Simulation of Antiphase Dynamics in Lasers with Cellular Automata. A Work in Progress [Póster]

NoLineal 2016. Book of abstracts. Posters. 91 Simulation of Antiphase Dynamics in Lasers with Cellular Automata. A Work in Progress F. Jiménez-Morales*, J.L. Guisado** (*)Dpto. Física de la Materia Condensada. (**) Dpto. Arquitectura y Tecnología de Computadores. Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, (Spain) emails: [email protected], [email protected] Cellularautomata(CA) are aclass ofspatially and temporallydiscrete mathematicalsystems characterized by local interactions and synchronous dynamical evolution. They have the ability to generate complex behavior from sets of components that follow simplerules. xAwidevariety ofphysicalsystems such as magnetization in solids, reaction diffusion processes, fluid dynamics, growth phenomena,... have beenmodeled by CA.In[1]a CAwas proposedto simulate laser dynamics which was able to capture the essential features and phenomenology encountered in lasers such as relaxation oscillations, spiking behavior and pattern formation. The model can also simulate the physics of pulsed pumped lasers [2]. 0 2000 4000 6000 0 2000 4000 6000 I1 0 2000 4000 6000 8000 0 2000 4000 6000 I1+I2 0 2000 4000 0 2000 4000 6000 I2 t -4000 -2000 0 2000 4000 0 2000 4000 6000 I1-I2 t FIGURE 1. To model antiphase dynamics in lasers with a CA two laser subsystems are considered. Time series of the intensity of both populations, the total intensityandthe differenceof intensities. The pumping probability is p=0.01 and the coupling parameter β=0.8. In this work we extend the original CA to study antiphase oscillations in lasers that was experimentally observed in a class B Nd:YAG laser [3]. The CA rule of evolution is composed of four different processes representing the pumping of electrons, the stimulated emission, and the decaying of electrons and photons. We also consider the laser to be composed of two subsystems associated with two orthogonal polarization eigenstates. Therefore, each one is described by its intensity I1,2 and population inversion D1,2. The two subsystems are coupled by crosssaturation phenomena: the intensity of one polarization is amplified by the population inversion associated to the other population and the stimulated emission in one polarization saturates the population inversion of the other polarization. Theoretically it has been shown that the total intensity I1+I2and the total population inversion D1+D2present relaxation oscillations with a frequency fRwhile the difference I1−I2and D1−D2exhibit slow relaxation oscillations whose frequency is fL=1−β 1+βfR. Preliminary results of the CA simulations are shown in Figure 1. The classical point of view to study the laser dynamics are theMaxwell-Blochequations howevertheCA models arecomplementarytoolsthatrepresentanadvantage in cases in which the system of differential equations have convergence problems. Keywords: cellular automata, lasers, antiphasedynamics. Bibliography [1]J.L. Guisado and F. Jiménez-Morales and J.M. Guerra. Cellular automaton model for the simulation of laser dynamics. Phys. Rev. E, 67:066708, 2003. [2]J.L. Guisado and F. Jiménez-Morales and J.M. Guerra. Simulation of the Dynamics of Pulsed Pumped Lasers Based on Cellular Automata. Lecture Notes in Computer Science, 3305, 278285,2004. [3]Eduardo Cabrera and Oscar G. Calderón and J.M. Guerra. Experimental evidence of antiphase population dynamics in lasers. Phys. Rev. A, 72:043824, 2005.