## 1 Introduction
It is immersed in a medium with a carefully selected relative permittivity, improving impedance matching between the antenna and brain tissues to enhance signal transmission and reception. [PERSON] [15] conducted a numerical analysis of a broadband waveform in a THz absorber, utilizing a dielectric cavity resonator integrated with a graphite disk. Moreover, [PERSON] [16] proposed a method to enhance the gain of a dielectric resonator antenna by utilizing metallic patches. The works above and references therein highlight that resonators can also enhance antenna performance through innovative material usage, driving advancements in diverse applications such as wireless communications, energy harvesting, and imaging systems. Despite these advancements, several challenges remain in improving the efficiency of embedded patch antennas in resonators. One notable issue is developing a clear view of how types of materials and geometries of resonators affect the electromagnetic performance of patch antennas with high dielectric constants. It is well-established that designing patch antennas with high dielectric materials is difficult, as a high dielectric constant often degrades overall efficiency, especially in terms of radiation pattern characteristics, such as main lobe magnitude (MLM), main lobe direction (MLD), half-Power Beamwidth (HPBW),and side lobe level (SLL) [17]. However, understanding the benefits of resonators in this context needs a comprehensive investigation. While several studies focus on simplified configurations of resonators [5], there is a gap in the literature in terms of a comprehensive analysis in which a unique set of specification designs and constraint are applied. Such an investigation is relevant as it would allow researchers to easily highlight and compare the benefits of geometric shapes and materials used to build resonators that will be employed to improve the performance of patch antennas. This paper addresses this gap by investigating the combining of dielectric and conductive materials with distinct geometries to build resonators and, consequently, to improve patch antenna performance when the decoupled method is adopted. The decoupled method means that the patch antenna and resonator are sequentially designed in that order. Consequently, it offers insights and guidelines for fostering patch antennas embedded in resonators. In this regard, this paper introduces the following contributions:  
* A comprehensive presentation of the combinations of dielectric and conductive materials (i.e., distilled water, glycerin, and graphite) and fifteen geometries for building resonators and improving a few characteristics or overall performance of patch antennas. * Numerical simulations of the possible combination of the selected sets of materials and geometries and analyses based on the radiation pattern and the magnitude of the scattering parameter \(S_{11}\) (i.e., \(|S_{11}|\)) when the decoupled approach is used, in which the resonator is designed to fulfill the specifications of an already designed patch antenna. Considering that the benefits of resonators are more relevant when the material of the substrate of the rectangular patch antenna is of low quality, the following findings are related to the use of flame retardant-4 (FR-4) when extensive numerical simulations are considered:  
* For distilled water (DW) resonators, the impact on scattering parameter \(S_{11}\) and radiation pattern varies depending on the geometry of the resonator. Specific geometries offer a broader BW, improved impedance matching, and support for multiple resonant frequencies. Others enhance characteristics of the radiation patterns, with some configurations achieving exceptional gain and radiation directionality while supporting multi-band operation. Moreover, specific geometries downshift the resonant frequencies, which can be used to reduce the antenna size.