The dispersion of the effective permittivity of a dielectric-composite slab is analyzed in a quasi-dynamic range using the simulated transmission and reflection data from the slab illuminated by an obliquely incident plane wave. Based on the retrieval results, the procedure for finding the dynamic trust region of the quasi-static Lord Rayleigh estimate for the effective permittivities of such composites is then developed. According to this process, the upper frequency limit of this trust region is numerically determined by an interpolation function. The proposed function of the inclusion area fraction p and relative permittivity ɛi is demonstrated as a good predictor within the ranges 0.1 ≤ p ≤ 0.5 and 10 ≤ ɛi ≤ 60. It is further shown that within the above ranges the effective wavelength inside the material should be at least 33 times the edge length of the unit cell, in order to ensure that the defined relative difference between the retrieved effective permittivity and the quasi-static estimate is not larger than 1%.
Qi, J., Kettunen, H., Wallén, H., & Sihvola, A. (2011). Different homogenization methods based on scattering parameters of dielectric-composite slabs. Radio Science, 46(5), 1-7. https://doi.org/10.1029/2010RS004622