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

Abstract

Abstract: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 2 "(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. PACS

Bifurcaciones Horquilla y Hopf en un sistema de Lorenz extendido

“…Las ecuaciones de Lorenz con algunas variaciones pueden ser aplicadas para analizar algunos fenómenos de la naturaleza. Por ejemplo, algunos modelos sobre climatología [3,4], teoría semiclásica de amplificación y emisión de laser aplicando el modelo Lorenz-Haken [5,7,8,9], generadores eléctricos [10], señales electrocardiográficas [11], entre otros. Dada su importancia, se resalta el interés en la identificación y caracterización de atractores de familias tipo Lorenz [12] o análisis sobre la dinámica de sistemas tipo Lorenz [1].…”