Circuit theory approach to the design of metamaterials

In this contribution we show that space-discretising numerical schemes can be considered the unifying framework behind metamaterials. Physical implementations of these schemes which obey the condition that the unit cell is small compared to the wavelength lead to either Drude or Lorentz dispersion with their immanent properties and hence limitations. This perspective on metamaterials as being physical implementations of space-discretising schemes is formulated for 1D, 2D, 3D supporting one polarisation and 3D supporting two polarisations. Two isotropic three-dimensional metamaterials are presented which are derived using this approach. Approaches to mass fabrication of maximally-symmetric 3D metamaterials are presented.