We present a complete design scheme, from theoretical formulation to experimental validation, exploiting the versatility of metagratings (MGs) for designing a rectangular waveguide (RWG) ${\mathrm{TE}}_{10}$-${\mathrm{TE}}_{20}$ mode converter (MC). MG devices, formed by sparse periodically positioned polarizable particles (meta-atoms), were mostly used to date for beam manipulation applications. In this paper, we show that the appealing diffraction engineering features of the MGs in such typical free-space periodic scenarios can be utilized to efficiently mould fields inside WGs. In particular, we derive an analytical model allowing harnessing of the MG concept for realization of perfect mode conversion in RWGs. Conveniently, the formalism considers a printed-circuit-board MG terminating the RWG, operating as a reflect-mode MC. Following the typical MG synthesis approach, the model directly ties the meta-atom position and geometry with the modal reflection coefficients, enabling resolution of the detailed fabrication-ready design by enforcement of the functionality constraints: elimination of the fundamental ${\mathrm{TE}}_{10}$ reflection and power conservation (passive lossless MG). This reliable semianalytical scheme, verified via full-wave simulations and laboratory measurements, establishes a simple and efficient alternative to common RWG MCs, typically requiring challenging deformation of the WG designed through time-consuming full-wave optimization. In addition, it highlights the immense potential MGs encompass for a wide variety of applications beyond beam manipulation.

中文翻译：

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矩形波导中完美模式转换的元分级：理论与实验

我们提出了一个完整的设计方案，从理论公式到实验验证，利用元光栅 (MG) 的多功能性来设计矩形波导 (RWG) ${\mathrm{TE}}_{10}$——${\mathrm{TE}}_{20}$模式转换器 (MC)。MG 装置由稀疏的周期性定位的可极化粒子（元原子）形成，迄今为止主要用于光束操纵应用。在本文中，我们展示了在这种典型的自由空间周期性场景中，MGs 吸引人的衍射工程特征可用于有效地塑造 WGs 内的场。特别是，我们导出了一个分析模型，允许利用 MG 概念在 RWG 中实现完美的模式转换。方便的是，形式主义考虑了终止 RWG 的印刷电路板 MG，作为反射模式 MC 运行。遵循典型的 MG 合成方法，该模型直接将元原子位置和几何形状与模态反射系数联系起来，${\mathrm{TE}}_{10}$反射和节能（被动无损MG）。这种可靠的半分析方案通过全波模拟和实验室测量进行了验证，建立了一种简单有效的普通 RWG MC 替代方案，通常需要通过耗时的全波优化设计的 WG 具有挑战性的变形。此外，它还强调了 MG 在光束操纵之外的各种应用中的巨大潜力。