## 1 Introduction  
The polarization of an electromagnetic (EM) wave is concerned with the oscillation direction of the electric field in the plane lying perpendicular to the propagation direction [1]. Polarization is one of the most basic characteristics of EM waves, and has significant applications in many fields including antennas [2; 3; 4; 5], asymmetric transmission [6; 7; 8; 9], biological detection [7], and microwave communication [10; 11; 12; 13; 14; 15; 16]. Many applications of EM phenomena are very sensitive to polarization [17; 18; 19; 20]. Hence, it is necessary to precisely control and manipulate the polarization states of EM waves. The traditional way to manipulate polarization is to use natural materials such as twisted nematic liquid crystals by utilizing the Faraday effect [21]. It means that sufficient phase accumulation occurs at the expense of a longer transmission distance. Therefore, the traditional polarization converters have a large volume and narrow bandwidths, rendering device miniaturization difficult. Fortunately, metasurface is a type of artificial layered material with a thickness that is less than the operating wavelength. Metasurfaces enable the flexible and effective control of EM waves and have many unique properties [22; 23; 24]. Many types of metasurface-based polarization converters have been designed because of their high efficiency, low profile, and small size [25; 26; 27; 28; 29; 30]. For example, [PERSON] et al. [31] designed a wide-band, multi-purpose, and switchable linear polarization converter based on a metasurface. [PERSON] et al. [32] proposed a V-shaped nanoantenna to achieve line-to-circular polarization conversion in the optical frequency band. A cross-reflective polarization converter operating over a large frequency range with high efficiency was reported by [PERSON] et al. [33]. The chiral metasurface is considered to be an effective method for transmission polarization manipulation components which can convert all polarization types, including linear-to-circular, linear-to-linear, and circular-to-circular polarization conversion. Chiral metasurface can achieve high conversion efficiency; however, it has the disadvantages of a complex multilayer structure and a narrow bandwidth. These restrict its practical applications. For reflective polarization conversion, the above mentioned problems can be avoided by using anisotropic structures [34; 35; 36]. Moreover, the operating bandwidth can be increased to a certain extent by the superposition of different resonant frequencies. For example, [PERSON] et al. [37] presented a broadband and high-efficiency linear polarization rotator based on anisotropic structures, which achieved 90\({}^{\circ}\) polarization rotation from 5.7 to 10.3 GHz and a polarization conversion ratio (PCR) above 90%. However, little information has been provided about dual-broadband or multi-broadband polarization converters with the polarization conversion efficiency close to 1, which are crucial to EM wave applications. For example, the dual-broadband polarization converter can improve the capacity and speed of data transmission when it is used in a wireless communication system. The system compatibility can also be improved as it works in two different frequency ranges. Therefore, it is very important to design a dual-frequency or multi-frequency polarization converter with a polarization conversion efficiency that is close to 1. In this work, a high-efficiency and dual-broadband linear polarization converter based on a reflective metasurface is proposed, constructed, and evaluated. The converter is composed of two symmetrical double-slotted metallic split-rings and one criss-cross structure, a dielectric layer, and a metallic ground, as well as four resonances within the 9.38-13.36 GHz and 14.84-20.36 GHz frequency ranges. The \(x\)-polarized or \(y\)-polarized incident wave can be converted almost perfectly into the corresponding cross-polarized wave in these dual-band ranges.