Discreteness, nonlinearity and dissipation in the temporal domain

该项目的目的是实验和理论研究的影响的离散在时间和频谱域。我们将集中讨论在光纤中传播的时间周期场及其与弱测试脉冲的相互作用。该项目将分为三个工作包：a)频谱域的离散动力学，b)时域的离散动力学和c)频谱域的布洛赫振荡。在工作包a)中，将通过监测时间周期光场的演化来研究光谱域的离散动力学。各自的场最初将由两个载波频率略有失谐的干扰w-波或由超短脉冲的周期性序列形成。光纤非线性产生一组离散的频率分量。因此，四波混频本身在谱域中造成了离散性。各谱线之间的耦合完全由非线性介导。色散关系所施加的相位匹配条件决定了这种相互作用是局部的还是远距离的。这种频谱离散系统的性质不同于传统的离散系统，不同分量之间的耦合是线性的。根据群速度色散（GVD）的实际值，存在由时间孤子链组成的定态。然而，只有通过耗散去除多余的辐射，才能接近定态。因此，损耗，放大和频谱滤波将严重影响演变。在工作包b中，将通过将具有不同波长的弱测试脉冲注入平稳时间周期场来研究时域中的离散动力学。这些脉冲将经历一个有效的周期电位由交叉相位调制。如果偏离很小，测试信号可以被诱导折射率分布所捕获，这与光折变晶体的实验非常相似，其中光在光学诱导晶格中传播。不同折射率最大值之间的耦合将允许在时域中再现众所周知的空间离散效应。此外，载波的频谱成分也会与测试场混合，从而产生对新频率的耦合。因此，离散性再次出现在谱域中。在测试和周期性载波之间的时间偏离的情况下，谱域中会出现布洛赫振荡，形成工作包c)的基础。时间离散性和光谱离散性之间的相互作用将成为我们研究的基本目标。我们将利用时间域中可用的高度灵活性。新型纤维可以调整群速度色散。光谱滤波器可以用来塑造耗散的光谱响应，非线性可以是局部的（瞬时的），也可以是非局部的（延迟的）。

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.