标题： 平面波在“层叠”周期系统中的散射的即插即用分析范式 显示英文标题

标题： Plug-and-play analytical paradigm for the scattering of plane waves by "layer-cake" periodic systems

摘要： 我们研究二维情况下由与边界方向平行的异质层对平面标量波的散射。 在将该层描述为周期性薄层的并集时，我们通过融合传播矩阵的概念和由每个薄层的单元体特征的布洛赫本征态来解决散射问题。 通过求解二次特征值问题（QEVP）获得的特征布洛克本征态，该问题在给定（i）激励频率和（ii）沿边界方向的实数值波数的情况下，寻找垂直于层边界的复数值波数——该波数在整个系统中保持不变。 QEVP的谱分析揭示了特征值谱离散性的充分条件以及所有特征值成复共轭对出现的事实。 通过部署传播矩阵方法提供的分解，我们证明了单个特征值（因此是本征模态）对解的贡献随着其虚部绝对值的增加呈指数衰减，这为分解后的布洛赫波解的截断提供了合理的依据。 所提出的方法适用于彩虹陷阱、能量收集器和超表面的最佳设计，这些结构操纵波的能力不仅由组成薄层的个体色散特性决定，还由后者在复合层中的排列和一般适配决定。 使用分解后的布洛赫方法，可以通过组件薄层的排列和窗口平移/拉伸生成的试验配置的评估可以加快数十倍。 显示英文摘要

摘要： We investigate the scattering of scalar plane waves in two dimensions by a heterogeneous layer that is periodic in the direction parallel to its boundary. On describing the layer as a union of periodic laminae, we develop a solution of the scattering problem by merging the concept of propagator matrices and that of Bloch eigenstates featured by the unit cell of each lamina. The featured Bloch eigenstates are obtained by solving the quadratic eigenvalue problem (QEVP) that seeks a complex-valued wavenumber normal to the layer boundary given (i) the excitation frequency, and (ii) real-valued wavenumber parallel to the boundary -- that is preserved throughout the system. Spectral analysis of the QEVP reveals sufficient conditions for discreteness of the eigenvalue spectrum and the fact that all eigenvalues come in complex-conjugate pairs. By deploying the factorization afforded by the propagator matrix approach, we demonstrate that the contribution of individual eigenvalues (and so eigenmodes) to the solution diminishes exponentially with absolute value of their imaginary part, which then forms a rational basis for truncation of the factorized Bloch-wave solution. The proposed methodology caters for the optimal design of rainbow traps, energy harvesters, and metasurfaces, whose potency to manipulate waves is decided not only by the individual dispersion characteristics of the component laminae, but also by ordering and generally fitting of the latter into a composite layer. Using the factorized Bloch approach, evaluation of trial configurations -- as generated by the permutation and window translation/stretching of the component laminae -- can be accelerated by decades.