OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 17, Iss. 2 — Feb. 1, 2000
  • pp: 188–197

Homoclinic orbits and chaos in the vibronic short-cavity standing-wave alexandrite laser

W. Gadomski and B. Ratajska-Gadomska  »View Author Affiliations

JOSA B, Vol. 17, Issue 2, pp. 188-197 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (272 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present an experimental and a theoretical investigation of the unstable behavior of the laser-pumped short-cavity alexandrite laser. Its chaotic dynamics is achieved by an increase of the pump laser power. The route to chaos depends on the cavity length and the pump wavelength. The experimental results are explained by the theoretical model, which includes the host-lattice phonons’ dynamics in the standard laser equations. We conclude that the observed laser instabilities are due to the competition between the laser field and phonons in the host crystal. A linear-stability analysis yields the conclusion that the observed chaos has a homoclinic character.

© 2000 Optical Society of America

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.1540) Lasers and laser optics : Chaos
(140.3430) Lasers and laser optics : Laser theory
(140.3580) Lasers and laser optics : Lasers, solid-state
(190.3100) Nonlinear optics : Instabilities and chaos
(270.3430) Quantum optics : Laser theory

W. Gadomski and B. Ratajska-Gadomska, "Homoclinic orbits and chaos in the vibronic short-cavity standing-wave alexandrite laser," J. Opt. Soc. Am. B 17, 188-197 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. W. Gadomski and B. Ratajska-Gadomska, “Self-pulsation in the phonon terminated lasers,” J. Opt. Soc. Am. B 15, 2681–2688 (1998). [CrossRef]
  2. B. Ratajska-Gadomska and W. Gadomski, “Quantum theory of the vibronic solid-state laser,” J. Opt. Soc. Am. B 16, 848–860 (1999). [CrossRef]
  3. J. C. Walling, O. G. Peterson, and R. C. Morris, “Tunable cw alexandrite laser,” IEEE J. Quantum Electron. QE-16, 120–121 (1980). [CrossRef]
  4. J. Walling, O. G. Peterson, H. P. Jenssen, R. C. Morris, and E. W. O’Dell, “Tunable alexandrite lasers,” IEEE J. Quantum Electron. QE-16, 1302–1314 (1980). [CrossRef]
  5. S. T. Lai and M. L. Shand, “High efficiency cw laser-pumped tunable alexandrite laser,” J. Appl. Phys. 54, 5642–5644 (1983). [CrossRef]
  6. R. Scheps, B. M. Gately, J. F. Mayers, J. S. Krasinski, and D. F. Heller, “Alexandrite laser pumped by semiconductor laser,” Appl. Phys. Lett. 56, 2288–2290 (1990). [CrossRef]
  7. L. P. Shil’nikov, “A contribution to the problem of the structure of an extended neighbourhood of a rough equilibrium state of saddle focus type,” Math. USSR Sbornik 10, 91–102 (1970). [CrossRef]
  8. A. Arneodo, P. H. Coullet, E. A. Spiegel, and C. Tresser, “Homoclinic chaos in chemical systems,” Physica D 62, 134–169 (1993). [CrossRef]
  9. A. Arneodo, P. H. Coullet, E. A. Spiegel, and C. Tresser, “Asymptotic chaos,” Physica D 14, 327–347 (1985). [CrossRef]
  10. P. Glendinning and C. Sparrow, “Local and global behavior near homoclinic orbits,” J. Stat. Phys. 35, 645–696 (1984). [CrossRef]
  11. F. Argoul, A. Arneodo, and P. Richgetti, “Experimental evidence for homoclinic chaos in Belolusov–Zabotinskii reaction,” Phys. Lett. A 120, 269–275 (1987). [CrossRef]
  12. A. Argoul, J. Huth, P. Merzeau, A. Arneodo, and H. L. F. Swinney, “Experimental evidence for homoclinic chaos in electrochemical growth process,” Physica D 62, 170–185 (1993). [CrossRef]
  13. M. R. Basset and J. L. Hudson, “Shil’nikov chaos during copper electrodissolution,” J. Phys. Chem. 92, 6963–6966 (1988). [CrossRef]
  14. F. T. Arecchi, R. Meucci, and W. Gadomski, “Laser dynamics with competing instabilities,” Phys. Rev. Lett. 58, 2205–2208 (1987). [CrossRef] [PubMed]
  15. F. T. Arecchi, W. Gadomski, A. Lapucci, H. Mancini, R. Meucci, and J. A. Roversi, “Laser with feedback: an optical implementation of competing instabilities, Shil’nikov chaos, and transient fluctuation enhancement,” J. Opt. Soc. Am. B 5, 1153–1159 (1988). [CrossRef]
  16. F. T. Arecchi, A. Lapucci, and R. Meucci, “Poincaré versus Boltzman in Shil’nikov phenomena,” Physica D 62, 186–191 (1993). [CrossRef]
  17. D. Hennequin, F. de Tomasi, B. Zambon, and E. Arimondo, “Homoclinic orbits and cycles in the instabilities of a laser with a saturable absorber,” Phys. Rev. A 37, 2243–2246 (1988). [CrossRef] [PubMed]
  18. M. Lefranc, D. Hennequin, and D. Dangoisse, “Homoclinic chaos in a laser containing saturable absorber,” J. Opt. Soc. Am. B 8, 239–249 (1991). [CrossRef]
  19. T. Braun, J. A. Lisboa, and J. A. C. Gallas, “Evidence of homoclinic chaos in the plasma of a glow discharge,” Phys. Rev. Lett. 68, 2770–2773 (1992). [CrossRef] [PubMed]
  20. R. Herrero, F. R. Pons, J. Farjas, F. Pi, and G. Orriols, “Homoclinic dynamics in experimental Shil’nikov attractors,” Phys. Rev. E 53, 5627–5636 (1996). [CrossRef]
  21. R. Herrero, F. Boixader, J. Farjas, F. Pi, G. Orriols, and F. Rossler, “Rossler chaos in opto-thermal bistable devices,” Opt. Commun. 113, 324–334 (1993). [CrossRef]
  22. D. Y. Tang and N. R. Heckenberg, “Homoclinic orbits and chaos in a multimode laser,” J. Opt. Soc. Am. B 14, 2930–2935 (1997). [CrossRef]
  23. R. Englman, Non-Radiative Decay of Ions and Molecules in Solids (North-Holland, Amsterdam, 1979).
  24. F. Sanchez and A. Kellou, “Laser dynamics with excited-state absorption,” J. Opt. Soc. Am. B 14, 209–213 (1997). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited