Discrete spatio-temporal dynamics in waveguide arrays with cubic nonlinearity

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Within this project discrete optical properties in permanent one- and two-dimensional waveguide arrays under different spatio-temporal conditions will be investigated. Such systems show unique fundamental properties in temporal and spatial field propagation differing from conventional propagation in homogeneous spaces (e.g. specific soliton formation, light bullets, periodic motion of beams, "non-diffractive" beams). As a basis for these investigations two complementary concepts for realizing high precision multidimensional waveguide arrays are used. With intensive ultrashort laser pulses focused into bulk material a permanent refractive index change can be induced which allows the inscription of complex and flexibly shaped embedded array structures. With optical fibre technologies large arrays with long propagation lengths and even active (gain) properties become feasible. Such evanescently coupled waveguide arrays will be used as a model system to study spatio-temporal propagation under linear and nonlinear conditions. Our work will be organized in six work packages.Work package (a) will address the study of linear propagation in one- and two-dimensional waveguide arrays. A wide field of interest is the investigation of the propagation in finite arrays, where interactions with the array boundaries have to be taken into account yielding a variety of new and interesting effects such as field self-recovery caused by harmonic oscillation or the discrete Talbot effect. Another consequence is the existence of a so-called quasi-incoherent propagation, where mutually fully coherent sources excite a light distribution which is equivalent to a distribution caused by mutually incoherent sources. Another focus of this package is the investigation of the propagation in different topologies. Using waveguide arrays written by fs laser pulses opens the possibility to analyze a variety of systems which can only be hardly fabricated by other technologies. Two-dimensional arrays consisting of curved waveguides allow the introduction of linear potentials causing two-dimensional field recovery. Furthermore the evanescent coupling concerning the shape and the distance of the waveguides will be analyzed since the investigation of the coupling to the next but one waveguide is intended. An additional point in this work package is the influence of interfaces between waveguide arrays. The interaction with the boundaries gives a significant insight in the propagation behaviour of the evolving light in the arrays since the band structure changes abruptly at the interface yielding staggered and unstaggered localized modes, dependent of the transmissivity of the interface.In work package (b) the nonlinear spatial propagation in one- and two-dimensional waveguide arrays will be investigated. The interaction of the propagating light with artificial defects will be precisely analyzed. Local defects can be linear (e.g. omitted waveguides) but also purely nonlinear. This causes so-called soliton emission which will be a main point of this work package. Another focus is the investigation of the influence of the dimensionality and the topology of the arrays. Since the band structure is a function of the array geometry the excitation of solitons in different topologies requires different input peak powers. So the transition from pure planar to two-dimensional solitons will be analyzed. The focus in work package (c) will be on the investigation of networking and all-optical switching. Propagating light may be blocked by localization in a single waveguide. Therefore, a propagating pulse may be routed at a waveguide junction into a specific direction. This effect has not been experimentally observed before. However, fs laser written waveguides provide an ideal basis for the investigation of this phenomenon since the paths of the waveguides can be chosen in an arbitrary way.The next consequential step will be the investigation of spatio-temporal nonlinear propagation in work package (d). In this work package we will primarily use waveguide arrays in fibres since they provide extraordinary long coupling lengths which allow the investigation of temporal dynamics in discrete systems. The interplay of the anomalous dispersion, Kerr-nonlinearity and array diffraction yields spatio-temporal localized objects, so-called light bullets. For spatially discrete systems theoretical studies predict the stability of discrete-continuous light bullets, which are otherwise dynamically instable in continuous media. Such phenomena have not been experimentally observed before. Hence, they will be a main focus in our work.In work package (e) waveguide arrays with dissipative effects (gain) will be fabricated and analyzed. A main goal is in particular the experimental observation of dissipative localizations in the form of dissipative light bullets and discrete spatio-temporal similaritons. Besides the gain resulting from cladding pumping, locally concentrated gain by core pumping is a further field of research. A detailed understanding of field formation and propagation in such active waveguide arrays with gain would be also of great interest for new types of fibre laser structures.Our work will be completed by work package (f) that is devoted to waveguide arrays in LiNbO3. This material exhibits an extraordinary strong quadratic nonlinearity which is the base for the investigation of a variety of effects possible only in discrete quadratic media. Furthermore, waveguide arrays in LiNbO3 allow the investigation of the interaction of linear, second- and third-order nonlinear discrete propagation.