Discreteness, nonlinearity and dissipation in the temporal domain

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The aim of the project is the experimental and theoretical investigation of effects of discreteness in the temporal and in the spectral domain. We will concentrate on time-periodic fields propagating in optical fibres and on their interaction with weak test pulses. The project will be organized in three work packages a) discrete dynamics in the spectral domain, b) discrete dynamics in the temporal domain and c) Bloch oscillations in the spectral domain. In work package a) discrete dynamics in the spectral domain will be studied by monitoring the evolution of time periodic light fields. Respective fields will initially be formed by either two interfering cw-waves having slightly detuned carrier frequencies or by a periodic train of ultra short pulses. The fibre nonlinearity generates a set of discrete frequency components. Hence, four-wave mixing by itself imposes discreteness in the spectral domain. The coupling between the various spectral lines is exclusively mediated by the nonlinearity. The phase-matching condition imposed by the dispersion relation determines whether this interaction is local or long range. The properties of this spectrally discrete system are different from those of conventional discrete ones, where coupling between different components is linear. Depending on the actual value of the group velocity dispersion (GVD) stationary states consisting of chains of temporal solitons exist. However, a stationary state can only be approached, if excess radiation is removed by dissipation. Hence, losses, amplification and spectral filtering will critically influence the evolution.In work package b) discrete dynamics in the temporal domain will be studied by injecting weak test pulses with a distinct wavelength into a stationary time periodic field. Those pulses will experience an effective periodic potential induced by cross-phase modulation. If the walk-off is small the test signal can be trapped by the induced index distribution, very similar to respective experiments in photorefractive crystals, where light propagates in an optically induced lattice. Coupling between different refractive index maxima will allow reproducing well-known effects of spatial discreteness in the temporal domain.In addition, the spectral components of the carrier wave also mix with the test field inducing a coupling to new frequencies. Hence, again discreteness occurs in the spectral domain. In case of temporal walk-off between the test and the periodic carrier wave Bloch oscillations In the spectral domain will occur forming the basis of work-package c).The mutual interplay between temporal and spectral discreteness will form the basic target of our research. We will take advantage of the high degree of flexibility available in the temporal domain. New types of fibres allow tailoring the group velocity dispersion. Spectral filters can be used to shape the spectral response of dissipation and nonlinearities can be local (instantaneous) as well as non-local (delayed) in the temporal domain.