This chapter presents the analysis of a grating consisting of periodic arrays of InSb-coated dielectric cylinders on a substrate at THz frequencies using the two-dimensional frequency-dependent finite-difference time-domain method based on the trapezoidal recursive convolution technique. The transmission characteristics of an infinite periodic array are studied not only at normal incidence but also at oblique incidence. It is shown that the incident field is coupled to the substrate due to the guided-mode resonance (GMR), indicating the practical application of a grating coupler. For the sensor application, the frequency shift of the transmission dip is investigated with respect to the variation of the background refractive index. It is found that the shift of the dip involving the surface plasmon resonance is almost ten times larger than that of the dip only from the GMR. We also analyze a finite periodic array of the cylinders. The field radiation from the array is discussed, when the field propagates through the substrate. It is shown that the direction of the radiation can be controlled with the frequency of the propagating field. Final investigation is given to the three-dimensional analysis of InSb spheres array on a dielectric substrate. It is shown that the propagation direction depends on the frequency at which the field is coupled to the substrate. An application to the sensor is also discussed with attention to the behavior of the coupled field.