Theory Models of Electromagnetic Metamaterials and Metasurfaces

Metamaterials are artificially engineered composite materials that exhibit special properties that are not found in nature and not observed in the constituent materials, including negative refraction, backward propagation, etc. With the subwavelength meta-atoms, the metamaterials can be characterized by the equivalent bulk parameters including permittivity and permeability. Metasurfaces can be considered as the two-dimensional (2D) equivalent of bulk metamaterials. The effective permittivity, permeability and refractive index are of less interest in metasurfaces. In contrast, of significant importance are the surface or interface reflection and transmission resulting from the tailored surface impedance, including their amplitude, phase, and polarization states. With the abrupt phase discontinuous, the anomalous reflection and transmission are achieved. In this chapter, the electromagnetic properties for metamaterials with double negative bulk parameters are first demonstrated. Then the generalized Snell’s law for metasurfaces is elaborated. Furthermore, the digital coding method for the metamaterials/metasurfaces are discussed. Finally, the group theory is introduced to analyse the symmetry of the metamaterials/metasurfaces.