###### Abstract  
In this article, a novel and high-efficiency dual-wideband linear-to-circular polarization conversion based on a rectangular-slot reflective metasurface is anticipated, one that can convert linearly polarized (LP) electromagnetic waves into right- and left-hand circularly polarized waves in two non-adjacent frequency bands. The converter is an orthotropic design, with a pair of mutually orthogonal symmetric axes (\(u\) and \(v\)) along orientations tilted at 45\({}^{\circ}\) to the \(y\)-axis. The simulated results indicate that the dual-wideband circularly polarized wave is achieved under a \(y\)-polarized an electromagnetic (EM) incidence wave over the bands of 16.49-23.54 GHz and 26.44-34.56 GHz with 3 dB axial ratio relative bandwidths of 35.23% and 26.62%, respectively, and a polarization conversion ratio (PCR) in excess of 99%. A detailed mathematical investigation is proposed to determine the fundamental factor causing the dual-wideband linear-to-circular polarization conversion. The phase difference (\(\Delta\varphi_{uv}\)) between \(r_{uu}\) and \(r_{vv}\) under \(u\)- and \(v\)- polarized incident waves is \(\pm 90^{\circ}\), and it entirely determines the 3 dB reflected wave axial ratio. Any reflective converter can work efficiently as a linear-to-circular polarization conversion if the phase difference (\(\Delta\varphi_{uv}\)) is close to \(\pm 90^{\circ}\). metasurface; axial ratio (AR); dual wideband; polarization conversion ratio (PCR); polarization extinction ratio (PER); linear-to-circular (LTC); RHCP (right-hand circular polarization) 202218917202202218917202218917202218917202218917202218917202218917  
Several procedures, including single-and multi-layer structures, have been considered to improve the efficiency of ultrawideband two-dimensional antennas via a frequency selective surface. The FSS single layer can be used as a reflector, similarly to partially reflecting surfaces (PRS), which transmit some frequencies (although they operate as bandpass filters) and reflect others (after operating as stopband filters). Polarizers have two types: transmissive and reflecting. For example, two separate polarizations received from two bands have been integrated with transmission-type circular polarizers to establish two distinct channels for up- and down-link satellite communications [3; 4]. Circular polarization on both bands was intended for a radio frequency identification dual-band artificial magnetic conductor reflector [5]. Most research has been confined to a single purpose, revealing that the design can only regulate and alter LTC, cross conversion, and cross-polarization conversion as polarization in a single band. Recently, numerous polarization converters based on different metasurfaces and capable of conducting a diversity of polarization conversions have been anticipated, including: transmissive [6; 7; 8; 9] and reflective [10; 11; 12; 13; 14; 15; 16; 17; 18; 19] LTC polarization converters under linearly polarized incidence, reflective linearly polarized [20; 21; 22; 23; 24; 25; 26; 27] or circularly polarized [28; 29; 30; 31; 32], and transmissive linearly polarized [33; 34; 35; 36; 37] or circularly polarized [38; 39; 40] incidence. Moreover, using the previously mentioned LTC polarization converters still poses problems in achieving the desired characteristics of an ultrawideband: high efficiency and compact design. Additionally, [PERSON] et al. created a dual-band transmission LTC polarization converter with angular stability via a metasurface. While the working frequency bands for these two polarization converters are 9.05-9.65 GHz and 12.55-13.1 GHz, respectively, both have relative bandwidths of only 6.0% and 4.0% [6]. Recently, [PERSON] et al. reported an ultrawideband LTC polarization conversion using a circular pie-shaped reflective metasurface, with a theoretical 3 dB axial ratio relative bandwidth of 50.8% [7]. On the other hand, in the THz region, [PERSON] et al.