## 1 Introduction  
With the rapid development of the new generation of mobile communication, radar systems, satellite communication, and other wireless communication systems [1], antennas with a high gain, wide bandwidth, and low profile have become research trends for modern millimeter-wave (mm-W) antennas. The reflectarray antenna (RA), as a type of antenna that combines the characteristics of a planar microstrip array antenna and a high-gain reflector antenna, has the advantages of a high gain, simple feeding, easy processing, and a low cost [2]. Moreover, due to the fact that the RA adopts the spatial feeding method, the profile between the feed source and the array surface of the RA is relatively high, making it bulky and difficult to integrate with other systems [3]. Compared with the RA, a folded reflectarray antenna (FRA) can reduce the profile between the feed source radiator and the aperture of the reflectarray surface effectively by using dual-polarized elements for polarization rotation and a polarizer grid right above them [4, 5]. Many publications have reported FRAs with various performances, such as multibeam [6], full-metal structure [7], dual-frequency [8, 9], ultra-low-profile [10] and planar feed source radiator arrays [11]. Among FRAs, circularly polarized folded reflectarray antennas (CPFRas) are more appropriate for long-distance communication systems, such as satellite communication systems and radio communication systems, because of the reduction in polarization loss and suppression of multipath fading [12]. Recently, many research works related to CPFRAs have been published. According to the polarization mode of the feed source antenna, CPFRAs can be classified into two types. The first type of CPFRA adopts a circularly polarized antenna as the feed source radiator [13; 14]. In [13], a folded reflectarray antenna using a CP conical horn antenna as the feed source was proposed. The physical fabrication of the CP conical horn antenna is complex and expensive. In [14], a folded reflectarray antenna using a planar CP microstrip patch array antenna as the feed source was proposed. Planar feeding can reduce the profile height of the antenna and is easy to integrate with other components, but the design of the feed source is often complex. The second type of CPFRA uses a linearly polarized (LP) antenna as the feed source radiator [15; 16; 17]. In [16], a folded reflectarray antenna based on an LP horn antenna was proposed. The design of the LP horn feed is simple, but it is accompanied by the disadvantages of a relatively high profile and high production costs. In [17], a folded reflectarray antenna using an open waveguide antenna as the feed source was proposed. The design of the waveguide antenna is simple and easy to process. In addition, a linear-to-circular polarization converter is needed as the sub-reflector in the second CPFRA so that the final electromagnetic waves radiated out are circularly polarized. Therefore, when taking the design simplicity and cost-effectiveness into consideration, the second type of CPFRA, which uses a linearly polarized feed source radiator, is preferred. In this work, a CPFRA with a low profile and broad bandwidth based on a transmissive linear-to-circular polarization converter for millimeter-wave applications is studied. This CPFRA is composed of a linear horn antenna as the feed radiator, a metasurface-based element as the basic structure of the primary reflector surface, and a transmissive polarization converter as the sub-reflector surface. This manuscript is organized as follows: Firstly, Section II introduces the architecture of the CPFRA. The primary reflector surface has the functions of polarization twisting and phase compensation. It can convert the linearly polarized electromagnetic waves (EWs) emitted by the feed source into linearly polarized EWs with vertical polarization and perform phase compensation. The sub-reflector surface reflects the incident linearly polarized electromagnetic waves from the feed radiator for the first time.