Nonlinear Discrete Optics in the Time Domain

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The dynamics of wave propagation together with the nonlinearly driven self organization of light are intensively investigated in modern optics. Recently main interest has focused on discrete optical systems as their field dynamics follows a much simpler scheme, which often allows even for analytical solutions. Because of striking similarities optical discrete systems can be analyzed with tools developed in solid state physics and quantum mechanics thus enabling a deeper understanding of complicated effects of light-matter interaction. Therefore the effects of discrete dynamics, which are the focus of the project, are not only relevant for optical systems, but concern general questions of nonlinear dynamics as they are important for Bose Einstein condensates, in plasma physics or for the energy transfer in complex molecular structures. Potential results of the project will therefore be relevant far beyond the concrete context of optics for which they were deduced. The project is concentrates on the experimental investigation of the nonlinear evolution of optical pulses in two coupled fiber loops of slightly different length in the presence of amplitude and phase modulation. This set up has recently also attracted some interest in the frame work of random quantum walks. Pulse evolution in this system happens in discrete round trips and is also discretized with respect to the position of the pulses in each round trip. Up to now the nonlinear properties of such a temporal double discrete system have not been studied in detail, but shall be experimentally investigated within the framework of this project. In addition our experimental set up allows studying the influence of various and even complex valued potentials and in particular to realize a so-called PT-symmetric system, the nonlinear properties of which we want to investigate within the project. We intend to experimentally study for the first time solitons in a double discrete and in particular in a PT symmetric system. We further want to exploit the versatility of our set-up, which allows us to modify the group velocity dispersion, respectively the effective mass, of propagating pulses and to monitor the resulting evolution. We are particularly interested in the nonlinear interaction between fields with effective masses of different sign. We expect to see self acceleration, anomalous damping and self-heating. The results we intend to obtain within the project are not only interesting from the point of view of fundamental physics, but may also become relevant for more practical issues as the optimization of supercontinuums generation in photonic crystal fibers or of the pulse evolution in fiber lasers.