This paper discusses the challenges in characterizing electromagnetic (EM) waves propagating through inhomogeneous media, such as reinforced cement concrete and hot mix asphalt. Understanding the EM properties of materials, including their dielectric constant, conductivity, and magnetic permeability, is crucial to analyzing the behavior of these waves. The focus of this study is to develop a numerical model for EM antennas using the finite difference time domain (FDTD) method, and to gain a deeper understanding of various EM wave phenomena. Additionally, we verify the accuracy of our model by comparing its results with experimental data. We analyze several antenna models with different materials, including the absorber, high-density polyethylene and perfect electrical conductors, to obtain an analytical signal response that is verified against the experimental response. Furthermore, we model the inhomogeneous mixture of randomly distributed aggregates and voids within a medium. We verify the practicality and reliability of our inhomogeneous models using experimental radar responses on an inhomogeneous medium.