# Sub-Diffraction Focusing Using Metamaterial-Based Terahertz Super-Oscillatory Lens
## 2 Materials and Methods
### Design and Fabrication
Figure 5d,e show the results of calculations using lenses with slit widths 10 um larger and 10 um smaller than the designed value. The upper graph shows the results using a lens with a slit width of 117.5 um, and the lower graph shows the results using a lens with a slit width of 137.5 um. Figure 5e shows the spot size relative to the direction away from the lens. As in Figure 5a,b, the spot intensity varies with the slit width but the location and size of the spot are almost the same, indicating that the slit width has little effect on the focal spot size. The depth of focus is also similar, with little effect of slit width. However, unlike the change in ring diameter, the focused intensity weakens as the slit width increases. This is expected because the diffraction caused by the slit is weakened as the slit width increases. Finally, the focusing ability of the lenses was compared by changing only the distance \(l\) between the rings, which is a lattice constant. Figure 5f shows the intensity distribution after light passes through the lenses when the distance \(l\) between the rings is either 20 um shorter (upper graph) or 20 um longer (lower graph) than the designed value. Figure 5g shows the spot size in the direction away from the lens, with the blue plot representing the results when the distance between the rings is shorter than the designed value and the red plot depicting the results when the distance between the rings is longer than the designed value. It can be seen that changing the distance between the rings does not affect the spot size. However, the positions where the spots are generated change depending on the spacing between the rings. The simulation results presented in Figure 5f,g are consistent with the Talbot distance formula, which shows that the focal length increases as  
Figure 5: Calculation results of the effect of the ring diameter, slit width, and distance between rings of the lens on hot spot generation: (**a**–**e**) simulated hot spots for different ring diameters; (**d**,**e**) hot spots and their sizes for different slit widths; and (**f**,**g**) results for different distances between rings. Upper graphs in (**a**,**d**,**f**) also show the intensity distribution after light passes through the lens when the parameter is shorter than the designed value, while the lower graphs depict the results when the parameter is longer than the designed value; (**b**,**e**,**g**) show the spot size along the z axis. the distance between the rings increases. The focal lengths obtained according to the Talbot distance formula are 7.6 mm when the distance \(l\) between the rings is 20 \(\upmu\)m shorter than the designed value and 8.2 mm when \(l\) is 20 \(\upmu\)m longer than the designed value. Since the circular patterns exhibited significantly better focusing efficiency than the square ones, we fabricated the lens with circular unit patterns. The fabricated super-oscillatory lens, which has a diameter of 101.6 mm, is shown in Figure 5(a) and the schematic of its cross-section is depicted in Figure 5(b). Figure 5(c) shows a microscopical image of the fabricated circular slit. The circular patterns were defined by photolithography on the surface of a 400 \(\upmu\)m thick glass substrate by depositing 10 nm thick chromium and 300 nm thick gold. Since gold does not adhere well to oxides such as glass, chromium was deposited as a buffer layer between the glass substrate and the gold layer. The thickness of the gold layer was intentionally set thicker than the skin depth for the opaque parts of the lens to sufficiently block THz waves.