# Sub-Diffraction Focusing Using Metamaterial-Based Terahertz Super-Oscillatory Lens
## 2 Materials and Methods  
### Design and Fabrication  
Metamaterial is a technology that uses periodic patterns smaller than electromagnetic wavelengths to achieve unique outcomes. When a plane wave is normally incident on a lens with evenly arranged circular slits, the transmitted wave pattern causes no phase delay. However, when five circular slits are arranged in a crisscross pattern on the lens, as shown in Figure 2a, a phase delay occurs, and the waves are focused at focal length from this pattern. This can be explained by the diffraction effect, otherwise called the Talbot effect [31]. The grating image is repeated at regular distances away from the grating plane when the plane wave is incident on the periodic diffraction grating. The distance at which a spot is generated can be expressed using the Talbot distance \(Z_{T}\) as follows:  
\[Z_{T}=\lambda/\left(1-\sqrt{\left(1-\lambda^{2}/a^{2}\right)}\right) \tag{3}\]  
where \(a\) is the diffraction grating period. The focal length can be adjusted by varying the wavelength and unit slit spacing. We designed two pattern types, circular and square, for subwavelength focusing with 0.1 THz (\(\lambda\) = 3 mm). Figure 2 shows the schematic of the lens comprising circular and square unit patterns (Figure 2a,b, respectively). The yellow sections are nontransparent to THz waves. For an effective metamaterial, the unit slit must be sufficiently small relative to the wavelength. Thus, we designed the parameter \(D\), which is the diameter of the circular patterns or the diagonal of the square patterns, as 690 \(\upmu\)m (approximately 0.23\(\lambda\)), which is sufficiently small compared to 3 mm. The width of these patterns is 127.5 \(\upmu\)m (approximately 0.04\(\lambda\)) and the distance \(l\) between each unit slit is 1275 \(\upmu\)m. The distance \(A\) between the centers of each unit pattern was 3875 \(\upmu\)m. With these dimensions, the focal length of the lens is 7.9 mm by design, as determined using Equation (3). The performance of the aforementioned SOL was elucidated through calculations according to the configuration illustrated in Figure 1 and by considering a circularly polarized ideal plane wave as the incident THz beam. The results of the simulations are shown in Figure 3. The intensity distribution profiles using square and circular slits (Figure 3a,b, respectively) exhibit spots generated at the same focal length of approximately 8 mm. In  
Figure 2: Schematic of the lens: (**a**) circular unit pattern and (**b**) square unit pattern, where \(l\) is the distance between each unit slit and \(D\) is the diameter (for circular patterns) or the diagonal (for square patterns). \(A\) is the distance between the centers of unit patterns. addition, the focal spots are repeatedly generated along the direction perpendicular to the lens and the distance between spots is consistent with the calculated Talbot distance of 7.9 mm. The bottom graph of Figure 3b shows the phase distribution through the circular patterns. Figure 3: _Cont_. The spot size as a function of the distance from the lens is plotted in Figure 3c, where blue and red dots represent the results for the square and circular patterns, respectively. The spot sizes generated by the two patterns are in good agreement although the circular patterns generated spots that are approximately three times more intense than those generated by the square patterns. Figure 3d shows the intensity distribution due to the 3 \(\times\) 3 circular unit patterns at a distance of 8 mm from the lens. The advantage of this type of metamaterial lens over conventional lenses can be clearly observed in these simulated results. While conventional lenses form only one spot at the focal length, each unit pattern of the SOL forms a spot at a focal distance. With this metamaterial lens, it is possible to access multiple inspection points simultaneously even though the intensity at each focal spot is just \(\sim\)19.5% of the incident beam intensity as the energy is distributed over all the unit patterns on the lens.