This paper presents a framework for analyzing and designing cylindrical $\mathrm{omega}$-bianisotropic metasurfaces, inspired by mode matching and digital signal-processing techniques. Using the discrete Fourier transform, we decompose the electromagnetic field distributions into orthogonal cylindrical modes and convert the azimuthally varying metasurface constituent parameters into their respective spectra. Then, by invoking appropriate boundary conditions, we set up systems of algebraic equations, which can be rearranged to either predict the scattered fields of prespecified metasurfaces, or to synthesize metasurfaces, which support arbitrarily stipulated field transformations. The proposed framework facilitates the efficient evaluation of field distributions that satisfy local power conservation, which is one of the key difficulties involved with the design of passive and lossless scalar metasurfaces. It represents a promising solution to circumvent the need for active components, controlled power dissipation, or tensorial surface polarizabilities in many state-of-the-art conformal metasurface-based devices. To demonstrate the robustness and the versatility of the proposed technique, we design several devices intended for different applications and numerically verify them using finite-element simulations.

中文翻译：

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基于离散傅里叶变换的圆柱欧米亚-各向异性各向异性元表面分析和合成框架

本文提出了一个分析和设计圆柱的框架 $\mathrm{欧米茄}$-各向异性的超表面，受到模式匹配和数字信号处理技术的启发。使用离散傅里叶变换，我们将电磁场分布分解为正交圆柱模式，并将方位角变化的超表面成分参数转换为它们各自的光谱。然后，通过调用适当的边界条件，我们建立了代数方程组，可以对其进行重新排列以预测预先指定的超颖表面的散射场，或者合成超颖表面，从而支持任意规定的场转换。所提出的框架促进了对满足局部功率守恒的场分布的有效评估，这是无源和无损标量超颖表面设计所涉及的关键难题之一。它代表了一种有前途的解决方案，可以避免在许多最新的基于形表面的表面形变设备中对有源组件，受控功耗或张量表面极化率的需求。为了证明所提出技术的鲁棒性和多功能性，我们设计了几种针对不同应用的设备，并使用有限元仿真对它们进行了数值验证。