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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 15, Iss. 1 — Jan. 1, 1998
  • pp: 103–117

Perturbative model for nonstationary second-order cascaded effects

Guido Toci, Matteo Vannini, and Renzo Salimbeni  »View Author Affiliations

JOSA B, Vol. 15, Issue 1, pp. 103-117 (1998)

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We report a semianalytical solution describing the type I second-order nonlinear interaction of the fundamental and the second-harmonic fields in a nonlinear crystal, which accounts for the phase- and group-velocity mismatch of the interacting pulses. The method uses a series-development solution of the propagation equations in respect to the second-harmonic conversion efficiency. The method describes the self-phase and self-amplitude modulation experienced by the fundamental pulse in single- and double-pass (i.e., reinjecting into the nonlinear crystal the outgoing pulses) interaction geometries, following better with respect to a numerical analysis, the dependence from the propagation parameters such as the crystal length, the pulse duration, and the phase- and group-velocity mismatch. It appears that it is possible to obtain an efficient self-phase modulation on the fundamental field even in nonstationary conditions. This paper describes the advantages of a double-pass configuration, which, for a given crystal length, allows a stronger nonlinear phase modulation of the fundamental field and minimizes its losses toward the second harmonic.

© 1998 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(320.7110) Ultrafast optics : Ultrafast nonlinear optics

Guido Toci, Matteo Vannini, and Renzo Salimbeni, "Perturbative model for nonstationary second-order cascaded effects," J. Opt. Soc. Am. B 15, 103-117 (1998)

