Inversion of Fresnel equations for the determination of effective parameters of periodic resonant and non-resonant metamaterials

The aim of this paper is to study the suitability of the inversion of Fresnel's equations for the calculation of effective parameters of resonant metamaterials. The validity of thus calculated electromagnetic parameters has been discussed by many authors. The first step of our study is to ensure that there is no anomaly due to numerical ambiguities in the inversion procedure. To this end, three different algorithms will be developed. The second step is to show the suitability of these inversion procedure to analyze various periodic media. Metamaterials having different electromagnetic responses will be treated. When the structure is resonant, peculiar frequency variation of the effective parameters is observed. Finally, the Split-Ring Resonator - SRR (main constituent of negative refractive index metamaterial) will be analyzed and an analogy between the results obtained for other resonant inclusions will be made.