## 2 Formulation  
The time-harmonic Maxwell's equations in a linear, source-free, electrically and magnetically anisotropic dispersive medium with \(e^{i\omega t}\) time dependence are as follows:  
\[\
abla\times\tilde{\mathbf{E}} =-j\omega\mu_{0}\overline{\overline{\mu}}(\omega)\tilde{\mathbf{ H}}, \tag{1a}\] \[\
abla\times\tilde{\mathbf{H}} =j\omega e_{0}\overline{\tilde{\mathbf{E}}}(\omega)\tilde{\mathbf{ E}}, \tag{1b}\]  
where the tilde on the fields denotes the frequency domain, and the frequency-dependent relative permittivity tensor \(\overline{\tilde{\mathbf{e}}}(\omega)\) is described by the following general expression:  
\[\overline{\tilde{\mathbf{e}}}(\omega)=\left( \begin{array}{ccc}\varepsilon_ {xx}(\omega)&\varepsilon_{xy}(\omega)&\varepsilon_{zz}(\omega)\\ \varepsilon_{yx}(\omega)&\varepsilon_{yy}(\omega)&\varepsilon_{yz}(\omega)\\ \varepsilon_{zx}(\omega)&\varepsilon_{zy}(\omega)&\varepsilon_{zz}(\omega) \end{array} \right). \tag{2}\]  
Similarly, the relative permeability tensor \(\overline{\overline{\mu}}(\omega)\) is given by  
\[\overline{\overline{\mu}}(\omega)=\left( \begin{array}{ccc}\mu_{xx}(\omega) &\mu_{xy}(\omega)&\mu_{xz}(\omega)\\ \mu_{yx}(\omega)&\mu_{yy}(\omega)&\mu_{yz}(\omega)\\ \mu_{zx}(\omega)&\mu_{zy}(\omega)&\mu_{zz}(\omega)\end{array} \right). \tag{3}\]  
In this work, we adopt the CCPR model for the description of the dispersive elements \(\varepsilon_{\alpha\beta}(\omega)\), \(\mu_{\alpha\beta}(\omega)\). We explicitly present the formulation for electric anisotropic dispersive media, according to which the complex relative permittivity of the tensor elements is given by [10]  
\[\varepsilon_{\alpha\beta}(\omega)=\varepsilon_{\omega,\alpha\beta}+\frac{ \sigma_{\alpha\beta}^{e}}{j\omega e_{0}}+\sum_{p}^{M_{\alpha\beta}}\left( \frac{c_{p,\alpha\beta}}{j\omega-a_{p,\alpha\beta}}+\frac{c_{p,\alpha\beta}^{ *}}{j\omega-a_{p,\alpha\beta}^{*}}\right), \tag{4}\]  
where \(\varepsilon_{\omega,\alpha\beta}\) is the relative permittivity at infinite frequency, \(\sigma_{\alpha\beta}^{e}\) is the static conductivity, \(\alpha,\beta\) denote \(x,y\) and \(z\) and \(*\) represents the complex conjugate. The tensor elements \(\mu_{\alpha\beta}(\omega)\) in the case of anisotropic magnetic materials are described by the same model, and the formulation follows the same steps described below, with Equations (5)-(15) referring to the magnetic instead of the electric field. By the proper selection of the coefficients in Equation (4), the CCPR model incorporates all the standard dispersion models (see Table 1), while also several more advanced models that have been recently proposed for metals, such as the Drude-critical points [15] and modified Lorentz [16]. As a consequence, it can also handle other dispersion models, which can be approximated with those in Table 1, such the Cole-Cole and Havriliak-Negami models that characterize certain biological media and polymers [17; 18]. Furthermore, one of the strengths of the proposed formulation lies in the ability of the CCPR model to accurately fit experimental data on material permittivity using the vector fitting technique [19; 20] or other related algorithms [21]. The \(x\)-component of Equation (1b) is written as  
\[ \begin{split}&(\
abla\times\mathbf{\hat{H}})_{x}=\\ & j\omega\varepsilon_{0}\varepsilon_{\infty,xx}\tilde{E}_{x}+ \sigma_{xx}^{\epsilon}\tilde{E}_{x}+j\omega\sum_{p=1}^{M_{xx}}\Bigl{(}\tilde{ Q}_{pxx}+\tilde{Q}_{pxx}^{\prime}\Bigr{)}\\ &+j\omega\varepsilon_{0}\varepsilon_{\infty,xy}\tilde{E}_{y}+ \sigma_{xy}^{\epsilon}\tilde{E}_{y}+j\omega\sum_{p=1}^{M_{xy}}\Bigl{(}\tilde{ Q}_{pxy}+\tilde{Q}_{pxy}^{\prime}\Bigr{)}\\ &+j\omega\varepsilon_{0}\varepsilon_{\infty,xz}\tilde{E}_{z}+ \sigma_{xz}^{\epsilon}\tilde{E}_{z}+j\omega\sum_{p=1}^{M_{xz}}\Bigl{(}\tilde{ Q}_{pxz}+\tilde{Q}_{pxz}^{\prime}\Bigr{)}\end{split}