The signs of the imaginary parts of the effective permittivity and permeability in metamaterials

It has been shown that the Lorentz model often used to describe the dispersive behavior of the complex shaped elements used to construct metamaterials (such as SRRs and strip wires) does not permit the imaginary parts of the permittivity or permeability to be negative in these structures. By considering a structure whose effective parameters could be calculated both analytically and from numerical simulations the retrieval technique could be put to scrutiny and it was shown that in the case of an array of dielectric spheres the retrieval technique predicted a negative imaginary part of the effective permittivity as a result of numerical error in the simulations. The permeability, index of refraction, and S-parameters on the other hand were still a good match. Therefore, when using the retrieval technique caution must be exercised when calculating the permittivity or permeability as these can be problematic.