Analytical model for coupling of waves between a homogeneous medium and a volumetric transmission-line network

The use of transmission-line networks as periodic structures emulating many interesting metamaterial-related phenomena, such as negative refraction ([1], [2]) and cloaking ([3], [4]), has gained increasing interest in the scientific community. Transmission-line networks offer a simple way to create non-resonant, broadband structures exhibiting exotic wave propagation characteristics. A big drawback of traditional transmission-line metamaterials is the fact that most such structures are not inherently coupled with electromagnetic waves propagating in a homogeneous material, such as free space for example. Recently various approaches to couple transmission-line networks to free space have been proposed, see, e.g., [3], [4], [5]. The approach of [3], [4], is based on matching the free space wave to a network by introducing a special transition layer which couples the different modes propagating in the two different “media”. Such a layer can be formed simply by creating metal tapers, which guide the wave with very small amount of reflections from one media to another [3]. This technique has been successfully employed to create an electromagnetic cloaking device based on transmission-line networks [4].