# A Novel Metasurface Lens Design for Synthesizing Plane Waves in Millimeter-Wave Bands
## 1 Introduction
Furthermore, the QZ is typically half the size of the reflector, and the upper frequency limit of the CATR depends on the surface smoothness, which needs careful manufacturing and maintenance, especially at millimeter frequency bands [17]. To avoid these problems in the CATR's setup, reducing the measurement distance, a compact and cost effective solution based on a metasurface lens, is introduced in this work. Metasurface lenses based on a Jerusalem-cross structure have been widely used for higher gain antennas with low sidelobes at sub-6 GHz, and most of them have not been integrated with antennas [18; 19; 20; 21; 22; 23]. In [24], a very small focal-to-diameter (F/D) ratio transmitarray for generating a high-quality QZ at 2.6 GHz was proposed, but few studies have been conducted on millimeter waves. Consequently, further research on feed antenna and metasurface lens designs aimed at generating a large and high quality QZ at millimeter frequency bands for wireless device testing is needed. In this paper, to create a uniform plane wave and to further reduce the cost and size of the test system, a metamaterial metasurface lens fed by a planar 2 \(\times\) 2 patch-antenna array is proposed for synthesizing plane waves in millimeter wave bands at a reduced distance. The metasurface lens, based on frequency-selective surface (FSS) structures, is designed to achieve a phase-shift distribution of incident spherical waves from a patch-antenna array so that the metasurface lens can realize wave control. The planar \(2\times 2\) patch-antenna array is proposed to maximize the uniformity of illumination over some portions of the FSS structure whilst providing the field intensity windowing needed to minimize edge-diffraction effects, thereby enabling greater aperture efficiency to be achieved for a given QZ size. Traditionally, the PWG excitation weight is implemented with the aid of a programmable phase shifter or power dividers and programmable attenuators, but the plane-wave condition synthesized by the metasurface lens is realized through the geometry, dimensions, and periodicity of the proposed FSS structure. With the advantages of compactness, a low cost and a small space loss, the proposed metasurface lens can be an alternative to synthesizing plane waves in millimeter wave bands. The major contributions of this paper are summarized into three points. 1. A novel design based on a metasurface lens for generating a plane-wave condition in a reduced distance is introduced; it can be a cost-effective solution for mm-wave PWG systems. 2. The performance of the phase-shift element is investigated in millimeter wave bands; it can be used to replace expensive and inaccurate millimeter phase shifters. 3. The designed metasurface lens, working at a frequency range from 24.25 GHz to 27.5 GHz, is validated through simulations and experiments. The results show that a uniform amplitude and phase can be achieved. The rest of the paper is organized as follows. The proposed metasurface lens's geometry is described in Section 2. The principle and simulation of the metasurface lens's synthesizing plane wave are described in Section 3. The characterization and validation results of the metasurface lens are described in Section 4. A summary and conclusion are given in Section 5.