When creating various microwave devices using multiresonant metamaterials and radio-absorbing coatings based on them, it is assumed that the metamaterial is placed in the form of a plane-parallel layer on a metal substrate. Therefore, for the efficient design of such metamaterials, ensuring the necessary electrophysical parameters and their periodic quasi-homogeneity, appropriate measurement tools are required to assess their quality during the design and production processes. This paper substantiates a generalized method for locally testing the complex dielectric and magnetic permeabilities, as well as the thickness of flat-layered metamaterial samples with an arbitrary number of resonant regions on a metal substrate. In the developed method, the electrophysical parameters of the metamaterial are represented as parametric functions of frequency in accordance with the generalized Drude–Lorentz dispersion models for multiresonant metamaterials, and their evaluation is carried out by minimizing the objective function constructed from the discrepancy between the experimental and calculated theoretical values of attenuation coefficients of the surface electromagnetic wave field on a discrete frequency grid. To identify resonant regions of the metamaterial, the method includes an analysis of the frequency dependence of the surface electromagnetic wave field attenuation coefficient over a wide frequency band. The determined frequency values corresponding to the resonant regions are adopted as initial approximations for the Drude–Lorentz dispersion models when minimizing the objective function. To improve the stability of the inverse problem solution, a regularization of the solution based on a parametric optimization method is introduced into the objective function. To experimentally validate the method, a sample of a flat-layered dual-resonance metamaterial based on DBSRR (dual-band split-ring resonator) elements with negative refraction regions in the frequency ranges of 7.16–8.19 GHz and 10.1–10.9 GHz was studied. Experimental verification showed that the local values of the effective electrophysical parameters of the studied metamaterial differ from the calculated ones by no more than 10%.
Kazmin et al. (Sun,) studied this question.