16 Antenna Designs with Electromagnetic Band Gap Structures Dalia M.N. Elsheakh, Hala A. Elsadek and Esmat A. Abdallah Electronics Research Institute, Giza, Egypt 1. Introduction The word “meta”, in Greek language, means beyond. It implies that the electromagnetic response of metamaterials (MTMs) is unachievable or unavailable in conventional materials. Many efforts have been done to search for an adequate definition for MTMs. In 2002, J.B. Pendry wrote in a conference paper: “meta-materials, materials whose permeability and permittivity derive from their structure”. Later, in 2006, C. Caloz and T. Itoh wrote: “Electromagnetic metamaterials are broadly defined as artificial effectively homogeneous electromagnetic structures with unusual properties not readily available in nature” [1]. Perhaps, a serious obstacle on the road to a universal definition for the term MTMs is the fact that researchers working with these objects do not commonly agree on their most essential characteristics. In [2] and [3], some of the problematic aspects of the non-naturality definition were raised, like the difficulty in separating classical composites from the new class of metamaterials. Another argument against the “not found in nature” property is that it unnecessary excludes impressive examples of natural media that could be called metamaterials par excellence, such as structural colors [4]. MTMs cover an extremely large scientific domain which ranges from optics to nanoscience and from material science to antenna engineering. In this chapter, we focus primarily on the subject of MTMs in the electromagnetic field. Personally, We prefer the definition given by D.R. Smith: Electromagnetic metamaterials are artificially structured materials that are designed to interact with and control electromagnetic waves [5]. The term “artificial” refers to the fact that the electromagnetic response of these materials is dominated by scattering from periodically or amorphously placed inclusions (e.g., metallic or dielectric spheres, wires, and loops) [6]. In the family of MTMs, “left-handed” (LH) media drew an enormous amount of interest. This concept was first put forward by a Russian physicist, Victor Veselago, in 1968, for whom the medium is characterized by a simultaneously negative electric permittivity and negative magnetic permeability [7]. Veselago argued that such media are allowed by Maxwell’s equations and that electromagnetic plane waves can propagate inside them, but the phase velocity of such a plane wave is in the opposite direction of the Poynting vector. Hence, some researchers use the term “backward wave media” (BWM) to describe these LH materials [8]. When such media are interfaced with conventional dielectrics, Snell’s Law is reversed, leading to the negative refraction of an incident plane wave as shown in figure 1. www.intechopen.com