Discrete spatio-temporal dynamics in waveguide arrays with quadratic nonlinearity

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The aim of this project is the investigation of spatial-temporal dynamics of excitations in waveguide arrays of periodically poled lithium niobate (PPLN). The studied systems possess a high degree of freedom in terms of their linear diffraction and dispersion properties, their type of nonlinearity, and their degree of dissipation. This extreme variability of the properties of the underlying experimental system will be achieved by combining a versatile nonlinear material (LiNbO3) with advanced micro-structure-technologies.The Ti-indiffused and fs-written PPLN waveguides offer a variable nonlinearity due to the simultaneous existence of a quadratic and a photorefractive nonlinearity. Both nonlinearities can be combined to synthesize a desired type of the effective nonlinear response. Moreover, l D and 2D waveguide arrays together with induced photorefractive inhomogeneities and Bragg gratings result in almost arbitrary diffraction properties for a certain interval of the angular spectrum and a shaping of the frequency band-structure providing control on group velocity and group velocity dispersion. Unlike the traditional strict distinction between conservative and dissipative systems, waveguide resonators with adjustable feedback based on photorefractive Bragg gratings provide a variability of the conservative/dissipative properties. Based on this extreme versatility of the experimental configuration we want to observe nonlinear dynamical phenomena which are connected to certain system properties. Particular emphasis will be paid to the transitions between the well-categorized system classes. The work will be organized in three work packages:I. Control of linear and nonlinear properties of PPLN waveguide arrays: Here the fundamental linear and nonlinear effects in PPLN waveguide arrays will be investigated. Furthermore the basic experimental techniques will be developed to provide the prerequisites for the other work packages by identifying adequate means of controlling the linear and nonlinear system parameters.II. Spatial-temporal dynamics in nonlinear waveguide arrays: The first aim of this work package is the investigation of linear beam diffraction in waveguide arrays with different types of inhomogeneities which are induced by additional beams via photorefractive effects. The second aim is to study the spatial-temporal nonlinear dynamics in homogeneous and inhomogeneous waveguide arrays, whose linear and nonlinear properties are again modified by additional photorefraction.III. Spatial-temporal nonlinear dynamics in waveguide resonator arrays: This work package will be committed to the study of the nonlinear dynamics in discrete dissipative systems which are formed by coupled waveguide resonators. We will investigate the specific solutions arising from the introduction of dissipation for different types of effective nonlinearities. Hence, criteria will be derived for the shaping of attractors and stability properties of particular discrete pattern and cavity solitons.