龙伯透镜天线是一种独特的渐变折射率透镜天线, 但因为某些缺陷其应用受到限制。近年来, 人们采用变换光学方法和超材料理论设计了许多以平板龙伯透镜为代表的新型透镜天线。本文对比总结了变换光学设计透镜的3种方法, 即坐标变换法、保角变换法和准保角变换法; 指出了准保角变换法由于设计灵活、可使用全介电材料制备而更具研究和应用前景; 详细阐述了准保角变换法设计透镜的原理和步骤; 介绍了国内外关于透镜变换和制备具有影响力的研究成果; 指出了变换光学透镜天线今后的研究方向。

Luneburg lens antenna is a kind of gradient index lens antenna, but its application is restricted due to certain disadvantages. In recent years, various new-type lens antennas, the most representative of which was planar Luneburg lens, were designed by means of transformation optics and metamaterial theories. In this paper, three transformation optics techniques of lens design including coordinate transformation, conformal mapping and quasi-conformal mapping are summarized and compared. Quasi-conformal mapping has better research and application prospect because of its flexibility in lens design and easy fabrication by all dielectric materials. Principles and procedures of quasi-conformal mapping in lens design are elaborated, and important research fruits about lens transformation and fabrication are introduced. Finally, the research directions of transformation optics lens antenna in the future are proposed.