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飞秒激光聚焦到LiF晶体内部, 晶体的加工形貌随偏振改变. 实验表明, 偏振方向平行于110 晶向时, 加工起点到表面的距离是100偏振下的1.08 倍; 而110偏振下加工终点到表面的距离是100 偏振下的1.01 倍. 为了解释加工形貌的偏振依赖, 建立了逆韧致辐射、雪崩电离和无辐射跃迁的模型, 首先, 价带电子通过强场电离和雪崩电离, 从激光中吸收能量跃迁到导带, 该过程用电子密度演化方程和傍轴非线性薛定谔方程描述, 求解方程得到导带电子密度; 其次, 导带电子通过无辐射跃迁过程释放能量给晶格, 由能量守恒计算出晶格温度沿激光传播方向的分布; 最后, 晶格温度超过熔点以上的区域被加工. 模拟结果显示, 110偏振下加工起点到表面的距离是100 偏振下的1.03倍, 而110偏振下加工终点到表面的距离是100偏振下的0.981 倍, 与实验结果基本一致. 虽然Z扫描技术测量的非线性折射率随偏振方向变化, 但是非线性折射率的变化趋势与实验结果相反. 模拟和实验证明逆韧致辐射导致加工形貌随偏振变化.The processing morphology of cubic crystal LiF irradiated by femtosecond laser varies with the polarization direction. When the polarization direction is parallel to the crystal orientation 110, the distance between the starting point and the surface is 1.08 times that along 100 polarization, and the distance between the end point and the surface is 1.01 times. While the cubic crystal is irradiated by a femtosecond laser, self-focusing and inverse bremsstrahlung are two probable mechanisms dependent on polarization. In order to investigate the relation between the self-focusing and polarization, in this paper we report the nonlinear refractive index n2 of LiF crystal which is linear with respect to selffocusing coefficient. The Z-scan technique is used to measure the nonlinear refractive indexes at different polarizations. As the polarization direction is rotated from 110 to 100, the nonlinear refractive index decreases, and the self-focusing effect becomes weaker. If self-focusing leads to the dependence of morphology on polarization, the distance between the starting point and the surface for 100 polarization should be longer than that for 110 polarization. However, the experiment exhibits an opposite result that the distance between starting point and the surface for 100 polarization is shorter than that for 110 polarization. Therefore, the processing morphology which changes with polarization is not a consequence of the self-focusing. So in order to understand why the processing morphology varies with polarization, in this paper we present a model which combines inverse bremsstrahlung, avalanche ionization and radiationless transition. We believe that the recombination due to radiationless transition has a great effect on laser machining. The inverse bremsstrahlung coefficient of 110 polarization is less than that of 100 polarization, as a result, the density of free electrons which are produced by inverse bremsstrahlung and avalanche ionization at 110 polarization is less than that at 100 polarization. At first, the laser energy is transferred to the free electrons by inverse bremsstrahlung and avalanche ionization, which is described by the paraxial nonlinear Schrodinger equation and evolution equation of electron density. The density of free electrons is obtained by solving the equations. Then free electrons transfer the energy to the crystal lattice in the process of recombination through radiationless transition, which is depicted by energy conservation and gives the distribution of lattice temperature along the propagation direction. Finally, the area in LiF crystal of which the lattice temperature climbs up to above the melting point is processed. According to the simulation, the distance between the starting point and the surface at 110 polarization is 1.03 times that at 100 polarization, and the distance between the end point and the surface at 110 polarization is 0.981 times that at 100 polarization. These are consistent with the experimental results. Simulation and experimental results demonstrate that the inverse bremsstrahlung, which is dependent on polarization, is the main reason for morphology changing with the polarization of femtosecond laser. These research results may contribute to inducing microstructure in transparent dielectrics through femtosecond laser.
