Spatio-temporal dynamics of lasers and photorefractive oscillators under rockingphase-bistable patterns and localized structures

Resumen

The objective of this thesis is the theoretical, analytical and numerical, study of the spatio-temporal dynamics of optical oscillators under bichromatic forcing (rocking). This kind of injection possesses the feature of breaking the phase invariance (any phase of the complex field is possible) of the free-running system and generates a phase-bistable system in which two only phases are allowed for the homogeneous stationary solutions. This change in the nature of the system enables a new dynamics characterized by the presence of a new kind of spatial structures in the bidimensional transverse plane: bistable phase patterns in which both phases coexist separated by domain walls (Ising if they have null intensity or Bloch if it is different from zero). These domains can evolve either to homogeneous patterns (in which only one phase is present) or to more complex ones, in which curvature effects lead to the emergence of labyrinthic patterns depending on the value of the parameters of the system. Moreover, localized structures (stable minimum-size domains) as dark-ring cavity solitons can exist. In the scope of this thesis, we have focused on the influence of rocking in two systems which have been studied profusely in the literature, as they are very interesting both from a fundamental and a practical point of views: lasers and photorefractive oscillators. Along this thesis, we will study the influence of rocking in those systems in detail. As it is usual in nonlinear science, is convenient to derive equations describing the behaviour of those systems close to (critical) points where the stationary solutions emerge. These equations (called order parameter equations) are relatively simple and are able to describe a large number of nonlinear systems: physical, chemical, biological.. (the meaning ot the parameters being the only difference , but the mathematical structure is the same). Moreover, we will analyze the stability of the solutions and we will perform numerical simulations of the theoretical models. The following results will be presented: Starting from the MB equations under rocking injection, an order parameter equation will be derived for class C lasers with positive cavity detuning and the patterns of the system will be studied numerically. A reduced model of two equations will be obtained for class B lasers and its temporal dynamics and the influence of the detuning of rocking injection will be studied. We will also show spatial patterns obtained from simulations of the MB equations. A unified model (valid for positive and negative cavity detunings) for two level lasers (class C and A) and photorefractive oscillators will be developed, providing the stability domains of the phase bistable states and studying numerically the spatial patterns that arise from the system. The temporal dynamics of a bidirectional laser under rocking injection will be analyzed and some preliminary results regarding spatial patterns will be given.