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The development of renewable energy sources has attracted increasing interest because of negative externalities associated with fossil fuel use. Thermophotovoltaics is a promising technology, in which a thermal emitter radiates photons which are directly converted into electricity using a photovoltaic diode. However, blackbody emission includes a broad range of wavelengths, but only higher energy photons can be converted into electricity. Thus, tailoring the selectivity of thermal emission is needed to improve the efficiency of TPV. A physics-based simulation tool is needed to understand the fundamental nature of thermal radiation, and the extent to which it may be controlled. The goal is to simulate directional thermal emission that results from coupling of Surface Plasmon Polaritons on lamellar metallic gratings into radiation modes. A rigorous coupled wave analysis in S4 can calculate absorption or emission versus angle. In the absorption mode, light is launched from air, and total absorption is calculated, including specular and diffracted modes. In the emission mode, a number of obliquely incident plane waves at different angles are launched from the metal side to simulate thermal emission. Highly selective emission is observed around angles that satisfy the diffraction law. For one experimental test case, the simulation results have been shown to match the angle and angular width of emission to good accuracy. Hence, our simulation will allow researchers to find an optimum geometric design of the metallic structure at which the emission characteristics best match their particular application. This will help in designing a selective emitter for higher-efficiency TPV.