通过具有饱和位间非线性的二聚体缺陷的多通道非对称传输
Multichannel asymmetric transmission through a dimer defect with saturable inter-site nonlinearity
摘要：
我们考虑了离散非线性薛定谔型二聚体的非对称传输特性，二聚体之间存在可饱和的非线性位间耦合，同时存在立方位非线性和非对称线性位势。与以前研究的情况下，纯现场非线性，固定传输的传输系数示出为一个多值函数的传输强度，在制度的低饱和度和小或中等的传输强度。相应的后向传输映射进行了分析和数值计算，并显示有一个或三个不同的解决方案饱和耦合，零或两个解决方案的纯立方非线性耦合。随着饱和强度的增加，多解区域通过分叉消失，现场模型的单值区域恢复。多个解决方案分支的存在产生新的机制，不对称的左/右静止传输：除了传输峰的位置的移位，在一个方向上的传输峰可能对应于不存在的静止的解决方案，在相反的方向上传播，在相应的分支和传输强度。此外，这些传输通道中的一个表现为输入信号的近乎完美的反射镜。的线性稳定性的固定的解决方案进行了分析，通常观察到的不稳定性，并说明了直接数值模拟，在政权与大的传输系数。研究发现，在不稳定性诱导的动力学中，位间非线性可以防止局部二聚体模式的形成。最后，部分反射和传输的高斯激发进行了研究，和非对称传输特性进行了比较，以前研究的现场模型。
英文摘要：
We consider the asymmetric transmission properties of a Discrete Nonlinear Schr{ö}dinger type dimer with a saturable nonlinear intersite coupling between the dimer sites, in addition to a cubic onsite nonlinearity and asymmetric linear onsite potentials. In contrast to previously studied cases with pure onsite nonlinearities, the transmission coefficient for stationary transmission is shown to be a multivalued function of the transmitted intensity, in regimes of low saturability and small or moderate transmitted intensity. The corresponding backward transfer map is analyzed analytically and numerically, and shown to have either one or three distinct solutions for saturable coupling, and zero or two solutions for the purely cubic nonlinear coupling. As saturation strength is increased, the multi-solution regimes disappear through bifurcations and the single-valued regime of the onsite model is recovered. The existence of multiple solution branches yields novel mechanisms for asymmetric left/right stationary transmission: in addition to shifts of the positions of transmission peaks, peaks for transmission in one direction may correspond to nonexistence of stationary solutions propagating in the opposite direction, at the corresponding branch and transmitted intensity. Moreover, one of these transmission channels behaves as a nearly perfect mirror for incoming signals. The linear stability of the stationary solutions is analyzed, and instabilities are typically observed, and illustrated by direct numerical simulations, in regimes with large transmission coefficient. Intersite nonlinearities are found to prevent the formation of a localized dimer mode in the instability-induced dynamics. Finally, the partial reflection and transmission of a Gaussian excitation is studied, and the asymmetric transmission properties are compared to previously studied onsite models.
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