## 1 Introduction
LCPC MSs designed using this second method offer greater flexibility, allowing the polarization direction of the radiated EM waves to be dynamically adjusted. Recent advancements in EM metamaterials have contributed to the growing application of MSs as LTC polarization converters across various scenarios requiring flexible CP wave radiation. For example, the reduction of radar scattering cross section (RCS), enhancement of stealth capabilities, and exploitation of circular polarization (CP) diversity can significantly improve system performance. These techniques enable frequency multiplexing, thereby increasing channel capacity [19]. However, most of the reported MSs are constrained by their fixed structures and limited to a single function, with only a small number of operable frequency bands, thus restricting their practical applications. In contrast, MSs utilizing equal amplitude, self-phase-shifting functionalities can be realized through common tunable materials such as p-i-n diodes [18; 20], varactor diodes [17], and liquid metals [21], facilitating polarization reconfigurability and contributing to size reduction. For instance, in reference [22], a polarization reconfigurable liquid dielectric resonator MS is presented. This MS employs gravity-controlled ethylacetate as a reconfigurable variable, enabling adaptation to the device's orientation and allowing independent switching between LP and LHCP or RHCP. In reference [23], a dual broadband LTC polarization converter based on rectangular slot MS is proposed, which can convert LP into RHCP in two non-adjacent frequency bands. However, this design only supports broadband CP waves for \(y\)-polarized incident waves and does not function under EM waves with other polarization orientations. Liquid crystals (LCs), owing to their excellent electrical tunability and low cost, have garnered increasing attention for use in tunable MSs [3; 24]. The tunability provided by LCs allows for polarization by switching across multiple frequency bands. Despite their potential, there are relatively few reports on the application of LCs for polarization conversion in MSs. For example, in reference [25], a reconfigurable chiral metal surface absorber based on LC was proposed. By controlling the arrangement of liquid crystal molecules, this device can alter the direction of circular polarization in incident light, effectively reversing the original CP direction. It exhibits strong absorption of CP waves in one spin state and reflection of CP waves in the opposite state. However, the operating frequency range is limited to between 340 THz and 1000 THz, resulting in significant signal loss during transmission. Moreover, the device operates within a single frequency band, which limits its applicability in real-world communication environments. In reference [26], the proposed MS-based antenna consists of square and L-shaped patches separated by L-shaped slots. A 3 dB ARBW of 26.2% (4.8-6.25 GHz) was achieved. In reference [27], a dual CP Fabry-Perot resonator antenna was proposed. In this, an LCPC MS is used as a cover layer for the FP resonator antenna. Different linearly polarized waves are converted into different CP by this MS. In reference [28], a MS-based LTC polarization converter with a flexible structure for conformal and wearable applications is proposed. The converter consists of S-shaped and C-shaped open-ring resonators nested in a unit cell, which can convert an LP incident wave into an LHCP at 12.4 GHz. In this article, we propose a multi-band LCPC RMS design for application in the X-band. By manipulating the relative dielectric constants of the LCs, we successfully convert the \(x\) or \(y\) polarization wave into LHCP- or RHCP-reflected EM waves at several different frequency bands. The choice of two dielectric substrate materials in the microstrip structure was made strategically.