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  1. H. J. Bakker, P. C. M. Planken, L. Kuipers, and A. Lagendijk, “Phase modulation in second-order non-linear-optical processes,” Phys. Rev. A 42, 4085 (1990). [CrossRef] [PubMed]
  2. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Varhenzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28 (1992). [CrossRef] [PubMed]
  3. D. Pierrotet, B. Berman, M. Vannini, and D. McGraw, “Parametric lens,” Opt. Lett. 18, 263 (1993). [CrossRef]
  4. M. L. Sunderheimer, Ch. Bossard, E. W. Van Stryland, G. I. Stegeman, and J. D. Bierlein, “Large nonlinear phase modulation in quasi-phase-matched KTP waveguides as a result of cascaded second-order processes,” Opt. Lett. 18, 1397 (1993). [CrossRef]
  5. G. I. Stegeman, M. Sheik-Bahae, E. V. Van Stryland, and G. Assanto, “Large nonlinear phase shifts in second-order nonlinear-optical processes,” Opt. Lett. 18, 13 (1993). [CrossRef] [PubMed]
  6. G. Toci, D. McGraw, R. Pini, R. Salimbeni, and M. Vannini, “Time-dependent analysis of a parametric lens detected with a 100-fs Ti:sapphire laser,” Opt. Lett. 20, 1547 (1995). [CrossRef] [PubMed]
  7. F. Hache, A. Zéboulon, G. Gallot, and G. M. Gale, “Cascaded second-order effects in the femtosecond regime in β-barium borate: self-compression in a visible femtosecond optical parametric oscillator,” Opt. Lett. 20, 1556 (1995). [CrossRef] [PubMed]
  8. R. Danielius, A. Dubietis, and A. Piskarkas, “Linear transformation of pulse chirp through a cascaded optical second-order process,” Opt. Lett. 20, 1521 (1995). [CrossRef] [PubMed]
  9. C. R. Menjuk, R. Schieck, and L. Torner, “Solitary waves due to χ(2)(2) cascading,” J. Opt. Soc. Am. B 11, 2434 (1994). [CrossRef]
  10. G. Toci, R. Pini, R. Salimbeni, S. Siano, and M. Vannini, “Optical modulators based on second order non-linear processes in non-stationary conditions,” Proceedings of the International Conference on Lasers, 1995 (STS, McLean, Va., 1996), p. 761.
  11. K. A. Stankov and J. Jethwa, “A new mode-locking technique using a nonlinear mirror,” Opt. Commun. 66, 41 (1988). [CrossRef]
  12. M. B. Danailov, G. Cerullo, V. Magni, D. Segala, and S. De Silvestri, “Nonlinear mirror mode locking of a cw Nd:YLF laser,” Opt. Lett. 19, 792 (1994). [CrossRef] [PubMed]
  13. G. Cerullo, S. De Silvestri, A. Monguzzi, D. Segala, and V. Magni, “Self-starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities,” Opt. Lett. 20, 746 (1995). [CrossRef] [PubMed]
  14. G. Cerullo, V. Magni, and A. Monguzzi, “Group-velocity mismatch compensation in continuous-wave lasers mode locked by second-order nonlinearities,” Opt. Lett. 20, 1785 (1995). [CrossRef] [PubMed]
  15. K. A. Stankov, V. P. Tzolov, and M. G. Mirkov, “Frequency-doubling mode locker: the influence of group-velocity mismatch,” Opt. Lett. 16, 1119 (1991). [CrossRef] [PubMed]
  16. K. A. Stankov, V. P. Tzolov, and M. G. Mirkov, “Compensation of group-velocity mismatch in the frequency-doubling modelocker,” Appl. Phys. B 54, 303 (1992). [CrossRef]
  17. I. Buchvarov, G. Christov, and S. Saltiel, “Transient behavior of frequency doubling mode-locker. Numerical analysis,” Opt. Commun. 107, 281 (1994). [CrossRef]
  18. Y. R. Shen, The Principles of the Nonlinear Optics (Wiley, New York, 1984).
  19. N. Bloembergen, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1992), and references therein.
  20. R. C. Eckardt and J. Reintjes, “Phase-matching limitation of high efficiency second harmonic generation,” IEEE J. Quantum Electron. 20, 1178 (1984). [CrossRef]
  21. E. Sidick, A. Knoesnen, and A. Dienes, “Ultrashort-pulse second-harmonic generation. I. Transform-limited fundamental pulses,” J. Opt. Soc. Am. B 12, 1704 (1995). [CrossRef]
  22. E. Sidick, A. Knoesnen, and A. Dienes, “Ultrashort-pulse second-harmonic generation. II. Non-transform-limited fundamental pulses,” J. Opt. Soc. Am. B 12, 1713 (1995). [CrossRef]
  23. MATHCAD 5.0 Plus, MathSoft, Inc. (Cambridge, Mass., 1995).
  24. J. T. Manassah, “Effects of velocity dispersion on a generated second harmonic signal,” Appl. Opt. 27, 4365 (1988). [CrossRef] [PubMed]
  25. H. J. Bakker, P. C. M. Planken, and H. G. Muller, “Numerical calculation of optical frequency-conversion processes: a new approach,” J. Opt. Soc. Am. B 6, 1665 (1989). [CrossRef]
  26. K. Kato, “Second harmonic generation to 2048 Å in β-BaB2O4,” IEEE J. Quantum Electron. QE-22, 1013 (1986). [CrossRef]
  27. R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second harmonic generation,” IEEE J. Quantum Electron. QE-26, 922 (1990). [CrossRef]
  28. S. P. Velsko, M. Webb, L. Davis, and C. Huang, “Phase-matched harmonic generation in lithium triborate,” IEEE J. Quantum Electron. 27, 2182 (1991). [CrossRef]
  29. M. J. Weber, CRC Handbook of Laser Science and Technology, Vol. 3 (CRC Press, Boca Raton, Fla., 1986), p. 108.
  30. G. C. Ghosh and G. C. Bhar, “Temperature dispersion in ADP, KDP, KD*P for nonlinear devices,” IEEE J. Quantum Electron. QE-18, 143 (1982). [CrossRef]
  31. R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996).
  32. D. Wearie, B. S. Wherret, D. A. B. Miller, and S. D. Smith, “Effect of low-power nonlinear refraction on laser beam propagation in InSb,” Opt. Lett. 4, 331 (1974). [CrossRef]
  33. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990). [CrossRef]
  34. G. Toci, M. Vannini, and R. Salimbeni, “Temporal dynamic of the non-linear mirror: an analytical description,” Opt. Commun. (to be published).
  35. G. Toci, R. Pini, R. Salimbeni, M. Vannini, “Group velocity mismatch effects in ultrafast optical modulators based on cascaded second order nonlinearities,” in Ultrafast Processes in Spectroscopy, O. Svelto, S. De Silvestri, and G. Denardo, eds. (Plenum, New York, 1996).
  36. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Wetterling, Numerical Recipes (Cambridge University, Cambridge, England, 1989).

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