用矢量球面波理论和互易原理分析伦伯透镜天线

伦伯透镜是一种球形分层介质天线，考虑到数值计算的复杂性，本文提出用矢量球面波理论和互易原理相结合，分析其性能。该方法首先用矢量球面波理论计算平面波入射到多层介质球的散射场，在此基础上，用互易原理将散射场转变成天线的远区辐射场。基于这种方法，本文着重研究了伦伯透镜天线的焦区场和远区场特性，包括透镜分层总数以及层与层之间存在的空气间隙对实际应用可能造成的影响。最后，对卫星通信中伦伯透镜天线多波束应用的可行性给出了分析结果。

Analysis of Luneburg Lens Antenna Using Spherical Vector Wave Method and Reciprocity Theorem

The Luneburg lens antenna is composed of a series of concentric shells of constant permittivity. Considering the complexity of numerical calculation, this paper presents a closed-form approach, which combines the spherical vector wave method and the reciprocity theorem. The hybrid method first calculates the scattered fields of the Luneburg lens using the spherical vector wave method. Then it transforms the calculated results into the radiation fields in the far region using the reciprocity theorem. This paper applies the approach to investigate the characteristics of the Luneburg lens in the focal region as well as in the far region. The effects of the shell number and the air gaps between the layers on the antenna performance have been also investigated, in the end, the paper presents the analysis result on the feasibility of the multiple-beam Luneburg lens antenna for satellite communication.