# Terahertz Wideband Filter Based on Sub-Wavelength Binary Simple Periodic Structure
## 3 Redundancy Analysis  
Due to manufacturing errors, the structural parameters of the terahertz wideband filter will affect the performance of the filter (i.e., 3-dB bandwidth and average diffraction efficiency in the filter band). It is necessary to study the redundancy of each structural parameter to ensure device performance. The effect of the period on the transmission efficiency at each filter frequency point is shown in Figure 3. When the duty ratio and the groove depth were fixed to the design value, we swept from 100 to 180 \(\upmu\)m, containing the design value of 129.817 \(\upmu\)m. Figures 3a and 3b show the effect diagram and the filter transmission spectrum. Figures 3c and 3d are graphs of the 3-dB bandwidth and the average transmission efficiency of each sampling point in the main lobe as a function of period. Figure 2: Optimal filtering effect. As shown in Figure 3c, when the grating period was more than 129.817 \(\upmu\)m, the 3-dB bandwidth of the filter dropped rapidly below 1.8 THz. When the grating period was 5.5 \(\upmu\)m less than 129.817 \(\upmu\)m, the 3-dB bandwidth of the filter dropped to 2 THz or less. It can be seen from Figure 3d that there was a slight increase in the grating period of 131 \(\upmu\)m, and the average transmission efficiency in the main lobe was a relatively flat straight line. Therefore, it can be considered that the grating period had a significant influence on the 3-dB bandwidth of the filter, but the average transmission efficiency within the inside lobe hardly changed around the value of 40%. When the period and groove depth were fixed to the design value and the duty ratio changed around the design value of 0.432, the effect on the transmission efficiency at each filter frequency point was as shown in Figure 4.  
Figure 4: _Cont._  
Figure 3: Effect of periodic variation on filter performance: (**a**) and (**b**) show the effect diagram and the filter transmission spectrum; (**c**) and (**d**) are graphs of the 3-dB bandwidth and the average transmission efficiency of each sampling point in the main lobe as a function of period. As shown in Figure 4c, when the duty ratio was less than 0.041, the 3-dB bandwidth of the filter dropped to less than 2 THz. Meanwhile, when the duty ratio was shifted by 0.041 or more, and the 3-dB bandwidth of the filter fell sharply below 1.8 THz. The graph shows a relatively gentle curve in Figure 4d when the average transmission efficiency in the main lobe was substantially above 40%. Therefore, the duty ratio shift had a significant effect on the 3-dB bandwidth of the filter, but it did not affect the average transmission efficiency in the main lobe of the filter. When the duty ratio was less than 0.041, the 3-dB bandwidth was above 2 THz--which is 15% less than that of the designed value of the ideal filter--and the average transmission efficiency in the filter main lobe was kept at about 40%. When the period and duty ratio were fixed to the design value 30.379 \(\upmu\)m and the groove depth changed, the effect on the transmission efficiency at each filter frequency point was as shown in Figure 5.  
When the grating period was kept at 129.817 \(\upmu\)m and grating duty ratio at 0.432, the grating groove depth was shifted around the ideal design value of 30.379 \(\upmu\)m, and the corresponding influence on the transmission efficiency at each filtering frequency point is shown in Figure 5.  
Figure 4: Effect of duty ratio variation on filter performance: (**a**) and (**b**) show the effect diagram and the filter transmission spectrum; (**c**) and (**d**) are graphs of the 3-dB bandwidth and the average transmission efficiency with different duty ratios. Figure 5: Effect of groove depth variation on filter performance: (**a**) and (**b**) show the effect diagram and the filter transmission spectrum; (**c**) and (**d**) are graphs of the 3-dB bandwidth and the average transmission efficiency with different groove depths.