周期柱中的波散射和导模
Wave Scattering and Guided Modes in Periodic Pillars
摘要：
本文研究了标量谐波源场被周期柱体散射的问题。周期柱体是一种一维周期性空间结构，另二维是有限的。散射解的唯一性可以用导模来抽象。扩展周期板的支柱的结果，我们给出的条件下，“逆”支柱不能承认导模。此外，我们提出了一种新的导模的频率$ω$和布洛赫波数$κ$与$ω$嵌入在连续谱中的每个$κ$。这些导模的周期大于结构的周期，并且具有实色散关系$ω=ω(κ)$，这是嵌入频率处的模式的非典型。
英文摘要：
We investigate the scattering of scalar harmonic source fields by a periodic pillar, that is, a spatial structure that is periodic in one dimension and of finite extent in the other two. Uniqueness of scattering solutions can be abstracted by guided modes. Extending results for periodic slabs to pillars, we give conditions under which "inverse" pillars cannot admit guided modes. In addition, we present a new construction of guided modes at frequency $ω$ and Bloch wavenumber $κ$ with $ω$ embedded in the continuous spectrum for each $κ$. These guided modes have period larger than the period of the structure, and possess a real dispersion relation $ω=ω(κ)$, which is atypical of modes at embedded frequencies.
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