Rigorous coupled-wave approach (RCWA) is formulated and applied to the computational modeling of problems involving 1D gratings and periodic structures. The RCWA is based on the expansion of the permittivity and permeability of the periodically varying material in terms of a Fourier series. A similar expansion of the electromagnetic field phasors is also used. This numerical method can be used to find the scattered and transmitted fields from surface-relief gratings and volume gratings.

In this thesis, the RCWA is used to study three important applications that require illumination from the planar side of periodic interface or periodic material. These applications involve surface plasmon-polariton (SPP) waves and anti-reflection coatings for solar cells. SPP waves are the electromagnetic surface waves that propagate at an interface of a metal and a dielectric material and find applications in sensitive (bio)chemical sensors, increasing the efficiency of light harvesting in the solar cells, imaging, microscopy, fiber optics, and waveguide. The SPP wave is excited only when the phase speed of the component of the incident light parallel to the interface is nearly equal to the phase speed of the possible SPP wave that can exist at that interface. Therefore, phase matching has to be achieved either by using a prism, or a surface-relief grating.

As a first application, SPP waves guided by an interface of a metal and a dielectric material using grating and prism couplings are numerically investigated for optical sensing. A new scheme is introduced by combining a prism on the planar side of the grating to excite the SPP waves. This new combination is only possible because of excitation from the planar side. Both the prism-coupled configuration and the grating-coupled configurations have different advantages in an optical sensor. As a second application, the excitation of SPP waves at an interface of a metal and a one-dimensional photonic crystal (1DPC) along the direction of periodicity of the photonic crystal is theoretically studied. This interface was accessible only for illumination from the planar side. As a third application, we have proposed anti-reflection coatings of zero index metamaterials (ZIMs) for maximum absorption of light in solar cells. A thin layer of a ZIM is shown to help trap light inside a solar cell. The outer surface of the ZIM layer is planar, and the inner surface has periodic corrugations in order for the incident light to pass through but block the re-transmission of the light back into free space.