Computing the effective complex permittivity of corrugated slabs by inverse scattering under oblique incidence

The numerical method presented herein attempts to equate the scatterer under test to a prescribed equivalent scatterer by adjusting some geometrical and/or constitutive parameters of the equivalent scatterer to reproduce the given values of plane-wave scattering coefficients of the scatterer under test as a function of the incidence angle. Hence, the equivalence is based on the assumption that two different scatterers could have exactly the same curves of plane-wave scattering coefficients as a function of the incidence angle. However, this is not generally the case because to be able to adjust independently all eight variables of the plane-wave scattering coefficients, namely the four magnitudes |R_TM|, |R_TE|, |T_TM|, |T_TE|, and the four phases angR_TM, angR_TE, angT_TM, angT_TE, would require at least eight degrees of freedom for each desired value of the incidence angle. In this paper, the equivalent scatterer is a uniform homogeneous isotropic slab, and the two degrees of freedom are the relative permittivity epsiv´_r and the conductivity sigma. Hence, it is not always possible to make the values of plane-wave scattering coefficients for the uniform homogeneous isotropic slab be exactly equal to the given values of plane-wave scattering coefficient as a function of the incidence angle by adjusting only the values of epsiv´_r and sigma.