## 3 Results
\begin{table}
\begin{tabular}{l l l l l} \hline \hline  & \multicolumn{2}{l}{First slab: \(np=1\), \(d_{eff}=180\) nm} & \\ \hline \(\epsilon_{\infty}\) & 1.8 & \(\mu_{\infty}\) & 1.0 \\ \(\epsilon_{s,1}\) & 2.0 & \(\mu_{s,1}\) & 1.3 \\ \(\omega_{oe,1}\) & 2\(\pi\)-0.695 PHz & \(\omega_{om,1}\) & 2\(\pi\)-0.7 PHz \\ \(\gamma_{e,1}\) & 0.08 PHz & \(\gamma_{m,1}\) & 0.05 PHz \\ \hline  & \multicolumn{2}{l}{Second slab: \(np=2\), \(d_{eff}=300\) nm} & \\ \hline \(\epsilon_{\infty}\) & 1.8 & \(\mu_{\infty}\) & 1.0 \\ \(\epsilon_{s,1}\) & 2.5 & \(\mu_{s,1}\) & 1.8 \\ \(\epsilon_{s,2}\) & 2.0 & \(\mu_{s,1}\) & 1.3 \\ \(\omega_{oe,1}\) & 2\(\pi\)-0.695 PHz & \(\omega_{om,1}\) & 2\(\pi\)-0.7 PHz \\ \(\omega_{oe,2}\) & 2\(\pi\)-0.895 PHz & \(\omega_{om,2}\) & 2\(\pi\)-0.899 PHz \\ \(\gamma_{e,1}\) & 0.09 PHz & \(\gamma_{m,1}\) & 0.07 PHz \\ \(\gamma_{e,2}\) & 0.08 PHz & \(\gamma_{m,2}\) & 0.05 PHz \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters for the Lorentzian model adopted in this study. Figure 1: Path \(\gamma(\omega)\) traced by Equation (8) on the complex punctured plane \(\hat{\mathbb{C}}\) for the slab with \(d_{eff}=180\) nm. Green diamond marker: path starting point, \(\omega=0\) Hz. Red diamond marker: path end point, \(\omega=1\) PHz. \begin{table}
\begin{tabular}{l l l l l} \hline \hline \(n_{s}\) & \multicolumn{2}{l}{**PE**} & \\ \multicolumn{1}{c}{**PUNWOS**} & \multicolumn{1}{c}{**K-K**} & \multicolumn{1}{c}{**PUNW\({}_{KK}\)**} & \multicolumn{1}{c}{**PUNW\({}_{HT}\)**} \\ \hline
512 & 303.88 & 13.97 & \(1.51\times 10^{-3}\) & \(1.51\times 10^{-3}\) \\
1024 & 260.49 & 13.67 & \(1.11\times 10^{-3}\) & \(1.11\times 10^{-3}\) \\
2048 & 130.14 & 13.61 & \(2.63\times 10^{-3}\) & \(2.63\times 10^{-3}\) \\
4096 & \(2.01\times 10^{-3}\) & 13.63 & \(2.01\times 10^{-3}\) & \(2.01\times 10^{-3}\) \\ \hline \(n_{s}\) & \multicolumn{2}{l}{**_t_** (s)} & \\ \multicolumn{1}{c}{**PUNWOS**} & \multicolumn{1}{c}{**K-K**} & \multicolumn{1}{c}{**PUNW\({}_{KK}\)**} & \multicolumn{1}{c}{**PUNW\({}_{HT}\)**} \\ \hline
512 & 0.25 & 0.29 & 0.35 & 0.34 \\
1024 & 0.28 & 0.42 & 0.34 & 0.33 \\
2048 & 0.26 & 1.01 & 0.54 & 0.69 \\
4096 & 0.33 & 2.92 & 1.16 & 0.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Percentage Error (PE) and computational time t for the slab with \(d_{eff}=180\) nm. in the cases of the \(\text{PUNW}_{KK}\) and \(\text{PUNW}_{HT}\) methods, it is already factually negligible. In correspondence to \(n_{s}=1024\), the value of this parameter related to the \(\text{PUNW}_{HT}\) and the \(\text{PUNW}_{KK}\) methods is still factually insignificant, whereas in the cases of the \(\text{PUNWOS}\) and K-K methods, it turns out to be comparable to the previous case. While increasing to \(n_{s}=2048\), the above trend remains stationary for all methods. Finally, for \(n_{s}=4096\), we have three unnrapping methods (\(\text{PUNWOS}\), \(\text{PUNW}_{KK}\) and \(\text{PUNW}_{HT}\)) that provide a factually insignificant PE, whereas we have no improvements for the PE in the case of the K-K method. As indicated by the PE parameter, values reported in Table 2 are confirmed by the results shown in Figure 2, which reports the plot of the retrieved refractive index \(n_{eff}(\omega)\) compared with the exact refractive index \(n_{ex}(\omega)\) for the four recovering methods for all the considered \(n_{s}\) values. Figure 3 shows the sequence of \(p\) integers needed to give continuity to \(arg_{\pi}(\cdot)\) provided by \(\text{PUNWOS}\), \(\text{PUNW}_{HT}\), and \(\text{PUNW}_{KK}\) for \(n_{s}=2048\). The high PE related to the \(\text{PUNWOS}\) method is clearly due to its incorrect calculation of the \(p\) sequence until an adequate number of sample points \(n_{s}\) is used. Figure 4 shows path \(\gamma(\omega)\) traced by Equation (8) for the slab with \(d_{eff}=300\) nm. This last case we analyzed is characterized by a double pole Lorentzian model for its pair \((\varepsilon_{r}(\omega),\mu_{r}(\omega))\).