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Keywords:
- inverse bremsstrahlung /
- radiationless transition /
- avalanche ionization /
- nonlinear refractive index
[1] Beresna M, Gecevičius M, Kazansky P G 2011 Opt. Mater. Express 1 10117
[2] Dong M M, Wang C W, Wu Z X, Zhang Y, Pan H H, Zhao Q Z 2013 Opt. Express 21 15522
[3] Shimotsuma Y, Hirao K, Kazansky P G, Qiu J 2005 Jpn. J. Appl. Phys. 44 4735
[4] Song J, Wang X, Hu X, Dai Y, Qiu J, Cheng Y, Xu Z 2008 Appl. Phys. Lett. 92 092904
[5] Qiu J, Jiang X, Zhu C, Shirai M, Si J, Jiang N, Hirao K 2004 Angew. Chem. Int. Ed. Engl. 43 2230
[6] Shimotsuma Y, Kazansky P G, Qiu J, Hirao K 2003 Phys. Rev. Lett. 91 247405
[7] Balling P, Schou J 2013 Rep. Prog. Phys. 76 036502
[8] Dharmadhikari A, Alti K, Dharmadhikari J, Mathur D 2007 Phys. Rev. A 76 033811
[9] Kaiser A, Rethfeld B, Vicanek M, Simon G 2000 Phys. Rev. B 61 11437
[10] Stoian R, Ashkenasi D, Rosenfeld A, Campbell E E B 2000 Phys. Rev. B: Condens. Matter Mater. Phys. 62 13167
[11] Ter-Mikirtychev V V 1995 Opt. Commun. 119 109
[12] Li S X, Bai Z C, Huang Z, Zhang X, Qin S J, Mao W X 2012 Acta Phys. Sin. 61 115201 (in Chinese) [李世熊, 白忠臣, 黄政, 张欣, 秦水介, 毛文雪 2012 物理学报 61 115201]
[13] Liu T H, Hao Z Q, Gao X, Liu Z H, Lin J Q 2014 Chin. Phys. B 23 085203
[14] Vailionis A, Gamaly E G, Mizeikis V, Yang W, Rode A V, Juodkazis S 2011 Nat. Commun. 2 445
[15] Mermillod-Blondin A, Burakov I, Meshcheryakov Y, Bulgakova N, Audouard E, Rosenfeld A, Husakou A, Hertel I, Stoian R 2008 Phys. Rev. B 77 104205
[16] de Salvo R, Said A A, Hagan D J, van Stryland E W, Sheik-Bahae M 1996 IEEE J. Quantum Electron. 32 1324
[17] Bombach R, Hemmerling B 1992 Appl. Opt. 31 367
[18] Maker P, Terhune R 1964 Phys. Rev. 137 801
[19] Milam D, Weber M J, Glass A J 1977 Appl. Phys. Lett. 31 822
[20] Liu F, Xing Q R, Hu M L, Li Y F, Wang C L, Chai L, Wang Q Y 2011 Acta Phys. Sin. 60 017806 (in Chinese) [刘丰, 邢岐荣, 胡明列, 栗岩锋, 王昌雷, 柴路, 王清月 2011 物理学报 60 017806]
[21] Couairon A, Mysyrowicz A 2007 Phys. Rep. 441 47
[22] Wu S, Wu D, Xu J, Hanada Y, Suganuma R, Wang H, Makimura T, Sugioka K, Midorikawa K 2012 Opt. Express 20 28893
[23] Sirdeshmukh D B, Rao K K 1988 J. Mater. Sci. Lett. 7 567
[24] Brookes C A, O'Neill J B, Redfern B A W 1971 Proc. R. Soc. A: Math. Phys. Eng. Sci. 322 73
[25] Zhao Q Z, Qiu J R, Yang L Y, Jiang X W, Zhao C J, Zhu C S 2003 Chin. Phys. Lett. 20 1858
[26] Yin Q, Wu J, Qian G, Ma X H 2008 Opt. Optoelectron. Technol. 6 25
[27] Kogelnik H 1969 Bell Syst. Tech. J. 48 2909
[28] Nolte S, Momma C, Kamlage G, Ostendorf A, Fallnich C, von Alvensleben F, Welling H 1999 Appl. Phys. A 68 563
[29] Collins A, Rostohar D, Prieto C, Chan Y K, Oconnor G M 2014 Opt. Lasers Eng. 60 18
