Transmission and Reflection Characteristics of a Concrete Block Wall Illuminated by a TM-polarized Obliquely incident wave

Typically, many of the modern buildings have concrete walls constructed from cinder block walls, that have periodic nature in their relative dielectric constant. This periodic nature excites higher-order Floquet harmonic modes at microwave frequencies, which leads to the propagation of scattered waves along with non-specular directions. Periodic structures exhibit different behaviors when illuminated by different types of incident polarizations. Previous studies mainly focus on the Transverse Electric (TE) incident wave, where the behavior of a periodic layer is characterized easily by only considering the function of the relative permittivity in the equations. But, for a Transverse Magnetic (TM) incident plane wave, the first-order derivative of the relative permittivity function must be taken into account in the formulations. Accordingly, in this paper, reflection and transmission coefficients from a typical concrete block wall are formulated for a TM polarized incident wave. Exact boundary equations are written, and the effect of oblique incidence is taken into account. Also, the periodic nature of the inhomogeneous layer is represented by the Fourier series. In addition, two types of numerical validation are provided to prove the accuracy of the given theory. The ability to calculate Fourier series coefficients by taking the Fast Fourier Transform (FFT) of the relative permittivity function enables the introduced method to treat any type of periodic inhomogeneities.