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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 21, Iss. 11 — Nov. 1, 2004
  • pp: 2008–2016

Propagation of self-focusing laser pulses in atmosphere: experiment versus numerical simulation

Todd A. Pitts, Ting S. Luk, James K. Gruetzner, Thomas R. Nelson, Armon McPherson, Stewart M. Cameron, and Aaron C. Bernstein  »View Author Affiliations

JOSA B, Vol. 21, Issue 11, pp. 2008-2016 (2004)

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Numerical simulations of self-focusing laser pulses obtained via a slowly evolving wave approach (modified nonlinear Schrödinger equation) are compared with published experimental results in fused silica as well as with experimental results in air and fused silica obtained in our laboratory. The mathematical model includes group-velocity dispersion and third-order dispersion, optical shock, and both instantaneous Kerr and delayed Raman nonlinearities as well as a perfectly matched layer absorbing boundary condition. Second-harmonic frequency-resolved optical gating data taken after 10.91 m of propagation allow a direct comparison between experimental and computational envelopes at a number of pulse energies. FWHM measurements of the spectral width, intensity autocorrelation duration, and pulse radius at distances of 4.35, 10.91, 17.47, and 22.73 m provide a view of model fidelity across both energy and propagation distance variables. The magnitude of the nonlinear refractive index, n2, is inferred.

© 2004 Optical Society of America

OCIS Codes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(350.5500) Other areas of optics : Propagation

Todd A. Pitts, Ting S. Luk, James K. Gruetzner, Thomas R. Nelson, Armon McPherson, Stewart M. Cameron, and Aaron C. Bernstein, "Propagation of self-focusing laser pulses in atmosphere: experiment versus numerical simulation," J. Opt. Soc. Am. B 21, 2008-2016 (2004)

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  1. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989).
  2. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999).
  3. J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
  4. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995).
  5. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale, Optics and Photonics, 1st ed. (Academic, San Diego, 1996).
  6. A. Chiron, B. Lamouroux, R. Lange, J.-F. Ripoche, M. Franco, B. Prade, G. Bonnaud, G. Riazuelo, and A. Mysyrowicz, “Numerical simulations of the nonlinear propagation of femtosecond optical pulses in gases,” Eur. Phys. J. D 6, 383–396 (1999).
  7. A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999).
  8. T. Brabec and F. Krausz, “Intense few-cycle laser fields: frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545–591 (2000).
  9. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000).
  10. J. Moloney, M. Kolesik, M. Mlejnek, and E. Wright, “Femtosecond self-guided atmospheric light strings,” Chaos 10, 559–569 (2000).
  11. N. Aközbek, M. Scalora, C. Bowden, and S. Chin, “White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353–362 (2001).
  12. M. R. Junnarkar, “Short pulse propagation in tight focusing conditions,” Opt. Commun. 195, 273–292 (2001).
  13. A. C. Bernstein, T. S. Luk, T. R. Nelson, A. McPherson, J. C. Diels, and S. M. Cameron, “Asymmetric ultra-short pulse splitting measured in air using FROG,” Appl. Phys. B 75, 119–122 (2002).
  14. A. L. Gaeta, “Nonlinear propagation and continuum generation in microstructured optical fibers,” Opt. Lett. 27, 924–926 (2002).
  15. M. Kolesik, J. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
  16. N. Aközbek, C. M. Bowden, and S. L. Chin, “Propagation dynamics of ultra-short high-power laser pulses in air: supercontinuum generation and transverse ring formation,” J. Mod. Opt. 49, 475–486 (2002).
  17. S. Skupin, U. Peschel, C. Etrich, L. Leine, F. Lederer, and D. Michaelis, “Simulation of femtosecond pulse propagation in air,” Opt. Quantum Electron. 35, 573–582 (2003).
  18. A. C. Bernstein, J. C. Diels, T. S. Luk, T. R. Nelson, A. McPherson, and S. M. Cameron, “Time-resolved measurements of self-focusing pulses in air,” Opt. Lett. 28, 2354–2356 (2003).
  19. R. W. Boyd, Nonlinear Optics (Elsevier Science, New York, 1992).
  20. P. Sprangle, J. Peñano, and B. Hafizi, “Propagation of intense short laser pulses in the atmosphere,” Phys. Rev. E 66, 046418 (2002).
  21. A. A. Zozulya, S. A. Diddams, and T. S. Clement, “Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects,” Phys. Rev. A 58, 3303–3310 (1998).
  22. M. Mlejnek, M. Kolesik, E. Wright, and J. Moloney, “Recurrent femtosecond pulse collapse in air due to plasma generation: numerical results,” Math. Comput. Simul. 56, 563–570 (2001).
  23. A. C. Bernstein, “Measurements of ultrashort pulses self-focusing in air,” Ph.D. thesis (University of New Mexico, Albuquerque, New Mexico, 2004).
  24. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
  25. T. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
  26. G. P. Agrawal, Nonlinear Fiber Optics, Optics and Photonics, 3rd ed. (Academic, San Diego, 2001).
  27. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  28. M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).
  29. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
  30. J. R. Goates, J. B. Ott, and E. A. Butler, General Chemistry: Theory and Description (Harcourt Brace Jovanovitch, New York, 1981).
  31. A. Talebpour, J. Yang, and S. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
  32. E. T. J. Nibbering, G. Grillon, M. A. Franco, B. S. Prade, and A. Mysyrowicz, “Determination of the inertial contribution to the nonlinear refractive index of air, N2, and O2 by use of unfocused high-intensity femtosecond laser pulses,” J. Opt. Soc. Am. B 14, 650–660 (1997).
  33. D. Kane, “Recent progress toward real-time measurement of ultrashort laser pulses,” IEEE J. Quantum Electron. 35, 421–431 (1999).
  34. T. Pitts and J. Greenleaf, “Fresnel transform phase retrieval from magnitude,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1035–1045 (2003).
  35. T. Pitts and J. Greenleaf, “Three-dimensional optical measurement of instantaneous pressure,” J. Acoust. Soc. Am. 108, 2873–2883 (2000).
  36. P. Robert and C. Weast, eds., “General physical constants,” in Handbook of Chemistry and Physics, 65th ed. (CRC Press, Boca Raton, Fla., 1984–1985), p. E-359. Sellmeier coefficients for air are at 30 °C and 76 cm Hg.
  37. Y. Yamaoka, K. Minoshima, and H. Matsumoto, “Direct measurement of the group refractive index of air with interferometry between adjacent femtosecond pulses,” Appl. Opt. 41, 4318–4324 (2002).
  38. B. Edlén, “The refractive index of air,” Metrologia 2, 71–80 (1966).
  39. M. Mlejnek, M. Kolesik, E. Wright, and J. Moloney, “A dynamic spatial replenishment scenario for femtosecond pulses propagating in air—a route to optical turbulence?” Laser Phys. 10, 107–110 (2000).
  40. C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse, Vol. 163 of Applied Mathematical Sciences (Springer-Verlag, New York, 1999).
  41. M. Feit and J. J. A. Fleck, “Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams,” J. Opt. Soc. Am. B 5, 633–640 (1988).

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