[30] de Salvo R, Sheik-Bahae M, Said A A, Hagan D J, van Stryland E W 1993 Opt. Lett. 18 194
[31] Shang C, Hsu H 1987 IEEE J. Quantum Electron. 23 177
[32] van Stryland E W, Hagan D J 2009 Self-focusing: Past, Present (Berlin: Springer) p573
[33] Tolk N H, Albridge R G, Barnes A V, Haglund R F, Hudson L T, Mendenhall M H, Russell D P, Sarnthein J, Savundararaj P M, Wang P W 1987 Desorption Induced by Electronic Transitions DIET III, Springer Series in Surface Sciences (Berlin, Heidelberg: Springer Berlin Heidelberg) p284
[34] Burakov I M, Bulgakova N M, Stoian R, Mermillod-Blondin A, Audouard E, Rosenfeld A, Husakou A, Hertel I V 2007 J. Appl. Phys. 101 043506
[35] Keldysh L 1965 Sov. Phys. JETP 20 1307
[36] Chaney R, Lafon E, Lin C 1971 Phys. Rev. B 4 2734
[37] Hamrin K, Johansson G, Gelius U, Nordling C, Siegbahn K 1970 Phys. Scr. 1 277
[38] Li H H 1976 J. Phys. Chem. Ref. Data 5 329
[39] Chichkov B, Momma C, Nolte S, Alvensleben F, Tunnermann A 1996 Appl. Phys. A 63 109
[40] Stuart B, Feit M, Herman S, Rubenchik A, Shore B, Perry M 1996 Phys. Rev. B: Condens. Matter 53 1749
[41] Petite G, Daguzan P, Guizard S, Martin P 1996 Nucl. Instruments Methods Phys. Res. Sect. B: Beam Interact. Mater. Atoms 107 97
[42] Luque A, Martí A, Antolín E, Tablero C 2006 Phys. B: Condens. Matter 382 320
[43] Eaton S M, Zhang H B, Herman P R, Yoshino F 2005 Opt. Express 13 4708
[44] Douglas T B, Dever J L 1954 J. Am. Chem. Soc. 76 4826
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[1] Beresna M, Gecevičius M, Kazansky P G 2011 Opt. Mater. Express 1 10117
[2] Dong M M, Wang C W, Wu Z X, Zhang Y, Pan H H, Zhao Q Z 2013 Opt. Express 21 15522
[3] Shimotsuma Y, Hirao K, Kazansky P G, Qiu J 2005 Jpn. J. Appl. Phys. 44 4735
[4] Song J, Wang X, Hu X, Dai Y, Qiu J, Cheng Y, Xu Z 2008 Appl. Phys. Lett. 92 092904
[5] Qiu J, Jiang X, Zhu C, Shirai M, Si J, Jiang N, Hirao K 2004 Angew. Chem. Int. Ed. Engl. 43 2230
[6] Shimotsuma Y, Kazansky P G, Qiu J, Hirao K 2003 Phys. Rev. Lett. 91 247405
[7] Balling P, Schou J 2013 Rep. Prog. Phys. 76 036502
[8] Dharmadhikari A, Alti K, Dharmadhikari J, Mathur D 2007 Phys. Rev. A 76 033811
[9] Kaiser A, Rethfeld B, Vicanek M, Simon G 2000 Phys. Rev. B 61 11437
[10] Stoian R, Ashkenasi D, Rosenfeld A, Campbell E E B 2000 Phys. Rev. B: Condens. Matter Mater. Phys. 62 13167
[11] Ter-Mikirtychev V V 1995 Opt. Commun. 119 109
[12] Li S X, Bai Z C, Huang Z, Zhang X, Qin S J, Mao W X 2012 Acta Phys. Sin. 61 115201 (in Chinese) [李世熊, 白忠臣, 黄政, 张欣, 秦水介, 毛文雪 2012 物理学报 61 115201]
[13] Liu T H, Hao Z Q, Gao X, Liu Z H, Lin J Q 2014 Chin. Phys. B 23 085203
[14] Vailionis A, Gamaly E G, Mizeikis V, Yang W, Rode A V, Juodkazis S 2011 Nat. Commun. 2 445
[15] Mermillod-Blondin A, Burakov I, Meshcheryakov Y, Bulgakova N, Audouard E, Rosenfeld A, Husakou A, Hertel I, Stoian R 2008 Phys. Rev. B 77 104205
