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

• Authors: Samia Ayadi , Olivier Haeberlé
• 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.

Keywords

EN

Laser instabilities; Lorenz-Haken equations; Self-pulsing; Chaos

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 3
• Pages: 203-214

Dates

published

1 - 3 - 2014

online

13 - 3 - 2014

Contributors

author

Samia Ayadi

• Faculté de physique, Laboratoire d’électronique quantique, USTHB, Bp N 32 El Alia Bab Ezzouar, 16111, Alger, Algeria

author

Olivier Haeberlé

• Laboratoire MIPS EA2332, Université de Haute-Alsace, 61 rue Albert Camus, 68093, Mulhouse, France

References

• [1] H. Haken, Phys. Lett. A 53, 77 (1975) http://dx.doi.org/10.1016/0375-9601(75)90353-9[Crossref]
• [2] E. N. Lorenz, J. Atmos. Science 20, 130 (1963) http://dx.doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2[Crossref]
• [3] L. Bougoffa, S. Bougouffa, Appl. Math. Comput. 177, 553 (2006) http://dx.doi.org/10.1016/j.amc.2005.07.070[Crossref]
• [4] S. Bougouffa, AIP Conf. Proc. 1048, 109 (2008) http://dx.doi.org/10.1063/1.2990867[Crossref]
• [5] S. Bougouffa, S. Al-Awfi, L. Bougoffa, Appl. Math. Sciences 1, 2917 (2007)
• [6] S. Ayadi, B. Meziane, Opt. Quant. Elect. 39, 51 (2007) http://dx.doi.org/10.1007/s11082-007-9065-9[Crossref]
• [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)
• [13] B. Meziane, Atomic, Molecular and Optical Physics: New Research, Nova Science Publisher, New York, 61 (2009)
• [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]

Identifiers

DOI

10.2478/s11534-014-0440-4