Invariance of parameter identification in multiscales of meta-atoms in metamaterials

The concept of metamaterials has led to extraordinary schemes of wave propagation, which has been verified using various meta-atoms, constituent units of metamaterials, as well as applied to a number of categories in physics. Although its definition clarifies the maximum size of meta-atoms as a fraction of one wavelength, the size may vary by several orders, like from millimeters (‘macroscopic level’) to atomic scales (‘microscopic level’) for microwaves. This review surveys several patterns of parameter combinations, like permittivity and permeability in electromagnetic metamaterials, which have been achieved at either macroscopic or microscopic levels, with the similar analogy under the concept of metamaterials. Various experimental and theoretical efforts reported so far and shown here verify that the parameter identification of these values (permittivity, permeability, and refractive index) is independent of meta-atom sizes, with importance of spatial integration procedure on the order of a wavelength