Spatio-temporal localization in dissipative and discrete systems

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As in the previous period this theoretical project aims at both providing genuine contributions to the theory of nonlinear localization in dissipative and/or discrete optical systems and bridging the gap to the experiments performed in the research unit. The work will be organized in four work packages a) temporal dissipative solitons, b) cavity solitons in metamaterials, c) spatio-temporal localization in waveguide arrays and d) theoretical support for experimental groups. In work package (a) temporal solitons in dissipative optical systems will be investigated. We shall focus on two systems, namely first a periodic semiconductor device that consists of a semiconductor optical amplifier (SOA), a saturable absorber (SA) and a filter and secondly a short-pulse fibre laser system with an appropriate passive mode-locking mechanism. Our previous studies imply that the former system may exhibit dissipative soliton solutions, not really categorized and understood to date, but may potentially serve as ultrafast pulse regenerator. The latter system is of paramount interest for the generation of short pulses with definite properties, but is also considered as one of the most promising test beds for dissipative soliton dynamics. Both subjects are related to a fundamental issue still to be addressed, namely to really identify all properties and to take advantage of the attractive peculiarities of dissipative solitons in systems with a future large application potential.Work package (b) will address the study of cavity solitons metamaterials as a natural continuation of our work on discrete cavity solitons. The aim is to investigate the interplay between tailorable linear properties of micro- and nanostructured metamaterials and various nonlinearities in planar cavities. It is expected that by engineering dispersion and diffraction new classes of cavity solitons will exist. Metamaterials looked at will range from 2D waveguide arrays, via photonic crystals to negative refractive index materials. Using the gain inherent to dissipative systems, which are characterized by a steady energy exchange with the environment, the losses, which are considered a critical issue for so-called negative index metamaterials, can potentially be overcome here.Spatio-temporal effects and light localization in discrete systems will be the focus in work package (c). Novel effects are expected from exploiting the versatile dispersion relation of two-dimensional (2D) waveguide arrays and by using waveguide arrays with gain and loss (dissipative system). Optical bullets in conservative as well as dissipative configurations will be studied in general. These bullets will be discrete-continuous objects. One major goal will be to study pulse generation in coherently coupled active fibres. Theoretical models will include tight-binding equations and the more general lattice approach.Our work will be completed by work package (d) that is devoted to providing our theoretical expertise in dissipative and discrete systems and the access to advanced modelling tools to the experimental partners in designing experiments and in evaluating their results. Within this collaboration also the necessary advanced modelling capacity will be provided.