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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 17, Iss. 7 — Jul. 1, 2000
  • pp: 1304–1312

Ultrashort pulsed sinc-Gaussian light beams

Qing Cao and Sien Chi  »View Author Affiliations

JOSA B, Vol. 17, Issue 7, pp. 1304-1312 (2000)

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A family of analytical solutions of the time-dependent wave equation, the ultrashort pulsed sinc-Gaussian light beams (UPSGLB’s), are presented in the paraxial approximation. Each of them has the product form of the monochromatic Gaussian light beam with the central frequency νc times the sinc function of the complex temporal–spatial beam parameter Pn. The complex temporal–spatial beam parameter Pn, which corresponds to the order n, is directly related to the temporal–spatial coupling properties of the nth-order UPSGLB. The UPSGLB’s are used, for the first time to our knowledge, as an analytical expansion set for bandwidth-limited ultrashort light pulses emitted from mode-locked lasers with stable resonators (ULPEMLLSR’s). Two special examples of bandwidth-limited ULPEMLLSR’s, a single zeroth-order UPSGLB and a novel model of a nearly temporal–spatial Gaussian beam, are analytically investigated and compared with experimental results.

© 2000 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(140.4050) Lasers and laser optics : Mode-locked lasers
(270.5530) Quantum optics : Pulse propagation and temporal solitons
(320.0320) Ultrafast optics : Ultrafast optics

Qing Cao and Sien Chi, "Ultrashort pulsed sinc-Gaussian light beams," J. Opt. Soc. Am. B 17, 1304-1312 (2000)

