Transmission-line formulation (TLF) is used to analyze two-dimensional low-loss metallic gratings at optical frequencies when plasmonic waves can propagate in the structure . This method , like any other Fourier-based method , suffers from numerical instabilities when applied to such structures . A systematic approach to avoid these instabilities is proposed in this research . These numerical artifacts are attributed to the violation of the so-called Li's inverse rule and the appearance of higher-order spurious modes . A new approach is proposed to identify and to greatly reduce the effect of these spurious modes based on the degree to which these modes satisfy conservation of momentum . Furthermore , periodically patterned graphene sheets (PPGS) embedded in planar multilayered media is modeled using TLF . Moreover , the numerical convergence can be slow because of the fact that the conductivity is zero in unfilled areas of the patterned surface where Li's inverse rule is not applicable. A simple and efficient approach is proposed to overcome this problem such that the exact boundary condition can be applied and the surface current density on PPGS can be obtained accurately . Fast convergence and accuracy of the method will be demonstrated by computing the absorption of PPGS . Moreover , the proposed method is utilized to design a wideband tunable wide-angle polarizer consisting of two parallel PPGS separated by a 50 µm layer of SiO 2 . For the final stage of this research and as an alternative to PPGS , we introduce a layer of randomly positioned spherical nano particles with the capability of being used in various optical applications. Here , we investigate the impact of such layer of silver nano-spheres on the absorption efficiency of thin-film silicon solar cells . The Coherent Potential Approximation (CPA) is used for the required computations . The metallic array of nano-spheres is assumed to be embedded inside the active layer of the solar cell . The formulation to compute the absorbed power by ordered (perfectly periodic) and disordered arrays of nanospheres embedded inside the lossy background is provided . It is shown that the disorder can considerably enhance light trapping and absorption . Higher disorder allows for more efficient diffraction and leads to wider bandwidth of optical absorption . Key Words: Metallic grating, periodically patterned graphene sheets, transmission-line formulation, disordered array of plasmonic nanoparticles, coherent potential approximation