Graphene material is inherent from carbon, its two-dimensional hexagonal lattice structure (also called honeycomb), which is the thinnest known at all material so far, equivalent to a thickness of one carbon atom only. Although it is considered one of the strongest (stronger) materials known. Developed by Russian Andrei Geim and Konstantin Novoselov in 2004, and both won Nobel Prize in Physics in 2010. The properties of graphene have attracted the attention of many disciplines. Also the results of several studies in the field of thermodynamics for graphene led to the growing interest for the study of graphene in the areas of optics and photonics to be used in a variety of applications. On the other hand, macroscopic systems that can be analyzed using Maxwell's equations, the study of waves guided by the existing structures on the graphene allow them to better understanding to the incorporated into electromagnetic devices. In this study, the dispersion relations for two sheets of parallel graphene in over Gigahertz and Terahertz ranges for two ships of polarization of the electromagnetic field are the magnetic field (TM-Modes), and field electrophoresis (TE -Modes) has been investigated. The behavior of electromagnetic waves in the presence of a layer of the left-handed material between two sheets of parallel graphene has been studied. The total power flow through the structure has been obtained. In addition, this article discusses the use of guides waves as sensor by the existence of two layers parallel of graphene with the installation of variables for remote sensing applications. The sensitivity of the sensing of the variables of electric permittivity and the magnetic permeability of the Left-Handed material has been presented. Moreover, the comparison between the layers that contain the Left-handed materials with layers containing insulating material. It can be concluded that the presence of a layer of left-handed materials between two layers of graphene gives better results for increased the sensitivity, which may be useful in optoelectronics and electromagnetic applications, such as the design of some of optoelectronic devices based on the scope of a private graphene sensors
