Analysis of Multilayered Metamaterial Structures with Frequency Dependent Constitutive Parameters Using Wave Matrices Approach

Combined with the Kramers-Kronig (KK) extraction method, the wave matrices approach is used in this work to compute the scattering parameters of metamaterial unit-cell consisting of three stacked layers along the z-direction. The proposed semi-analytical approach is taking into account the frequency dependence of the constitutive parameters
$(\varepsilon_{r}(\omega)$
and
$\mu_{r}(\omega))$
of each layer and the loss introduced when the wave traveling through each one. The validity of this method is proved through full wave simulations and analytical calculations, where the comparison between the two results are in good agreement. This semi-analytical approach could also be used to impose some necessary conditions on the structure geometrical parameters in order to maximize and/or minimize the reflection and/or the transmission coefficients.