光学阵列中的可饱和杂质：格林函数方法
Saturable impurity in an optical array: Green function approach
摘要：
我们研究了一维线性波导阵列包含一个单一的饱和波导。利用格点格林函数的形式，我们计算了封闭形式的局域模和通过杂质的透射率。对于体材料中的单个可饱和杂质，我们发现杂质态总是可能的，与杂质强度无关。对于表面可饱和杂质的情况下，一个最小的非线性强度是必要的，以创建一个束缚态。穿过杂质的透射系数显示出不存在任何共振的次线性行为。体杂质位的动态自陷没有表现出自陷跃迁，类似于弱线性杂质的行为。而对于表面杂质，在临界非线性值处存在自陷跃迁。在这两种情况下，光功率的渐近传播都表现出弹道特征，其速度随着非线性强度的增加而减小。
英文摘要：
We examine a one-dimensional linear waveguide array containing a single saturable waveguide. By using the formalism of lattice Green functions, we compute in closed form the localized mode and the transmission across the impurity in closed form. For the single saturable impurity in the bulk, we find that an impurity state is always possible, independent of the impurity strength. For the surface saturable impurity case, a minimum nonlinearity strength is necessary to create a bound state. The transmission coefficient across the impurity shows a sub-linear behavior with an absence of any resonance. The dynamical selftrapping at the bulk impurity site shows no selftrapping transition, and it resembles the behavior of a weak linear impurity. For the surface impurity however, there is a selftrapping transition at a critical nonlinearity value. The asymptotic propagation of the optical power shows a ballistic character in both cases, with a speed that decreases with an increase in nonlinearity strength.
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