随着微波毫米波电路系统和信息通信领域的迅速发展，相位梯度超表面透镜天线由于能够控制电磁波的波前相位和幅值，从而实现电磁波传播方向和形式的调控，成为当前学术界和工程领域研究的热点之一。针对传统透镜天线带宽较窄、难以实现各向异性相关功能等问题，本文着重研究了宽带超表面透镜天线以及一种应用于各向异性超表面透镜天线的机器学习设计方法。

本文重点研究相位梯度超表面理论，通过对比传统补偿相位计算方法调整相位前后的差值，引出宽带补偿相位计算与排布方法，验证该方法在宽带范围内降低了超表面透镜的补偿相位差值，从而提升超表面透镜天线的增益与带宽。

利用该宽带补偿相位计算方法设计出三种高性能宽带天线，并仿真分析天线相关性能。其中超表面透镜天线具有6GHz的1dB增益带宽；宽带圆极化超表面透镜天线实现了12GHz的1dB增益带宽与3dB轴比带宽；宽带涡旋波超表面透镜天线在22～30GHz的宽带范围内产生了一阶的涡旋波，平均能量权重高达64.6%，涡旋波相对带宽高达38%。

针对超表面透镜天线设计过程中相位难匹配、设计耗时较长等问题，提出了一种应用于各向异性超表面透镜天线的机器学习设计方法，由基于线性函数特征的DNN、基于相位分类的DNN以及灰狼优化算法组成，利用该机器学习设计方法可在超大频率范围内实现介质基础单元透射相位的精准预测，从而实现各向异性超表面透镜天线的快速设计。本文所提出的机器学习设计方法在10～25GHz内实现了介质基础单元尺寸参数与TE和TM透射相位之间的快速映射，达到了95%以上的精度。利用所设计的机器学习方法完成了一款涡旋波复用超表面透镜天线的设计，其在24GHz频率下可以实现轨道角动量阶数1和-1的涡旋波复用，证实了所设计机器学习方法的有效性。

With the rapid development of microwave millimeter wave circuit systems and information and communication fields, the phase-gradient metasurface lens antenna has become one of the current hot spots of research in academia and engineering fields due to its ability to control the wavefront phase and amplitude of electromagnetic waves, thus realizing the regulation of electromagnetic wave propagation direction and form. Aiming at the problems of narrow bandwidth of traditional lens antennas and difficulty in realizing anisotropic correlation functions, this paper focuses on broadband metasurface lens antennas and a machine learning design method applied to anisotropic metasurface lens antennas.

This thesis focuses on the phase gradient metasurface theory, by comparing the difference before and after adjusting the phase with the traditional compensation phase calculation method, leading to the broadband compensation phase calculation and scheduling method, and verifying that the method reduces the compensation phase difference of the metasurface lens in the broadband range, thus enhancing the gain and bandwidth of the metasurface lens antenna.

The broadband compensated phase calculation method is used to design three high-performance broadband antennas and simulate and analyze the antenna-related performance. Among them, the metasurface lens antenna has 6GHz 1dB gain bandwidth; the broadband circularly polarized metasurface lens antenna achieves 12GHz 1dB gain bandwidth with 3dB axial ratio bandwidth; the broadband vortex wave metasurface lens antenna generates first-order vortex wave in the broadband range of 22-30GHz with an average energy weight of 64.6% and a vortex wave bandwidth of 38%.

A machine learning design method is proposed for anisotropic metasurface lens antennas, which consists of linear function-based DNN, phase-classification-based DNN and gray wolf optimization algorithm. The machine learning design method can be used to achieve accurate prediction of the transmission phase of the dielectric base unit in a large frequency range, thus realizing the fast design of anisotropic metasurface lens antennas. The proposed machine learning design method achieves a fast mapping between the dielectric base unit size parameters and the TE and TM transmission phases with more than 95% accuracy in the range of 10 to 25 GHz. The design of a vortex wave multiplexing metasurface lens antenna is completed using the designed machine learning method, which can achieve vortex wave multiplexing of orbital angular momentum order 1 and -1 at 24 GHz, confirming the effectiveness of the designed machine learning method.

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