## 1 Introduction  
In the past few decades, the development of metamaterials (MMs) [1; 2; 3] has shifted from three-dimensional (3D) structures to two-dimensional (2D) planar structures. Compared with 3 DMMs, metasurfaces [4; 5; 6; 7] have attracted extensive attention because of their advantages of low loss and low profile. In recent years, many technologies have been developed, such as metastructures [8], near-zero-index materials [9], plasmonics [10], nanoparticles [11], graphene [12] and multi-functional structures [13]. Due to their powerful ability to manipulate EM waves, the metasurface has been applied in many devices, including absorbers [14; 15], polarizers [16; 17], holography [18], antennas [19], beam generator, filters and sensors [20].  
A gradient metasurface was first proposed by [PERSON] et al. to prove the generalized Snell's law [21]. At present, the general method to achieve a phase gradient is to rotate the direction or change the geometry of the structure. In particular, the Pancharatnam-Berry phase in space will be generated under the incident circularly polarized waves, and many peculiar physical phenomena have been realized. For example, anomalous reflection/refraction [22; 23; 24; 25], beam focusing [26; 27] and vortex beams [28; 29; 30].  
Furthermore, with the development of radio frequency and microwave technologies, effective RCS reduction is one of the most promising methods in stealth technology. The traditional methods to achieve RCS reduction are radar absorption MMs and phase interference cancellation techniques [31]. However, problems such as EM absorption energy being easily captured by the infrared detector and the very narrow bandwidth limit these two methods [32]. Polarization converters and multilayer structures [33] have been proposed to expand the bandwidth, but these methods complicate the structural design and deteriorate the antenna performance. In recent years, the concept of a coding metasurface was proposed by [PERSON] et al. They designed the \"0\" and \"\(\pi\)\" phase cells to simulate a digitally encoded \"0\" and \"1\" and combined these with optimization algorithms to accurately control the EM waves. This approach also provides possibilities for the design of RCS reduction. According to this principle, RCS reduction from 1-bit [34] to multi-bit [35] encoded metasurfaces has been demonstrated. A multi-static radar stealth metasurface based on a particle swarm optimization algorithm was proposed by [PERSON] et al. [36]. However, design challenges remain in achieving excellent RCS reduction characteristics for greater bandwidth and ultra-thin structures.  
In this paper, we report the design of an ultra-thin and ultra-wideband linear polarizer. The simulated results show that the conversion from linearly polarized waves to cross-polarized waves is realized in the 14.8-28.0 GHz range, and the corresponding PCR is more than 95%. In addition, a gradient metasurface is simulated at 15 GHz, achieving an anomalous reflection of \(-23^{\circ}\). The coded metasurface is composed of anisotropic units derived by rotating the double semicircular gap patch structure by 90\({}^{\circ}\) to meet the phase difference requirements. The meta-unit is composed of 4 \(\times\) 4 identical meta-atom classes. The simulated results show that a 10 dB RCS reduction can be attained in the 15.3-28.0 GHz range. The RCS reduction is more significant than in the checkerboard pattern.