## 2 Materials and Methods
These spectra are collected for each angle of incidence and used later for normalizing procedures. Green and red lines represent TM and TE polarizations, respectively. The dashed variants show the stability of each after one hour. strip are those of the real sample, while the effective parameters of the strips are what we seek, and are also the only set of unknown variables. A unique ability of MIST is that it allows the calculation of any arbitrary diffraction order as well as anisotropic magnetic behavior. In this way, we can provide any tabulated dispersion for a range of frequencies for all permittivity and permeability functions. We briefly mention that, for inclined illumination and the wavelengths we use, it is only necessary to analyze a single diffraction order. Namely \(m=-1\), the first order, contributes to a meaningful relative intensity at the output. Minus is due to geometrical convention. The other orders either do not exist, or their efficiencies are negligible--as is the case for orders higher than the first order. Any arbitrary complex function for both \(\epsilon(\lambda)\) and \(\mu(\lambda)\) can be supplied to MIST. Typically, in anisotropic media the electric (magnetic) susceptibility and therefore permittivity (permeability) functions exist in the form of a second rank tensor. Each function will uniquely have three nonzero effective medium components, namely:  
\[\varepsilon=\left( \begin{array}{ccc}\varepsilon_{x}&0&0\\ 0&\varepsilon_{y}&0\\ 0&0&\varepsilon_{z}\end{array} \right)\qquad\text{ and }\qquad\mu=\left( \begin{array}{ccc}\mu_{x}&0&0\\ 0&\mu_{y}&0\\ 0&0&\mu_{z}\end{array} \right), \tag{3}\]  
where each component is a complex and frequency dependent quantity. The off-diagonal components are zero due to the geometry of the grating. Figure 4 shows the coordinate system being used. If only normal incidence transmission is utilized, it is not guaranteed that all the components of the effective permittivity and permeability of the strips are involved. We find that there are several functions that will provide a suitable match to the transmission data. Additionally, the z-components of the permittivity and permeability are concealed at normal incidence, and we only begin to noticeably detect their effect at larger angles of incidence. Only when the normal incidence matching is used in conjunction with the incline illumination results can we obtain the correct set of effective optical properties of the system. We next discuss the physical grounds for the accepted fitting formulas on the six unknown components. Different polarizations and incident angles are used to isolate and better capture specific components of the effective permittivity and permeability. Moreover, we find there is a significant polarization dependency on the output, due to the strong resonance occurring with the TM polarization and lack of resonance with TE polarization. Figure 4 illustrates that when the E-field lies along the strip axis, this TE-polarized wave is unable to produce any resonant effects, and thus the strip will behave as a diluted metal. In this case the observable permeability is unity, hence, \(\mu_{x}=\mu_{z}=1\). We note that by keeping the x- and z-components of the effective permeability, nonmagnetic response is an enforced condition. Meanwhile the observable component when using TE polarization will be strictly that of \(\varepsilon_{y}\), though as we shall see it differs moderately from the standard EMT of a dilute metal. Hence by using TE polarized light, we can isolate the y-component of the permittivity. Figure 4: Representation of the actual trapezoidal shape of the grating due to fabrication limitations. A TM-polarized beam is incident at an incline; depending on frequency, either a symmetric (**Left**) or antisymmetric (**Right**) mode may be excited. Note that the strips are still considered to be infinite in the y-direction. On the other hand, when the incident wave is TM polarized, both symmetric and antisymmetric resonant current modes may be excited.