## 1 Introduction  
Patch antennas are fundamental components in various compact devices for wireless communication. As they work by transmitting and receiving electromagnetic waves, patch antennas directly influence system performance [1, 2, 3]. Recently, their applications have expanded significantly to meet the growing needs of emerging technologies, including energy harvesting and smart cities [3, 4]. Traditionally, patch antennas are constructed using copper and rigid dielectric materials; however, as demand for flexible and adaptable systems increases, novel antennas have emerged that diverge from conventional ones. These new antennas employ flexible and reconfiguration materials, which are not present in traditional copper-based designs. Among the unconventional materials investigated for new antennas are textiles, polymers, graphene, and liquid materials. Currently, liquid dielectrics, including water and other materials, have become a focal point of recent investigations due to their unique properties and potential for improving antenna design and performance [3]. In this regard, integrating unconventional materials in patch antennas aligns with the growing interest in resonators, as both approaches aim to enhance antenna performance across several frequency bands while meeting the demands of modern applications. Strategically placed resonators effectively confine electromagnetic fields, improving patch antenna performance. Furthermore, this arrangement of embedded patch antennas in resonators can operate across multiple frequency bands, making them ideal for modern applications that demand high versatility, such as wireless communications, sensor networks, and satellite communication systems. The ability to manipulate the properties of the resonator offers new opportunities for the development of efficient multi-band antennas [5; 6]. Recent research has explored using various liquid and solid materials as resonators in patch antenna designs. For instance, [PERSON] et al. [7] review the design and applications of liquid metal antennas, highlighting their adaptability and versatility for modern wireless communications. Their study explored innovative fabrication techniques and the advantages of conductive fluids for creating mechanically flexible, reconfigurable antennas. Similarly, [PERSON] et al. [8] introduced a hybrid dual-tube water antenna, where distilled water acts as the dielectric load while salty water serves as the radiating element. This configuration significantly increased the radiation efficiency, reaching up to 84% across its operating band. Another example is the work of [PERSON] and [PERSON] [9], which investigated the use of water as a dense dielectric patch antenna. The water patch functioned similarly to a traditional metallic patch in its design, achieving a broader bandwidth (BW) and improved radiation efficiency. [PERSON] et al. [6] presented a tunable 24 GHz antenna array based on noncrystalline graphite, demonstrating the significant potential for high-performance microwave components and their usefulness for advancing the next generations of wireless communication technologies. Moreover, [PERSON] et al. [10] review advanced techniques and geometries in dielectric resonator antennas, focusing on size miniaturization, BW optimization, and radiation pattern stability. In addition, the authors of [11] explored the development of multi-beam conformal antennas using liquid metal, showing that antennas using liquid metal can sustain their performance when the geometry is reshaped. Furthermore, [PERSON] et al. [12] proposed an encapsulated dielectric resonator antenna design, which enables efficient radiation across two widely separated frequency bands. Meanwhile, [PERSON] et al. [13] provided an overview of dielectric resonators for applications in radio frequency (RF) energy harvesting and systems and wireless power transmission. Additionally, the authors of [14] proposed a broadband antenna designed as an array element for advanced microwave brain imaging systems.