No abstract

The study of photonic crystals (PCs) is very importance for the development of new optical technologies. An interest in the investigation of PCs is the search of totally optical control of information in a circuit, with the idea of developing new technological applications that have great advantages over conventional electronic devices in the miniaturization of circuits. In the present work, we show a numerical study of the electromagnetic response of two-dimensional square lattices such as finite photonic structures formed by cylinders embedded in air and air holes in a finite plate composed of metamaterial. We applied a numerical technique known as Integral Equation Method (IEM) to calculate the optical response by calculating reflectance and transmittance as a function of the angle of incidence of finite systems proposed. The calculations were performed by varying the filling fractions and introducing a random roughness on the surfaces of the cylindrical inclusions that form our proposed systems, for the transverse magnetic field (TM) polarization. The results obtained show that the random roughness on the surfaces of the cylindrical inclusions affects their reflective and transmissive properties of two-dimensional square lattices. This is an important result to consider in manufacturing of finite two-dimensional square lattices, despite the existence of a well-developed technology for the manufacture of surfaces. These structures can be used, for example, for the development of filters, mirrors and lenses.

The interest to develop nanoscale devices is due to their ability to manipulate the optical properties through their structure. With an increasing interest in the recent decades, different types of Photonic Crystals (PC) have also been proposed. A PC is a periodically ordered material in which the refractive index is modulated. It has been shown in recent years that adding new materials to the structure of photonic crystals results in novel properties of these systems, which were originally conceived as composed of purely dielectric materials. One option is to consider this type of systems with dispersive Left-Handed Materials or metamaterials. The optical properties of the PCs depend on the type of periodicity, the geometry of the inclusions, the contrast of the refractive index and the filling fraction of the photonic structure. In this work, a numerical technique known as the Integral Equation Method was used to model the optical response of a two-dimensional photonic structure with a hexagonal lattice of cylindrical inclusions containing smooth and random rough surfaces that include dispersive LHM. It was obtained that the roughness of the inclusions modulates the optical response, in some cases varying the intensity and in others the direction of propagation. This property is very useful and has multiple applications in waveguides, filters, omnidirectional mirrors, beam splitters, etc.