For citation:
Krenc A. A., Molevich N. E. Birth of a stable torus from the critical closed curve and its bifurcations in a laser system with frequency detuning. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, iss. 5, pp. 67-80. DOI: 10.18500/0869-6632-2010-18-5-67-80
Birth of a stable torus from the critical closed curve and its bifurcations in a laser system with frequency detuning
Realization of stable twofrequency oscillations is shown in the Maxwell–Bloch model. Birth of a stable ergodic twodimensional torus from the critical closed curve is observed. The conditions of the passage to chaos via a cascade of torus doubling bifurcations are obtained. It is established that at bifurcations points a structurally unstable threedimensional torus is produced, which gives rise to a stable doubled ergodic torus. Analytical approximation describing dynamics of the system near a point of torus birth is found.
- Lorenz EN. Deterministic nonperiodic flow. J. Atm. Sci. 1963;20(2):130–141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
- Grasiuk AZ, Oraevsky AN. Proceedings of the Fourth International Congress on Microwave Tubes Sheveningen. Holland; 1962, 446 p. Paper at Course 31, Enrico Fermi Summer School. Varenna, Italy; 1963. (in Russian).
- Oraevsky AN. Masers, lasers, and strange attractors. Sov. J. Quantum. Electron. 1981;11(1):71–78.
- Haken H. Analogy between higher instabilities in fluids and lasers. Phys. Lett. A. 1975;53(1):77–78. DOI: 10.1016/0375-9601(75)90353-9.
- Letellier C. Modding out a continuous rotation symmetry for disentangling a laser dynamics. International Journal of Bifurcation and Chaos. 2003;13(6):1573–1577. DOI: 10.1142/S0218127403007424.
- Weiss CO, Larionova Ye. Pattern formation in optical resonators. Rep. Prog. Phys. 2007;70(2):255–335. DOI: 10.1088/0034-4885/70/2/R03.
- Hollinger F, Jung Chr, Weber H. Simple mathematical model describing multitransversal solid-state lasers. J. Opt. Soc. Am. B. 1990;7(6):1013–1018. DOI: 10.1364/JOSAB.7.001013.
- Hollinger F, Jung Chr. Single-longitudinal-mode laser as a discrete dynamical system. J. Opt. Soc. Am. B. 1985;2(1):218–225. DOI: 10.1364/JOSAB.2.000218.
- Cabrera E, Calderon OG, Melle S, Guerra JM. Development of spatial turbulence from boundary-controlled patterns in class-B lasers. Phys. Rev. A. 2006;73(5):053820. DOI: 10.1103/PhysRevA.73.053820.
- Huyet G, Tredicce JR. Spatio-temporal chaos in the transverse section of lasers. Physica D. 1996;96:209–214. DOI: 10.1016/0167-2789(96)00021-8.
- Huyet G, Martinoni MC, Tredicce JR, Rica S. Spatiotemporal dynamics of lasers with a large Fresnel number. Phys. Rev. Lett. 1995;75(22):4027–4030. DOI: 10.1103/PhysRevLett.75.4027.
- O‘Neil E, Houlihan J, McInerney JG, Huyet G. Dynamics of traveling waves in the transverse section of a laser. Phys. Rev. Lett. 2005;94(14):143901. DOI: 10.1103/PhysRevLett.94.143901.
- Jacobsen PK, Moloney JV, Newell AC, Indik R. Space-time dynamics of wide-gain-section lasers. Phys. Rev. A. 1992;45(11):8129–8137. DOI: 10.1103/physreva.45.8129.
- Jacobsen PK, Lega J, Feng Q, Staley M, Moloney JV, Newell AC. Nonlinear transverse modes of large-aspect-ratio homogeneously broadened lasers: I. Analysis and numerical simulation. Phys. Rev. A. 1994;49(5):4189–4200. DOI: 10.1103/physreva.49.4189.
- Jacobsen PK, Lega J, Feng Q, Staley M, Moloney JV, Newell AC. Nonlinear transverse modes of large-aspect-ratio homogeneously broadened lasers: II. Pattern analysis near and beyond threshold. Phys. Rev. A. 1994;49(5):4201–4212. DOI: 10.1103/physreva.49.4201.
- Zaikin AP, Molevich NE. Effect of the cross-relaxation rate on the transverse radiation dynamics of a wide-aperture laser. Quantum Electron. 2004;34(8):731–735.
- Zaikin AP, Kurguzkin AA, Molevich NE. Periodic self-wave structures in a wide-aperture laser with frequency detuning. I. Bifurcation analysis. Quantum Electron. 1999;29(6):523–525.
- Zaikin AP, Kurguzkin AA, Molevich NE. Periodic self-wave structures in a wide-aperture laser with frequency detuning. II. Distributed model. Quantum Electron. 1999;29(6):526–529.
- Zaikin AP, Kurguzkin AA, Molevich NE. Influence of frequency tuning on the space-time structure of the optical field of a wide-aperture laser. Izvestiya VUZ. Applied Nonlinear Dynamics. 1999;7(5):87–96 (in Russian).
- Krents AA, Molevich NE. Cascade of torus doubling bifurcations in a detuned laser. Quantum Electron. 2009;39(8):751–756.
- Amroun D, Brunel M, Letellier C, Leblond H, Sanchez F. Complex intermittent dynamics in large-aspect-ratio homogeneously broadened single-mode lasers. Physica D. 2005;203:185–197. DOI: 10.1016/j.physd.2005.03.015.
- Lugiato LA, Oldano C, Narducci LM. Cooperative frequency locking and stationary spatial structures in lasers. J. Opt. Soc. Am. B. 1988;5:879–888. DOI: 10.1364/JOSAB.5.000879.
- Arrowsmith D, Place C. Ordinary differential equations : a qualitative approach with applications. Moscow: Mir; 1986. (in Russian).
- Kuznetsov SP. Dynamical Chaos: Course of Lectures. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
- Schuster G. Deterministic Chaos. An Introduction. Moscow: Mir; 1988. (in Russian).
- Anishchenko VS, Nikolaev SM. Generator of quasi-periodic oscillations featuring two-dimensional torus doubling bifurcations. Tech. Phys. Lett. 2005;31(10):853–855. DOI: 10.1134/1.2121837.
- Anishchenko VS. Complex Oscillations in Simple Systems. Moscow: Nauka; 1990. (in Russian).
- Zeghlache H., Mandel P. Influence of detuning on properties of laser equations. J. Opt. Soc. Am. B. 1985;2(1):18–22. DOI: 10.1364/JOSAB.2.000018.
- 1978 reads