多层分类的几何设置
A geometrical setting for the classification of multilayers
摘要：
我们阐述的后果的因式分解的任何无损多层的传输矩阵的三个基本矩阵的简单解释。考虑到这种传递矩阵在复平面上引起的双线性变换，我们引入了多层传递函数的概念，并研究了它在单位圆盘上的性质。在这种几何设置中，我们的因式分解转化为三个动作，可以被视为理解多层行为的基本部分。此外，我们引入了一个简单的跟踪标准，使我们能够分类多层在三种类型的属性密切相关的这三个基本矩阵之一（只有一个）。我们应用这种方法来分析一些实际的例子，这些类型的矩阵的代表。
英文摘要：
We elaborate on the consequences of the factorization of the transfer matrix of any lossless multilayer in terms of three basic matrices of simple interpretation. By considering the bilinear transformation that this transfer matrix induces in the complex plane, we introduce the concept of multilayer transfer function and study its properties in the unit disk. In this geometrical setting, our factorization translates into three actions that can be viewed as the basic pieces for understanding the multilayer behavior. Additionally, we introduce a simple trace criterion that allows us to classify multilayers in three types with properties closely related to one (and only one) of these three basic matrices. We apply this approach to analyze some practical examples that are representative of these types of matrices.
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