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V C 2014 Wiley Periodicals, Inc. GRAPHENE LOADED WAVEGUIDE FOR MILLIMETER-WAVE APPLICATIONS Ahmed M. Attiya Microwave Engineering Department, Electronics Research Institute, El-Tahreer St., Dokki, Giza, Egypt 12622; Corresponding author: attiya@eri.ci.eg Received 14 April 2014 ABSTRACT: This article presents a full wave analysis of a rectangular wave guide loaded with a double-layered graphene sheet mounted on a finite-thickness dielectric slab. The chemical potential of the graphene sheet is controlled by the applied electrical potential between the two layers of the graphene sheet which subsequently controls the surface conductivity of the graphene sheet. This property is found to have a sig- nificant effect at frequencies above 50 GHz. By controlling the conduc- tivity of the graphene sheet it would be possible to control the amplitude and phase of the transmission and refraction coefficients along the waveguide section. This feature can be used in different applications in mm-wave range like switches, attenuators, filters, resonators, and modu- lators. V C 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:2762–2766, 2014; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.28694 Key words: graphene; nanotechnology; millimeter-wave 1. INTRODUCTION Graphene is a one-layer of carbon atoms arranged in a hexago- nal two-dimensional lattice. Early theoretical study of this con- figuration shows that this structure has unique physical properties including quite high electron mobility [1]. However, the main interest in graphene has been mainly increased in last 2 decades after discovering experimentally related nanostruc- tures like carbon nanotubes and quantum dots. However, the graphene sheet itself could be extracted for first time in 2004 [2]. More recently, Li et al. [3] introduced an efficient technique for synthesizing large-area graphene sheets of the order of centi- meters on copper substrates. This discovery was the introduction for a huge research in different areas related to the possibility of using these one-layer carbon atoms in different applications. One of the main properties of graphene sheet is that its sur- face conductivity can be tuned by applying normal electric and/ or magnetic fields [4–6]. This property makes graphene sheets are good candidate for tunable devices in mm-waves, THz, and infrared frequency ranges. In this article, we present an analytical solution for the prob- lem of a rectangular waveguide loaded with a double-layered graphene diaphragm as shown in Figure 1. The graphene dia- phragm has a width w 1 5a2w and is mounted on a dielectric slab of thickness d. This graphene diaphragm is composed of two graphene sheets separated by a thin layer Aluminum oxide of thickness t which is much smaller than the thickness of the supporting dielectric slab such that the double-layered graphene sheet is assumed to be of zero thickness in calculations. The thickness t is conventionally about 5–20 nm [7–12]. The con- ductivity of this double-layered graphene sheet is approximated as twice the conductivity of a single graphene sheet [9]. The advantage of this double-layered configuration is that by apply- ing a potential difference between the two layers of the gra- phene sheets a normal electric field is introduced between them. Thus, by controlling the applied voltage between the two gra- phene sheets, it would be possible to tune the conductivity of 2762 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 56, No. 12, December 2014 DOI 10.1002/mop