论文标题
多通道不对称传播通过二聚体缺陷，可饱和地点非线性
Multichannel asymmetric transmission through a dimer defect with saturable inter-site nonlinearity
论文作者
论文摘要
我们考虑了离散非线性Schr {Ö} dinger型二聚体的不对称传输特性，除了立方内的非线性和不对称的线性现场电位外，二聚体位点之间的饱和非线性互换偶联。与先前研究的纯粹现场非线性病例相反，在低饱和性和小或中等传输强度的状态下，固定传输的传输系数被证明是传输强度的多相关函数。分析和数值分析相应的向后传输图，并显示出具有一个或三个不同的溶液以饱和耦合，而纯立方体非线性耦合的零或两个解。随着饱和强度的提高，多条解决方案通过分叉消失，现场模型的单值制度被恢复。多个溶液分支的存在还产生了不对称左/右静止传播的新机制：除了传输峰位置的移位外，沿一个方向传输的峰值可能对应于在相反方向上传播的固定溶液的不存在，在相应的分支和透射强度。此外，这些传输通道之一是传入信号的几乎完美的镜子。分析了固定溶液的线性稳定性，通常观察到不稳定性，并通过直接数值模拟在具有较大传输系数的机制中进行说明。发现位点非线性可防止在不稳定性诱导的动力学中形成局部二聚体模式。最后，研究了高斯激发的部分反射和传播，并将不对称传输特性与先前研究的现场模型进行了比较。
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.