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  1. M. Kempe, U. Stamm, B. Wilhelmi, and W. Rudolph, “Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems,” J. Opt. Soc. Am. B 9, 1158–1165 (1992).
  2. Z. Bor and Z. L. Horváth, “Distortion of femtosecond pulses in lenses. Wave optical description,” Opt. Commun. 94, 249–258 (1992).
  3. M. Kempe and W. Rudolph, “Femtosecond pulses in the focal region of lenses,” Phys. Rev. A 48, 4721–4729 (1993).
  4. Z. L. Horváth and Z. Bor, “Focusing of femtosecond pulses having Gaussian spatial distribution,” Opt. Commun. 100, 6–12 (1993).
  5. R. W. Ziolkowski and D. B. Davidson, “Designer pulsed beams for enhanced space–time focusing,” Opt. Lett. 19, 284–286 (1994).
  6. A. S. Marathay, “Propagation of optical pulses with spatial and temporal dependence,” Appl. Opt. 33, 3139–3145 (1994).
  7. E. Ibragimov, “Focusing of ultrashort laser pulses by the combination of diffractive and refractive elements,” Appl. Opt. 34, 7280–7285 (1995).
  8. J. Paye and A. Migus, “Space–time Wigner functions and their application to the analysis of a pulse shaper,” J. Opt. Soc. Am. B 12, 1480–1490 (1995).
  9. M. Gu and X. S. Gan, “Fresnel diffraction by circular and serrated apertures illuminated with an ultrashort pulsed-laser beam,” J. Opt. Soc. Am. A 13, 771–778 (1996).
  10. Z. Wang, Z. Xu, and Z. Zhang, “Diffraction integral formulas of the pulsed wave field in the temporal domain,” Opt. Lett. 22, 354–356 (1997).
  11. J. M. Anderson and C. Roychoudhuri, “Diffraction of an extremely short optical pulse,” J. Opt. Soc. Am. A 15, 456–463 (1998).
  12. I. P. Christov, “Propagation of femtosecond light pulses,” Opt. Commun. 53, 364–366 (1985).
  13. R. W. Ziolkowski and J. B. Judkins, “Propagation characteristics of ultrawide-bandwidth pulsed Gaussian beams,” J. Opt. Soc. Am. A 9, 2021–2030 (1992).
  14. Z. Wang, Z. Zhang, Z. Xu, and Q. Lin, “Space–time profiles of an ultrashort pulsed Gaussian beam,” IEEE J. Quantum Electron. 33, 566–573 (1997).
  15. M. A. Porras, “Ultrashort pulsed Gaussian light beams,” Phys. Rev. E 58, 1086–1093 (1998).
  16. E. Heyman and L. B. Felsen, “Complex-source pulsed-beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989).
  17. T. Melamed and L. B. Felsen, “Pulsed-beam propagation in lossless dispersive media. I. Theory,” J. Opt. Soc. Am. A 15, 1268–1276 (1998).
  18. M. A. Porras, “Nonsinusoidal few-cycle pulsed light beams in free space,” J. Opt. Soc. Am. B 16, 1468–1474 (1999).
  19. Q. Cao, “Pulsed negative-power-function light beams,” J. Opt. Soc. Am. B 16, 1786–1789 (1999).
  20. S. Feng and H. G. Winful, “Spatiotemporal transformation of isodiffracting ultrashort pulses by nondispersive quadratic phase media,” J. Opt. Soc. Am. A 16, 2500–2509 (1999).
  21. R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
  22. R. W. Hellwarth and P. Nouchi, “Focused one-cycle electromagnetic pulses,” Phys. Rev. E 54, 889–895 (1996).
  23. S. Feng, H. G. Winful, and R. W. Hellwarth, “Gouy shift and temporal reshaping of focused single-cycle electromagnetic pulses,” Opt. Lett. 23, 385–387 (1998).
  24. L. Xu, G. Tempea, C. Spielmann, F. Krausz, A. Stingl, K. Ferencz, and S. Takano, “Continuous-wave mode-locked Ti: sapphire laser focusable to 5×1013 W/cm2,” Opt. Lett. 23, 789–791 (1998).
  25. M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, C. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997).
  26. I. P. Bilinsky, J. G. Fujimoto, J. N. Walpole, and L. J. Missaggia, “Semiconductor-doped-silica saturable-absorber films for solid-state laser mode locking,” Opt. Lett. 23, 1766–1768 (1998).
  27. U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, “Sub-two-cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser,” Opt. Lett. 24, 411–413 (1999).
  28. D. H. Sutter, G. Steinmeyer, L. Gallmann, N. Matuschek, F. M. Genoud, U. Keller, V. Scheuer, G. Angelow, and T. Tschudi, “Semiconductor saturable-absorber mirror-assisted Kerr-lens mode-locked Ti:sapphire laser producing pulses in the two-cycle regime,” Opt. Lett. 24, 631–633 (1999).
  29. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, UK, 1975), pp. 494–499.
  30. H. Kogelnik and T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1566 (1966).
  31. W. Koechner, Solid-State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), pp. 482–485 and pp. 192–201.
  32. P. M. Mejias and R. Martinez-Herrero, “Time-resolved spatial parametric characterization of pulsed light beams,” Opt. Lett. 20, 660–662 (1995).
  33. Q. Cao and X. Deng, “Spatial parametric characterization of general polychromatic light beams,” Opt. Commun. 142, 135–145 (1997).
  34. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
  35. K. H. Lin and W. F. Hsieh, “Analytical design of symmetrical Kerr-lens mode-locking laser cavities,” J. Opt. Soc. Am. B 11, 737–741 (1994).
  36. K. H. Lin, Y. Lai, and W. F. Hsieh, “Simple analytical method of cavity design for astigmatism-compensated Kerr-lens mode-locked ring lasers and its applications,” J. Opt. Soc. Am. B 12, 468–475 (1995).
  37. H. Kogelnik, “Imaging of optical modes-resonators with internal lenses,” Bell Syst. Tech. J. 43, 455–494 (1965).
  38. G. Herziger and H. Weber, “Equivalent optical resonators,” Appl. Opt. 23, 1450–1452 (1984).

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