## 3 Analysis and Results
### Demultiplexer Formed by the MIM Waveguide with Multiple Output Channels  
With a bias voltage capable of tuning the transmission spectrum of an LC-infiltrated MIM waveguide, it is feasible to design a reconfigurable demultiplexer based on the MIM waveguide as long as its multiple output channels are properly designed. To achieve this, we need to make use of the variation of resonant frequencies of the LC-infiltrated waveguide owing to the change of the bias electric field of the LC. In Section 3.1, we concluded that under different bias electric fields of the LC, the field distributions of the mode \(m\) can be the same given that the operating frequency satisfies Equation (8). Therefore, the location of the output channel corresponding to the \(m\)-th mode can be chosen to be the location where the mode \(m\) has a peak field distribution. By allocating the output channel at this location, the maximum field will exist here when the operating frequency of the MIM waveguide satisfies Equation (8). Thus, the spectrum of the output channel set at this location will have a peak at the frequency \(f_{FP,m}\) corresponding to the resonant frequency of the \(m\)-th mode. Moreover, by adjusting the bias electric field, the frequency of the spectral peak of the output channel can be changed. Therefore, the passband of the output channel can be tuned by the bias electric field of the LC. Following the same principle, multiple output channels on the MIM waveguide can be set. Their passbands can be controlled simultaneously by adjusting the bias electric field of the LC, ultimately forming a tunable demultiplexer with multiple output channels. According to the above analysis, the output-channel location should be set at the positions where the maximum field of the mode \(m\) occurs. It is worth noting that the number of output channels is set to three to avoid too small intervals between them and prevent unwanted mutual couplings. Figure 6 shows the allocation of the output channels of the MIM waveguide whose dimension is the same as  
Figure 5: Normalized \(\mid H_{y}\mid\) distributions in the MIM waveguide with zero-biased electrical field of the LC: (a) Mode 1; (b) Mode 2; (c) Mode 3; (d) Mode 4.  
that shown in Figure 2. With three output channels etched on the upper copper plate, the voltage is applied between the four segments of the upper copper plate and the lower copper plate. Here, three output channels corresponding to modes 2, 3 and 4 are deployed. Their coordinates along the \(z\) axis are set to 179 \(\upmu\)m, 120 \(\upmu\)m and 99 \(\upmu\)m, respectively. According to the resonant frequencies from low to high, the ports at 179 \(\upmu\)m, 120 \(\upmu\)m and 99 \(\upmu\)m are named channels 1, 2 and 3, respectively. In order to minimize the cross talk between these output channels, the locations of output channels have been chosen delicately. In this way, the amplitude of transmission spectrum obtained by one output channel can be maximized at its resonant frequency while those of other output channels are minimized as much as possible. Following this criterion, the values of \(n\) in Equation (9) are all set to 1 for channel 1, 2 and 3 (or mode 2, 3 and 4). Then, the locations of the channels are meticulously tuned according to multiple simulations. Finally, the coordinates of the output channels 1, 2 and 3 along the \(z\) axis were optimized to be 179 \(\upmu\)m, 120 \(\upmu\)m and 99 \(\upmu\)m, respectively. For the output channels, they have the same width \(D\) that equals 0.25 \(\upmu\)m, which is much smaller than the width of the main channel. It should be noted that the voltage across the sidewalls of all output channels are zero. However, since the output channels are much narrower compared to the main channel, those channels infiltrated with the zero-biased LC have little effect on the field distribution of the main channel.