Research Article Extreme Events in Lasers with Modulation of the Field Polarization Alexis Gomel , 1 Jean Marc Boyer, 2 Cyrille Metayer, 2 and Jorge R. Tredicce 2 1 Departamento de Fisica, Universidad de Buenos Aires, Intendente Guiraldes 2160, CABA, Argentina 2 Universite de la Nouvelle Caledonie, ISEA, BP R4, 98851 Noumea Cedex, France Correspondence should be addressed to Jorge R. Tredicce; jorge.tredicce@inln.cnrs.fr Received 25 September 2018; Revised 13 December 2018; Accepted 6 January 2019; Published 4 February 2019 Academic Editor: Jan A. Jung Copyright © 2019 Alexis Gomel et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We develop a theoretical model for a unidirectional ring laser consisting of an isotropic active medium inside a cavity containing a birefringent Kerr cell. We analyze the dynamical behavior of the system as we modulate the voltage applied to the Kerr cell. We discuss the bifurcation diagram and we study the regions of control parameter space where it becomes possible to observe and predict extreme events. 1. Introduction Lasers have been used as test benches for nonlinear dynamics in many diferent confgurations, some of them requiring a complicated set up or involving a very large number of degrees of freedom. Lasers with optical feedback, laser with saturable absorbers, and lasers with large Fresnel number are typical examples appearing in recent literature. In particular, lasers with a modulated parameter are able to display a large variety of dynamical regimes [1–4]. Periodic behavior, period doubling transition to chaos [2–4], intermittency, crisis of chaotic attractors [5–7], and optical rogue waves [8–10] are among possible observed phenomena. Modulation of cavity losses [3], cavity length [4], and pump rate [11] have been reported as mechanisms generating chaotic behavior in Class B lasers. Today there is an increasing interest on the study of the so called optical rogue waves. Optical rogue waves are high intensity pulses much larger than average and therefore rare events [8–10, 12–17]. Several optical systems have been reported [9, 13, 14, 18–20] as showing such type of pulses more frequently than what would be expected for a normal distribution probability of the light intensity. However the analysis of the physical mechanism at the origin of extreme events remains difcult in those experiments and models. Here we analyze a theoretical model of a laser in which the modulation is applied to the relative phase between the two components of the linear polarizations of the feld. Mod- ulation of such parameter is usually achieved by introducing inside the cavity a birefringent material whose extraordinary refractive index is changed through a sinusoidal voltage. If we assume that the active medium and the cavity are isotropic, the laser may operate in principle at any polarization of the feld. We identify the existence of generalized multistability, period doubling transition to chaos, and three types of crises of strange attractors. However the main objective of this work is to show the appearance of optical rogue waves and to identify the physical mechanism at their origin. Special interest is put also in establishing our ability to predict them [21–25]. We establish clearly the relevance of the existence of generalized multistability and the role played by an external crisis of the chaotic attractor in order to generate optical rogue waves. We construct also bifurcation diagrams taking the amplitude of the modulation as the main control parameter. All other parameter values like gain, losses, and dissipation are compatible with Class B lasers [26]. 2. Theoretical Model Te theoretical model is based on a single mode, Class B unidirectional ring laser with an electro optic modu- lator (EOM) placed inside the cavity. Afer applying the rotating wave and slowly varying amplitude approximations Hindawi Advances in Condensed Matter Physics Volume 2019, Article ID 7632852, 6 pages https://doi.org/10.1155/2019/7632852