This study is focused on how to obtain the effective or equivalent properties of inhomogeneous materials, which, contrary to the usual metamaterials, are assumed to possess only a sandwichlike form of heterogeneity. More specifically, the aim is to see how the method of inversion, and associated type and amount of data, condition the outcome of the inversion, notably as concerns the possibility or not of exotic features such as simultaneous negative permittivity and permeability in certain frequency intervals. Two inversion schemes are considered and compared: the Nicolson-Ross-Weir (NRW) scheme and an optimization scheme. The adopted form of the optimization scheme provides only numerical retrievals, but it applies to any number of far-field data couples, which fact makes it a useful tool for determining whether the retrieved properties of an inhomogeneous material really are independent of the angle of incidence as is required for effective properties. It is shown, via the optimization scheme, that the apparently infinite number of solutions predicted by the NRW scheme is reduced to a single solution-closest to the predictions of a mixture model-when the constraint of independence with respect to angle of incidence is invoked. Moreover, this solution exhibits none of the exotic features of the properties of the usual metamaterials except temporal dispersion and loss even when the component materials of the inhomogeneous layer are neither dispersive nor lossy.
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