Fourier transform analysis of graphene-based multilayer structures

In this study, a generic multilayer structure containing metals, dielectrics, line sources and graphene sheets is considered and analysed. The spectral domain techniques (SDTs) have been known as an efficient method for analysis of planar structures. However, since existence of graphene sheet imposes a new boundary condition, conventional SDTs cannot deal with it. Therefore a spectral-based method is proposed by applying the two-dimensional Fourier transform to the fields´ equations. First, a graphene sheet described by a conductivity tensor is assumed to be placed between two arbitrary dielectric layers. A generalised transformation matrix is then calculated which relates the electromagnetic fields of the top layer in terms of the ones of the bottom layer. It is shown that considering the tangential electric fields as supporting field components makes an easier analysis and results in more simplified expressions. The proposed method is evaluated through some examples of guiding and radiating structures. Some novel characteristics are observed, which are promising in providing new applications.