ESM_File_Codes from A tunable electromagnetic metagrating

We explore electromagnetic (EM) wave incidence upon gratings of reconfigurable metamaterial cylinders, which collectively act as a metagrating, to identify their potential as reconfigurable subwavelength surfaces. The metacylinders are created by a closely spaced microstructured array of thin plates that, in the limit of small inter-plate spacing, are described by a semi-analytical continuum model. We build upon metacylinder analysis in water waves, translating this to EM for TE polarization (longitudinal magnetic field) for which the metacylinders exhibit anisotropic scattering; this is exploited for the multiple scattering of light by an infinite metagrating of uniform cylinder radius and angle, for which we retrieve the far-field reflection and transmission spectra for plane-wave incidence. These spectra reveal unusual effects including perfect reflection and a negative Goos–Hänchen shift in the transmitted field, as well as perfect symmetry in the far-field scattering coefficients. The metagrating also hosts Rayleigh–Bloch surface waves whose dispersion is contingent on the uniform cylinder angle, shifting under rotation towards the light-line as the cylinder angle approaches the horizontal. For both plane-wave scattering and the calculation of the array-guided modes, the cylinder angle is the principal variable in determining the wave interaction, and the metagrating is tunable simply through rotation of the constituent metacylinders.

我们研究了入射至可重构超材料圆柱光栅的电磁波（electromagnetic, EM），这类圆柱整体构成超光栅（metagrating），旨在探究其作为可重构亚波长表面（subwavelength surfaces）的应用潜力。该超圆柱（metacylinders）由间距紧密的薄板微结构阵列构成，当板间距极小时，可通过半解析连续介质模型（semi-analytical continuum model）对其进行描述。我们基于水波领域的超圆柱分析方法，将其拓展至电磁波领域，针对TE极化（longitudinal magnetic field）场景展开研究，此时超圆柱会呈现各向异性散射特性。我们利用该特性研究了圆柱半径与角度均一致的无限大超光栅对光的多重散射行为，并计算得到了平面波入射下该超光栅的远场反射与透射光谱。这些光谱展现出多种反常效应，包括透射场中的全反射与负古斯-汉欣（Goos–Hänchen）位移，以及远场散射系数的完美对称性。该超光栅还承载有瑞利-布洛赫表面波（Rayleigh–Bloch surface waves），其色散特性取决于圆柱的统一角度；当圆柱角度趋近水平时，该表面波的色散曲线会随圆柱转动向光行线（light-line）偏移。无论是平面波散射还是阵列导模的计算，圆柱角度都是决定波相互作用的核心变量，且仅通过转动构成超光栅的超圆柱，即可实现对该超光栅的可调谐调控。