携带轨道角动量（OAM）的涡旋电磁波被视为解决频谱资源紧张，提高信道容量的 新方法，因而成为了重要的研究内容。电磁超表面由于具有易加工、可灵活地调控电磁 波等优点，能够高效地生成 OAM 涡旋波。本文以电磁超表面为研究工具，针对不同的 应用需求对涡旋波反射阵天线的设计方法进行了研究，主要研究内容如下： 本文针对不同的应用需求设计了几款基于超表面的涡旋波反射阵天线。（1）设计了 一款反射相移达到 360° 且对入射角度不敏感的谐振型超表面单元，并以该单元为基础设 计超表面结构。在涡旋波补偿相位的计算中引入汇聚相位补偿项，设计了工作于 26 GHz 的汇聚涡旋波反射阵天线。仿真结果表明该反射阵天线生成了具有场增强效果的汇聚涡 旋波。（2）通过对贝塞尔涡旋波的分析得到了贝塞尔相位补偿项，并将其引入反射面补 偿相位的计算中，设计了馈源偏馈 15°，工作于 26 GHz 的无衍射涡旋波反射阵天线。仿 真结果表明该反射阵天线生成了模态纯正的二阶无衍射涡旋波。（3）本文分析了沿任意 方向辐射的零阶贝塞尔波束所需的相位补偿，通过坐标变换得到传播方向上的螺旋补偿 相位，进而得到了沿任意方向辐射的高阶无衍射涡旋波补偿相位的计算方法。仿真结果 表明设计的反射阵天线生成了沿 θ=30° , φ= 0° 方向传播的二阶无衍射涡旋波。在补偿 相位的计算过程中结合电磁场的叠加原理，设计了生成多个高阶无衍射波束的超表面结 构，仿真结果表明在反射阵上方生成了分别沿 θ=30° , φ= 0° 和 θ=30° , φ= 180° 方向传播，OAM 模式分别为一阶和二阶的高阶无衍射涡旋波，验证了该方法的可行性。 通过琼斯矩阵分析超表面单元反射系数间的关系，得到基于几何相位原理的超表面 单元的结构特性，设计了适用于宽带应用场景的超表面单元。以该单元为基础设计了能 够生成高阶无衍射涡旋波的超表面结构，仿真结果表明在 26 GHz 至 31 GHz 的宽带范围 内生成了 OAM 模式为−2 阶的高阶无衍射涡旋波，验证了该方法的可行性。本文为不同 应用场景下基于超表面的涡旋波生成提供了设计方法，具有一定的参考价值。

Vortex electromagnetic waves carrying orbital angular momentum (OAM) are considered as a new method to solve the spectrum resource constraint and increase the channel capacity, and thus become an important research element. Electromagnetic supersurfaces can generate OAM vortex waves efficiently due to their advantages lor='red'>of easy processing and flexible modulation lor='red'>of electromagnetic waves. In this thesis, the design method lor='red'>of vortex wave reflectarray antenna is investigated for different application requirements using electromagnetic super-surface as a research tool, and the main research contents are as follows: 

In this thesis, several metasurface based vortex wave reflectarray antennas are designed for different application requirements. (1) A resonant metasurface unit with a reflection phase shift lor='red'>of 360° and insensitivity to the incident angle is designed, and the metasurface structure is based on this unit. The convergent phase compensation term is introduced in the calculation lor='red'>of the vortex wave compensation phase, and a convergent vortex wave reflectarray antenna operating at 26 GHz is designed. The simulation results show that the reflectarray antenna generates convergent vortex waves with field enhancement effect. (2) The Bessel phase compensation term is obtained by analyzing the Bessel vortex wave and introduced into the calculation lor='red'>of the reflected surface compensation phase to design a reflectarray antenna with a feed bias lor='red'>of 15° and operating at 26 GHz non-diffraction vortex wave. The simulation results show that the reflectarray antenna generates a second-order non-diffraction vortex wave with pure mode. (3) In this thesis, the phase compensation required for a zero-order Bessel beam radiating in any direction is analyzed, and the spiral compensation phase in the propagation direction is obtained by coordinate transformation, and then the calculation method lor='red'>of the compensation phase for a higher-order non-diffraction vortex wave radiating in any direction is obtained. The simulation results show that the designed reflectarray antenna generates a second-order non-diffraction vortex wave propagating along θ=30° , φ= 0° direction. During the calculation lor='red'>of the compensated phase, the metasurface structure is designed to generate multiple high-order non-diffraction beams in combination with the superposition principle lor='red'>of electromagnetic fields, and the simulation results show that high-order non-diffraction vortex waves with first- order and second-order OAM modes propagating along θ=30° , φ= 0° and θ=30° , φ= 180°  directions, respectively, are generated above the reflection array, which verifies the feasibility lor='red'>of the method.

By analyzing the relationship between the reflection coefficients lor='red'>of the metasurface unit by Jones matrix, the structural properties lor='red'>of the metasurface unit based on the geometric phase principle are obtained, and a metasurface unit is designed for broadband application scenarios. Simulation results show that a high-order non-diffraction vortex wave with OAM mode lor='red'>of  order is generated in the broadband range lor='red'>of 26 GHz to 31 GHz, which verifies the feasibility lor='red'>of the method. This thesis provides design methods for the generation lor='red'>of vortex waves based on metasurfaces in different application scenarios, which has certain reference value.

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