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Journal
2014 | 12 | 3 | 203-214
Article title

The Lorenz model for single-mode homogeneously broadened laser: analytical determination of the unpredictable zone

Content
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Languages of publication
EN
Abstracts
EN
We have applied harmonic expansion to derive an analytical solution for the Lorenz-Haken equations. This method is used to describe the regular and periodic self-pulsing regime of the single mode homogeneously broadened laser. These periodic solutions emerge when the ratio of the population decay rate ℘ is smaller than 0:11. We have also demonstrated the tendency of the Lorenz-Haken dissipative system to behave periodic for a characteristic pumping rate “2C
P”[7], close to the second laser threshold “2C
2th
”(threshold of instability). When the pumping parameter “2C” increases, the laser undergoes a period doubling sequence. This cascade of period doubling leads towards chaos. We study this type of solutions and indicate the zone of the control parameters for which the system undergoes irregular pulsing solutions. We had previously applied this analytical procedure to derive the amplitude of the first, third and fifth order harmonics for the laser-field expansion [7, 17]. In this work, we extend this method in the aim of obtaining the higher harmonics. We show that this iterative method is indeed limited to the fifth order, and that above, the obtained analytical solution diverges from the numerical direct resolution of the equations.
Publisher

Journal
Year
Volume
12
Issue
3
Pages
203-214
Physical description
Dates
published
1 - 3 - 2014
online
13 - 3 - 2014
Contributors
author
  • Faculté de physique, Laboratoire d’électronique quantique, USTHB, Bp N 32 El Alia Bab Ezzouar, 16111, Alger, Algeria, samia_ay@yahoo.com
  • Laboratoire MIPS EA2332, Université de Haute-Alsace, 61 rue Albert Camus, 68093, Mulhouse, France, olivier.haeberle@uha.fr
References
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  • [7] B. Meziane, S. Ayadi, Opt. Comm. 281, 4061 (2008) http://dx.doi.org/10.1016/j.optcom.2008.04.005[Crossref]
  • [8] H. Haken, Light, Vol. 2. (North-Holland Physics Publishing, 1985)
  • [9] Ya. I. Khanin, Fundamental of Laser Dynamics. (Cambridge Int. Science Publ., 2006)
  • [10] C. T. Sparrow, The Lorenz Equation: Bifurcation, Chaos and Strange Attractors. (Berlin Heidelberg, Springer-Verglas, 1982) http://dx.doi.org/10.1007/978-1-4612-5767-7[Crossref]
  • [11] S. Smale, Math. Intelligencer 20, 7 (1998) http://dx.doi.org/10.1007/BF03025291[Crossref]
  • [12] W. Tucker, Found. Comput. Math. 2, 53 (2002)
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  • [14] L. M. Narducci, H. Sadiky, L. A. Lugiato, N. B. Abraham, Opt. Comm. 55, 370 (1985) http://dx.doi.org/10.1016/0030-4018(85)90189-0[Crossref]
  • [15] L. M. Narducci, N. B. Abraham, Laser physics and laser instabilities. (World Scientific Publishing Co Pte Ltd, 1988) http://dx.doi.org/10.1142/0234[Crossref]
  • [16] R. G. Harrison, D. J. Biswas, Prog. Quant. Electron 10, 147 (1985) http://dx.doi.org/10.1016/0079-6727(85)90005-9[Crossref]
  • [17] S. Ayadi, B. Meziane, In Semiconductor Lasers and Laser Dynamics III. Proc. of SPIE Vol. 6997 (SPIE, Bellingham, WA, 69971D1-69971D9 2008)
  • [18] J. W. Swift, K. Weisenfeld, Phys. Rev. Lett. 52, 705 (1984) http://dx.doi.org/10.1103/PhysRevLett.52.705[Crossref]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-014-0440-4
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