We study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals, coupled by a junction. Using analyticity techniques and commutator methods in a two-Hilbert spaces setting, we determine the nature of the spectrum and prove the existence and completeness of the wave operators of the system.

中文翻译：

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一维耦合光子晶体的光谱和散射理论

我们研究了由两个渐近周期波导（也称为一维光子晶体）组成的系统中光传输的光谱和散射理论，通过一个结耦合。在双希尔伯特空间设置中使用解析技术和交换子方法，我们确定了谱的性质并证明了系统的波算子的存在性和完整性。