We present a rigorous theoretical framework for designing full-space spatial power dividers using metagratings. In our study, the current restrictions of spatial power dividing platforms such as reflection-only performance, operating at normal incidence, and small reflection/refraction angles have been totally relaxed. A modal expansion analysis based on the Floquet–Bloch theorem is established so that a discrete set of spatial harmonics is considered in both reflection and transmission sides of a compound metallic grating in which the unknown coefficients are calculated by applying proper boundary conditions. By eliminating the unwanted scattering harmonics, the proposed metagrating has the ability to realize different functionalities from perfect anomalous refraction to reflection/transmission spatial power dividing, without resorting to full-wave numerical optimizations. Our findings not only offer possibilities to realize arbitrary spatial power dividers but also reveal a simple platform for beam-forming applications.

中文翻译：

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使用元光栅的全空间空间功率分配器的分析设计

我们提出了使用元光栅设计全空间空间功率分配器的严格理论框架。在我们的研究中，空间功率分配平台的当前限制，例如仅反射性能、以法向入射和小反射/折射角工作，已经完全放宽。建立了基于 Floquet-Bloch 定理的模态扩展分析，以便在复合金属光栅的反射侧和透射侧考虑一组离散的空间谐波，其中通过应用适当的边界条件计算未知系数。通过消除不需要的散射谐波，所提出的元光栅能够实现从完美异常折射到反射/透射空间功率分配的不同功能，不诉诸全波数值优化。我们的发现不仅提供了实现任意空间功率分配器的可能性，而且还揭示了一个用于波束成形应用的简单平台。