2013/07/30 by Ayadi Samia, Samia Ayadi, Samia, Ayadi +2
Chemistry · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Amplitude #Bifurcation #Cascade #Chemistry #Dissipative system #FOS: Physical sciences #Harmonic #Harmonics #Instability #Laser #Laser Design and Applications #Mathematics #Mechanics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Optics #Optics (physics.optics) #Period-doubling bifurcation #Physics #Quantum mechanics #Work (physics) #physics.optics
paper · pdf · doi:10.48550/arxiv.1307.7942
20 pages, 4 figures, 1 annex
arxiv created 2013/07/30 · openalex publication_date 2013/07/30 · arxiv updated 2013/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 rates 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 "2CP" [4], close to the second laser threshold "2C2th" (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 the fifth order harmonics for the laser-field expansion [4, 14]. 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.