小窗口周期系统耦合波导中的带隙开口和分裂带边
Gap opening and split band edges in waveguides coupled by a periodic system of small windows
摘要：
在两个耦合波导的例子中，我们构造了一个周期性的二阶微分算子，它作用在欧几里得整环中，并且具有严格在布里渊区内达到边缘的谱隙。在两个不同宽度的无限长的带，有一个共同的内部边界的拉普拉斯算子的波导建模。在这个共同的边界上，我们施加诺依曼边界条件，但削减了一个周期性的系统的小孔，而其余的外部边界上，我们施加狄利克雷边界条件。它示出，通过改变带的宽度和孔之间的距离，可以控制的带函数的极值的位置以及开放的间隙的数量。我们计算了间隙长度和极值位置的渐近性中的首项。
英文摘要：
At the example of two coupled waveguides we construct a periodic second order differential operator acting in a Euclidean domain and having spectral gaps whose edges are attained strictly inside the Brillouin zone. The waveguides are modeled by the Laplacian in two infinite strips of different width that have a common interior boundary. On this common boundary we impose the Neumann boundary condition but cut out a periodic system of small holes, while on the remaining exterior boundary we impose the Dirichlet boundary condition. It is shown that, by varying the widths of the strips and the distance between the holes, one can control the location of the extrema of the band functions as well as the number of the open gaps. We calculate the leading terms in the asymptotics for the gap lengths and the location of the extrema.
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