[16] de Salvo R, Said A A, Hagan D J, van Stryland E W, Sheik-Bahae M 1996 IEEE J. Quantum Electron. 32 1324
[17] Bombach R, Hemmerling B 1992 Appl. Opt. 31 367
[18] Maker P, Terhune R 1964 Phys. Rev. 137 801
[19] Milam D, Weber M J, Glass A J 1977 Appl. Phys. Lett. 31 822
[20] Liu F, Xing Q R, Hu M L, Li Y F, Wang C L, Chai L, Wang Q Y 2011 Acta Phys. Sin. 60 017806 (in Chinese) [刘丰, 邢岐荣, 胡明列, 栗岩锋, 王昌雷, 柴路, 王清月 2011 物理学报 60 017806]
[21] Couairon A, Mysyrowicz A 2007 Phys. Rep. 441 47
[22] Wu S, Wu D, Xu J, Hanada Y, Suganuma R, Wang H, Makimura T, Sugioka K, Midorikawa K 2012 Opt. Express 20 28893
[23] Sirdeshmukh D B, Rao K K 1988 J. Mater. Sci. Lett. 7 567
[24] Brookes C A, O'Neill J B, Redfern B A W 1971 Proc. R. Soc. A: Math. Phys. Eng. Sci. 322 73
[25] Zhao Q Z, Qiu J R, Yang L Y, Jiang X W, Zhao C J, Zhu C S 2003 Chin. Phys. Lett. 20 1858
[26] Yin Q, Wu J, Qian G, Ma X H 2008 Opt. Optoelectron. Technol. 6 25
[27] Kogelnik H 1969 Bell Syst. Tech. J. 48 2909
[28] Nolte S, Momma C, Kamlage G, Ostendorf A, Fallnich C, von Alvensleben F, Welling H 1999 Appl. Phys. A 68 563
[29] Collins A, Rostohar D, Prieto C, Chan Y K, Oconnor G M 2014 Opt. Lasers Eng. 60 18
[30] de Salvo R, Sheik-Bahae M, Said A A, Hagan D J, van Stryland E W 1993 Opt. Lett. 18 194
[31] Shang C, Hsu H 1987 IEEE J. Quantum Electron. 23 177
[32] van Stryland E W, Hagan D J 2009 Self-focusing: Past, Present (Berlin: Springer) p573
[33] Tolk N H, Albridge R G, Barnes A V, Haglund R F, Hudson L T, Mendenhall M H, Russell D P, Sarnthein J, Savundararaj P M, Wang P W 1987 Desorption Induced by Electronic Transitions DIET III, Springer Series in Surface Sciences (Berlin, Heidelberg: Springer Berlin Heidelberg) p284
[34] Burakov I M, Bulgakova N M, Stoian R, Mermillod-Blondin A, Audouard E, Rosenfeld A, Husakou A, Hertel I V 2007 J. Appl. Phys. 101 043506
[35] Keldysh L 1965 Sov. Phys. JETP 20 1307
[36] Chaney R, Lafon E, Lin C 1971 Phys. Rev. B 4 2734
[37] Hamrin K, Johansson G, Gelius U, Nordling C, Siegbahn K 1970 Phys. Scr. 1 277
[38] Li H H 1976 J. Phys. Chem. Ref. Data 5 329
[39] Chichkov B, Momma C, Nolte S, Alvensleben F, Tunnermann A 1996 Appl. Phys. A 63 109
[40] Stuart B, Feit M, Herman S, Rubenchik A, Shore B, Perry M 1996 Phys. Rev. B: Condens. Matter 53 1749
[41] Petite G, Daguzan P, Guizard S, Martin P 1996 Nucl. Instruments Methods Phys. Res. Sect. B: Beam Interact. Mater. Atoms 107 97
[42] Luque A, Martí A, Antolín E, Tablero C 2006 Phys. B: Condens. Matter 382 320
[43] Eaton S M, Zhang H B, Herman P R, Yoshino F 2005 Opt. Express 13 4708
[44] Douglas T B, Dever J L 1954 J. Am. Chem. Soc. 76 4826
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