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为了研究超短激光脉冲和液滴相互作用过程中电子密度和光场的变化，基于非线性麦克斯韦方程组和电离速率方程，构建了激光等离子体非线性瞬态时域耦合模型，对飞秒激光脉冲击穿微米量级水滴时的电子密度和光场的时空分布进行了计算.结果显示水滴的击穿阈值最小可达2 TW/cm2，为同等条件下无边界水介质击穿阈值的1/4.随着脉冲能量增强，水滴内自由电子密度峰值区域逆着激光入射方向移动，且入射光越强，水滴对光传播的屏蔽越明显.光束在水滴出射端外部汇聚，汇聚点的光功率密度可达入射光的5倍，且时域波形出现压缩和变形.另外，水滴对激光能量的吸收系数随光强增大而增大，并最终趋于饱和.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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