By definition, metamaterials are realized as lattices whose periodicity is assumed to be much smaller than the wavelength. However, it is important that, though small, the periodicity is not negligible with respect to the wavelength. For this reason, if one formally introduces constitutive parameters for such regime, they will not be measurable response functions, and it will not be possible to use them for a sample of other dimensions or for a sample excited in another way. In other words, such formally introduced material parameters cannot satisfy the conditions of locality. In 2007, Tretyakov and colleagues explained the physical meaning of calculated material parameters, different from the meaning of the local constitutive parameters
