## 2 Materials and Methods
Here we see no effect from either \(\mu_{x}\) or \(\mu_{z}\) due to the fixed direction of the magnetic field along the strip. However, a magnetic dipole response manifests with \(\mu_{y}\) via the oscillations of the light wave's magnetic field. In fact, it is this magnetic resonance which is precisely the desired effect that we hope to observe. The electric permittivity takes form with \(\varepsilon_{x}\) and \(\varepsilon_{z}\). It should be clear that with normal incidence measurements, the total anisotropy cannot be recovered. Let us now summarize the results provided by polarization:  
\[\varepsilon =\left[ \begin{array}{ccc}0&0&0\\ 0&\varepsilon_{y}&0\\ 0&0&0\\ \end{array} \right]+\left[ \begin{array}{ccc}\varepsilon_{x}&0&0\\ 0&0&0\\ 0&0&\varepsilon_{z}\\ 0&0&0\\ 0&\mu_{y}&0\\ 0&0&0\\ \end{array} \right], \tag{4}\]  
where the left matrices are sensed with TE polarization and the right matrices are sensed with TM polarization. It is only \(\varepsilon_{x}\) and \(\mu_{y}\) which display resonant behavior, while \(\varepsilon_{y}\) shows dilute metal characteristics, and \(\mu_{x}\) and \(\mu_{z}\) are simply unity. The z-component of the permittivity is not expected to be resonant in the visible spectrum, though its form via simulation will turn out to be that of a somewhat modified Drude function. There are, then, a total of four unknown parameters that must be modeled. For the TM resonant modes, both the permittivity and permeability functions have asymmetry of the resonance (see, for example [5; 18]). Because of this asymmetry, we choose a transversal optical longitudinal optical (TOLO) oscillator function [19] to describe these modes, rather than a classical Lorentzian. These take the form  
\[\varepsilon_{x}=A_{\varepsilon_{x}}\frac{\omega_{LO}^{2}-\omega^{2}-i\Gamma_{ LO}\omega}{\omega_{TO}^{2}-\omega^{2}-i\Gamma_{TO}\omega} \tag{5}\]  
and  
\[\mu_{y}=A_{\mu_{y}}\frac{\omega_{LO}^{2}-\omega^{2}-i\Gamma_{LO}\omega}{\omega _{TO}^{2}-\omega^{2}-i\Gamma_{TO}\omega} \tag{6}\]  
where, after matching, we find \(A_{\varepsilon_{x}}=0.11\), \(\omega_{LO}=4.5\) eV, \(\omega_{TO}=2.17\) eV, \(\Gamma_{LO}=1.5\) eV, and \(\Gamma_{TO}=0.3\) eV, while for \(\mu_{y}\), \(A_{\mu_{y}}=0.13\), \(\omega_{LO}=4.0\) eV, \(\omega_{TO}=1.77\) eV, \(\Gamma_{LO}=2.0\) eV, and \(\Gamma_{TO}=0.4\) eV. Here, \(\omega=hc/\lambda\) is the photon energy. For these dielectric functions to remain physical with \(\mathrm{Im}\{\varepsilon_{x}\}\geq 0\) and \(\mathrm{Im}\{\mu_{y}\}\geq 0\), the constraint \(\Gamma_{LO}-\Gamma_{TO}>0\) must be satisfied. Meanwhile, to model \"diluted metal\" for both \(\varepsilon_{y}\) and \(\varepsilon_{z}\), we use a Drude function of the form  
\[\varepsilon_{y,z}=\varepsilon_{\mathrm{ooy},z}-\frac{A_{y,z}\omega_{p}^{2}}{ \omega^{2}+i\Gamma_{y,z}\omega} \tag{7}\]  
where \(\omega_{p}=9\) eV and for \(\varepsilon_{y}\) we have \(A_{y}=0.07\), \(\Gamma_{y}=4\) eV, and \(\varepsilon_{\mathrm{ooy}}=3.5\), while for \(\varepsilon_{z}\) we have \(A_{z}=0.123\), \(\Gamma_{z}=1\) eV, and \(\varepsilon_{\mathrm{ooz}}=9\). It is interesting to note that without the large offset parameter, \(\varepsilon_{\mathrm{ooz}}\), for \(\varepsilon_{z}\) the Wood's anomaly peak will be hidden in transmission spectra. The details regarding the exact spectral position, amplitude, and sharpness of each resonance and the parameters for the dielectric functions are initially unknown. Therefore, an iterative technique must be performed until an acceptable match has been made for both normal incidence transmission as well as for each angle of incidence and polarization of the spectral angular map. As previously mentioned, TE polarization is employed to uniquely determine \(\varepsilon_{y}\). As an example, for this case there are three parameters from the Drude relationship above that must be found. Values for each parameter are initially chosen with some physical justification, and subsequently the simulation is completed for all angles of incidence.