Optical properties of two-dimensional square lattices with smooth and randomly rough surfaces that include dispersive left-handed materials

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.