016 Phys. Rev. Appl. 6 014018
[3] Peng X Y, Zhang J, Jin Z, Liang T J, Zhong J Y, Wu H C, Liu Y Q, Wang Z H, Chen Z L, Sheng Z M, Li Y T, Wei Z Y 2004 Acta Phys. Sin. 53 2625 (in Chinese) [彭晓昱, 张杰, 金展, 梁天骄, 仲佳勇, 武慧春, 刘运全, 王兆华, 陈正林, 盛政明, 李玉同, 魏志义 2004 53 2625]
[4] Banine V Y, Koshelev K N, Swinkels G H P M 2011 J. Phys. D: Appl. Phys. 44 253001
[5] Lindinger A, Hagen J, Socaciu L D, Bernhardt T M, Wste L, Duft D, Leisner T 2004 Appl. Opt. 43 5263
[6] Courvoisier F, Boutou V, Favre C, Hill S C, Wolf J 2003 Opt. Lett. 28 206
[7] Geints Y E, Kabanov A M, Matvienko G G, Oshlakov V K, Zemlyanov A A, Golik S S, Bukin O A 2010 Opt. Lett. 35 2717
[8] Klein A L, Visser C W, Bouwhuis W, Lhuissier H, Sun C, Snoeijer J H, Villermaux E, Lohse D, Gelderblom H 2015 Phys. Fluids 27 91106
[9] Wu B 2008 Appl. Phys. Lett. 93 101104
[10] Geissler M, Tempea G, Scrinzi A, Schnrer M, Krausz F, Brabec T 1999 Phys. Rev. Lett. 83 2930
[11] Kolesik M, Wright E M, Moloney J V 2004 Phys. Rev. Lett. 92 253901
[12] Dubietis A, Gaižauskas E, Tamoauskas G, Di Trapani P 2004 Phys. Rev. Lett. 92 253903
[13] Fan C H, Sun J, Longtin J P 2002 J. Appl. Phys. 91 2530
[14] Saxena I, Ehmann K, Jian C 2014 Appl. Opt. 35 8283
[15] Efimenko E S, Malkov Y A, Murzanev A A, Stepanov A N 2014 J. Opt. Soc. Am. B 31 534
[16] Jarnac A, Tamosauskas G, Majus D, Houard A, Mysyrowicz A, Couairon A, Dubietis A 2014 Phys. Rev. A 89 033809
[17] Hong Z F, Zhang Q B, Rezvani S A, Lan P F, Lu P X 2016 Opt. Express 24 4029
[18] Linz N, Freidank S, Liang X, Vogelmann H, Trickl T, Vogel A 2015 Phys. Rev. B 91 621
[19] Noack J, Vogel A 1999 IEEE J. Quant. Electron. 35 1156
[20] Kennedy P K 1995 IEEE J. Quant. Electron. 31 2241
[21] Kennedy P K, Hammer D X, Rockwell B A 1997 Prog. Quant. Electron. 21 155
[22] Zhang C, Lu J, Zhang H C, Shen Z H, Ni X W 2016 IEEE J. Quant. Electron. 52 1
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