I. Introduction
Nowadays, due to the abundant spectrum resources, high data transmission rate, and compact size, millimeter wave (mm-wave) bands will be widely used in the fifth-generation (5G) and beyond 5G communication systems [1], [2], [3]. In order to overcome the high transmission loss problem, mm-wave high-gain antennas have attracted significant attention and extensive research [4], [5], [6] in the past few years. Traditional high-gain antennas such as phase array antenna, reflectarray (RA) [7], [8], [9], transmitarray (TA) [10], [11], [12], and Fabry-Perot cavity (FPC) antenna [13], [14], [15] are widely investigated. Although phase array antenna can achieve directive radiation to compensate for atmospheric attenuation, it utilizes a large number of elements and a complex feeding network, which increases manufacturing complexity, additional loss, and costs [16]. The RA and TA with relative low cost, flat structure, and lightweight characteristics attract growing interests. However, feed blockage [17] and high profile [18] (including the feeding source) limit the application of them. Recently, folded transmitarray (FTA) following the ray tracing principle has been proposed, which can reduce the height to one-third or more [19], [20], [21] than a classical TA. Hence, FTA can also be widely used for future communication systems with low-profile and high-gain performances [22].