ABSTRACT
This chapter shows the space-discretizing algebraic schemes describing discrete fields can be considered the unifying framework behind metamaterials. Physical realizations of these schemes lead to either Drude or Lorentz dispersion with their immanent properties and hence limitations. Unconnected metamaterial structures may allow the wave propagation of an additional mode within the structure, usually referred to as the perturbed plane wave mode and sometimes also referred to as “acoustic branch” due to analogy with solid-state physics. Electric field penetration into the polyhedrons is low, making the metamaterial behavior insensitive to substrate losses within the polyhedrons. The chapter presents a network-based topological framework for the systematic study of meta-materials, derived from the assumption that metamaterials are compound structures implementing dispersion. Using the network topology of the unit cell, a physical realization is synthesized, which offers compatibility with planar fabrication techniques at the price of anisotropic behavior.
