## 1 Introduction  
In wireless communication scenarios, polarization mismatch between antennas is a significant issue that impacts communication quality. When polarization mismatch occurs, it can lead to signal attenuation or distortion. Therefore, achieving optimal polarization matching is crucial for enhancing the immunity of the communication system. CP electromagnetic (EM) waves offer a notable advantage over linearly polarized (LP) waves in terms of reducing absorption loss and signal attenuation during information transmission [1]. Furthermore, CP waves are more capable of bypassing obstacles in certain environments, such as between urban high-rise buildings, thereby improving coverage and signal strength. This helps mitigate polarization mismatch, multipath loss, and enhances signal integrity [2; 3]. Metasurfaces (MSs), composed of subwavelength microstructures arranged in periodic or quasi-periodic patterns, have attracted extensive research attention due to their exceptional ability to manipulate CP waves [4]. MSs are two-dimensional counterparts of metamaterials, capable of controlling the EM response of incident waves and offering functionalities such as polarization switching, beam steering, and phase control [5; 6]. Circularly polarized electromagnetic waves can be described as the result of synthesizing two linearly polarized waves with equal amplitudes and a 90\({}^{\circ}\) phase difference. In the plane perpendicular to the wave propagation direction, two independent directions of polarization can be defined [7]. When employing a dual-line-polarized feeder with high isolation and applying equal-amplitude orthogonal phase excitation, the synthesized electromagnetic field produces circularly polarized radiation. Moreover, by combining two circular polarization selectors with opposite chirality, a circular polarization convertor can be formed [8]. However, achieving broadband circular polarization in feed networks requires the integration of a power-dividing phase-shift unit. This addition significantly increases the overall size of the structure and severely limits the miniaturization of the device. The resulting trade-off between space requirements and compact design has become a key technical challenge for current circularly polarized phased array antennas aiming for broadband operation. In contrast to traditional phased array antennas, which rely on complex feed networks and circularly polarized MSs, linear-to-circular (LTC) polarized MSs offer a more attractive solution due to their simpler structure and greater flexibility in polarization conversion. Different types of polarization converters have been proposed and studied, with the main categories based on input and output polarization states, including linear-to-linear, LTC, and circular-to-linear polarization [9; 10]. Numerous geometrical designs of MSs for polarization conversion have been reported in the literature, such as three-layer chiral MS composed of deformed I-beam and cross-beam shapes [11], MS element structures employing orthogonal aperture-coupled feed technology to receive and radiate cross-polarized waves [12], and MS structures consisting of two curved lines and one cut line printed on a dielectric substrate to achieve broadband cross-polarization conversion [13]. A unit cell structure consisting of two square ring resonators is used to achieve cross-polarization conversion with high gain bandwidth by varying the length of the rings and mirror elements [14]. Compared to cross-polarization conversion MSs, LCPC MSs can better meet the communication needs in complex and dynamic application scenarios. There are primarily two types of designs for CP control in MSs: one involves the direct design of CP MS antennas [15; 16]. While this method is straightforward and efficient, it lacks flexibility, as the designed MS can only radiate CP waves once constructed. The other approach involves designing the LCPC MS first and then positioning it above the LP feeder to convert the LP waves radiated by the feeder into CP waves [17; 18].