# Tunable Mid-Infrared Graphene Plasmonic Cross-Shaped Resonator for Demultiplexing Application
## 3 Two-Channel Demultiplexer and Analysis  
By modifying the cross-shaped resonator described in previous section, we propose and analyze a two-channel plasmonic demultiplexer in this section. The 2D view of two-channel plasmonic demultiplexer is depicted in Figure 4a. Transmission spectra of the two output channels of the demultiplexer are presented in Figure 4b-e. The differences of the resonators of Figure 4b-e are respectively the lengths, Fermi energies, widths, and angles. Other parameters are the same as reported in Table 1. Electric field profiles of the proposed demultiplexer for the resonators with different lengths in the resonance wavelengths of \(\lambda\)=6.8 \(\upmu\)m and \(\lambda\)=8.05 \(\upmu\)m are respectively presented in Figure 4f,g.  
Figure 4: \(Cont.\)Figure 4: _Cont._  
Cross talk \(C\), between the two channels of the proposed demultiplexer of Figure 4a is calculated by [5]  
\[C\ =\ 10\ log\bigg{(}\frac{P_{o}}{P_{i}}\bigg{)} \tag{8}\]  
where \(P_{i}\) is the power of interested channel and \(P_{o}\) is the power of another channel. The crosstalk values of the proposed two-channel demultiplexer of Figure 4a for different states of Figure 4b-e are given in Table 3.  
The maximum transmission ratio, the full width at half maximum (FWHM), the cross talk, and tunability without need to re-fabricate the structures of some other works are reported and compared with our work in Table 4. References [24; 40; 41; 42; 43; 47; 48] did not report demultiplexing application of their proposed structures, so we leave dash for their cross talks in the table. References [41; 42] are absorbers with absorption spectra and they do not contain transmission spectra. Transmission spectra and FWHM are not reported in [44]. FWHMs in [24; 26; 39; 45; 46; 47] are not reported and we calculated them approximately. Transmission spectra of [40] contains some ripples and estimation of FWHM is  
Figure 4: **(a)** 2D top view (side view is the same as Figure 1b) of the MIR two-channel demultiplexer. Transmission spectra of the output ports of the proposed two-channel demultiplexer for the resonators with different (**b**) lengths (channels 1 and 2 with the lengths of L\({}_{1}\) = 80 nm and L\({}_{2}\) = 100 nm), (**c**) Fermi energies (channels 1 and 2 with the Fermi energies of E\({}_{1}\) = 0.6 eV and E\({}_{2}\) = 0.8 eV), (**d**) widths (channels 1 and 2 with the widths of \(W_{1}\) = 20 nm and \(W_{2}\) = 30 nm), and (**e**) angles (channel 1 and 2 with the angles of \(\theta_{1}\) = 40\({}^{\circ}\) and \(\theta_{2}\) = 60\({}^{\circ}\)). \(|E|\) Field profiles of the proposed two-channel demultiplexer for the resonators with different lengths of L\({}_{1}\)=80 nm and L\({}_{2}\)=100 nm in the resonance wavelengths of (**f**) \(\lambda\) = 6.8 \(\upmu\)m and (**g**) \(\lambda\) = 8.05 \(\upmu\)m.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cross Talk (dB)** & **Channel** & **1** & **2** \\ \hline \multirow{2}{*}{Figure 4b} & 1 & - & \(-\)48.30 \\ \cline{2-4}  & 2 & \(-\)33.64 & - \\ \hline \multirow{2}{*}{Figure 4c} & 1 & - & \(-\)25.67 \\ \cline{2-4}  & 2 & \(-\)42.24 & - \\ \hline \multirow{2}{*}{Figure 4d} & 1 & - & \(-\)22.38 \\ \cline{2-4}  & 2 & \(-\)34.26 & - \\ \hline \multirow{2}{*}{Figure 4e} & 1 & - & \(-\)11.63 \\ \cline{2-4}  & 2 & \(-\)7.12 & - \\ \hline \hline \end{tabular}
\end{table}
Table 3: Cross talk values of the proposed demultiplexer in dBnot possible. Even though some of the references have better transmission ratio or FWHM than our resonator, the proposed resonator is dedicated for demultiplexing application. Having better cross talk and a wide single mode resonance wavelength range are important parameters for demultiplexing application. These two items are improved in our demultiplexing structure compared to the literature.