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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 15, Iss. 4 — Apr. 1, 1998
  • pp: 1282–1290

Topological properties of laser phase

Vladislav Yu. Toronov and Vladimir L. Derbov  »View Author Affiliations

JOSA B, Vol. 15, Issue 4, pp. 1282-1290 (1998)

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Manifestations of the geometric properties of evolutionary laser-field phases are considered for some laser systems. It is shown that a bidirectional ring laser provides an effective opportunity to control geometric phases.

© 1998 Optical Society of America

OCIS Codes
(140.3570) Lasers and laser optics : Lasers, single-mode
(350.5030) Other areas of optics : Phase

Vladislav Yu. Toronov and Vladimir L. Derbov, "Topological properties of laser phase," J. Opt. Soc. Am. B 15, 1282-1290 (1998)

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  1. M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. London, Ser. A 392, 45–57 (1984); for reviews on the geometric phases see S. I. Vinitsky, V. L. Derbov, V. N. Dubovik, B. L. Markovski, and Yu. P. Stepanovskii, “Topological phases in quantum mechanics and polarization optics,” Sov. Phys. Usp. 33, 403–428 (1990); D. J. Moore, “The calculation of nonadiabatic Berry phases,” Phys. Rep. PRPLCM 210, 1–43 (1991); J. W. Zwanziger, M. Koenig, and A. Pines, “Berry’s phase,” Annu. Rev. Phys. Chem. ARPLAP 41, 601–646 (1990). [CrossRef]
  2. R. Vilaseca, G. J. de Valcarcel, and E. Roldan, “Physical interpretation of laser phase dynamics,” Phys. Rev. A 41, 5269–5272 (1990). [CrossRef] [PubMed]
  3. C. Z. Ning and H. Haken, “Quasiperiodicity involving twin oscillations in the complex Lorenz equations describing a detuned laser,” Z. Phys. B 81, 457–461 (1990). [CrossRef]
  4. C. Z. Ning and H. Haken, “Geometrical phase and amplitude accumulations in dissipative systems with cyclic attractors,” Phys. Rev. Lett. 68, 2109–2112 (1992); “The geometric phase in nonlinear dissipative systems,” Mod. Phys. Lett. B 6, 1541–1568 (1992). [CrossRef] [PubMed]
  5. V. Yu. Toronov and V. L. Derbov, “Geometric phases in lasers and liquid flows,” Phys. Rev. A 49, 1392–1399 (1994). [CrossRef] [PubMed]
  6. H. Haken, Laser Theory, Vol. XXV of Encyclopedia of Physics (Springer-Verlag, Berlin, 1970).
  7. J. Samuel and R. Bhandari, “General setting for Berry’s phase,” Phys. Rev. Lett. 60, 2339–2342 (1988). [CrossRef] [PubMed]
  8. C. Z. Ning and H. Haken, “Detuned lasers and the complex Lorenz equations: subcritical and supercritical Hopf bifurcations,” Phys. Rev. A 41, 3826–3837 (1990). [CrossRef] [PubMed]
  9. A. C. Fowler, J. D. Gibbon, and M. J. McGuinness, “The complex Lorenz equations,” Physica D 4, 139–163 (1982); J. D. Gibbon and M. J. McGuinness, “The real and complex Lorenz equations in rotating fluids and lasers,” Physica D 5, 108–122 (1982). [CrossRef]
  10. H. Zeghlache and P. Mandel, “Influence of detuning on the properties of laser equations,” J. Opt. Soc. Am. B 2, 18–22 (1985). [CrossRef]
  11. E. Roldan, G. J. de Valcarcel, R. Vilaseca, and P. Mandel, “Single-mode laser phase dynamics,” Phys. Rev. A 48, 591–598 (1993). [CrossRef]
  12. C. O. Weiss, N. B. Abraham, and U. Hubner, “Homoclinic and heteroclinic chaos in a single-mode laser,” Phys. Rev. Lett. 61, 1587–1590 (1988). [CrossRef] [PubMed]
  13. A. G. Vladimirov, V. Yu. Toronov, and V. L. Derbov, “On the complex Lorenz model,” Izv. Vuzov. Prikladnaya Nelneynaya Dinamika 3, 51–63 (1995).
  14. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors (Springer-Verlag, Berlin, 1982).
  15. M. Sargent III, M. O. Scully, and W. E. Lamb, Jr., Laser Physics (Addison-Wesley, London, 1974).
  16. Yu. L. Klimontovich, V. N. Kuryatov, and P. S. Landa, “On the wave synchronization in a gas laser with the ring cavity,” JETP 51, 3–7 (1966).
  17. T. H. Chyba, “Phase-jump instability in the bidirectional ring laser with backscattering,” Phys. Rev. A 40, 6327–6333 (1989). [CrossRef] [PubMed]
  18. D. V. Skryabin, A. D. Vladimirov, and A. M. Radin, “Spontaneous phase symmetry breaking due to cavity detuning in a class-A bidirectional ring laser,” Opt. Commun. 116, 109–114 (1995). [CrossRef]
  19. This fact can be understood directly from the equations of motion in R written with the spherical coordinates. One can verify that ρ does not enter the equations for the angular coordinates that therefore completely determine the dynamics of the system. Thus the phase space can be reduced to a two-dimensional sphere, which can possess only limit cycles and fixed points as attractors.
  20. N. B. Abraham and C. O. Weiss, “Dynamical frequency shifts and intensity pulsations in a FIR bidirectional ring laser,” Opt. Commun. 66, 437 (1988). [CrossRef]
  21. T. Bitter and D. Dubbers, “Manifestation of Berry’s topological phase on neutron spin rotation,” Phys. Rev. Lett. 59, 251–254 (1987). [CrossRef] [PubMed]
  22. R. Bhandari and J. Samuel, “Observation of topological phase by use of a laser interferometer,” Phys. Rev. Lett. 60, 1211–1213 (1988); R. Bhandari, “Evolution of light beams in polarization and direction,” Physica B 175, 111–122 (1991). [CrossRef] [PubMed]
  23. H. Zeglache, P. Mandel, N. B. Abraham, L. M. Hoffer, G. L. Lippi, and T. Mello, “Bidirectional ring laser: stability analysis and time-dependent solutions,” Phys. Rev. A 37, 470–497 (1988). [CrossRef]
  24. L. M. Hoffer, G. L. Lippi, N. B. Abraham, and P. Mandel, “Phase and frequency jumps in a bidirectional ring laser,” Opt. Commun. 66, 219 (1988). [CrossRef]
  25. D. Arovas, “Geometric phases in condensed matter physics,” lecture notes for a course on geometric phases (International Center for Theoretical Physics, Trieste, 1993).

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