# Sub-Diffraction Focusing Using Metamaterial-Based Terahertz Super-Oscillatory Lens
## 3 Results and Discussion  
The experimental results are shown in Figure 8. The normalized intensity distribution (Figure 8a) by maximum intensity through the fabricated lens confirms that the hot spots repeatedly appear along the direction perpendicular to the lens. The first and second hot spots appear around z = 8 and 16 mm, respectively. The distance between the hot spots is almost the same as the calculated Talbot distance of 7.9 mm, confirming that the proposed lens focuses the THz wave as desired. Figure 8: \(Cont.\)  
Figure 7: Schematic of the experimental setup. The spot size (Figure 8b) along the direction perpendicular to the lens agrees with the calculation results in Figure 3a. Here, the spot size refers to the focal spot area where the intensity remains at least more than 50% of the intensity at the center of the spot. In Figures 8b and 6c, the gray-shaded regions represent the distances where the terahertz wave is not focused, while the non-shaded ones represent the distances at which the focal spots are generated. In the non-shaded regions in Figure 8b, it can be clearly observed that the experimentally obtained size of the hot spots is close to the calculation result. The graph shows that the THz beam is focused at z = 7.5 mm and the spot size is 2.01 mm. However, the THz waves seem to be not well-focused between hot spots, contrary to the calculated results. This is most likely due to the resolution of the probe antenna with a 2.1 mm aperture diameter, which is significantly larger than the spatial resolution (0.01 \(\upmu\)m) used in the calculations. The other noticeable difference between the calculated and experimental results shown in Figure 8b is the very weak intensity between the hot spots of the fabricated SOL. Since this deviation between simulations and actual measurements only occurs at the weak intensity points, this does not pose a major problem when the lens is used for applications, such as product inspection, because only the points of high intensity would be used for measurements. Figure 8c shows the intensity distribution normalized to the intensity at z = 8 mm, where the red line represents the calculated results, and the blue dots represent the experimental results. The simulations show that the intensity of the first spot is about the same as the intensity of the second spot. However, the experimental results show that the second spot is slightly more intense. This could be due to either a slight lens tilt relative to the incident wave or the intensity distribution of the incident wave. The calculations were performed for an ideal plane wave, but the intensity distribution of the beam used in the experiments is Gaussian. The DOF is also an important parameter in lens performance. Figure 8c shows that the experimental DOF values (2.3 mm for the first spot and 2.2 mm for the second spot) are more-or-less consistent with the calculation values (2.1 mm for the first spot and 2.45 mm for the second spot). These results also show that the resolved spot size at around z = 8 mm from the SOL is 2.01 mm (0.67\(\lambda\)). Since the diffraction limit of a conventional lens is 2.46\(\lambda\), it is demonstrated that the SOL can focus light to about 30% of the spot size by a conventional lens, or 70% beyond the diffraction limit. Figure 8d shows the normalized intensity on x = 0 mm or y = 0 mm at z = 8 mm, and this shows that the spot is circularly focused when viewed in the xy plane. Thus, with the SOL fabricated for 0.1 THz, we were able to realize a lens that can focus light beyond the diffraction limit while maintaining a depth of focus equivalent to that of a conventional lens [33]. Figure 8: Experimental results: (**a**) intensity distribution through the SOL; (**b**) spot size: red line (calculation) and blue dots (experimental); (**c**) normalized intensity along the z direction; and (**d**) normalized intensity on x = 0 mm or y = 0 mm at z = 8 mm. Due to the characteristics of this lens, the focal size and focal length are affected by the frequency of the incident beam.