Terahertz (THz) electromagnetic waves have recently been applied to various fields such as biomedical diagnosis[1, 2, 3], non-destructive tests[4], and security[5, 6]. This is due to their optical characteristics, including low photon energy, non-ionization, and transparency in dielectric materials. To construct a system for the applications, optimized optics for THz waves, such as lenses and waveplates, are essential. In general, polymers including polymethylpentene (TPX) and polytetrafluoroethylene (Teflon) are widely used for THz optics due to their sufficiently low absorption. However, these materials have low refractive indices around 1.45[7, 8], which leads to thickness increases and aberrations by radius increasing. Thus, novel approaches to designing thin and efficient optics are required. Metamaterials are proposed as a promising solution to overcome these challenges. Metamaterials enable a range of advanced functionalities, such as refractive index control, boosting light-matter interaction, and phase manipulation, in optical systems that are not possible with conventional materials through artificial subwavelength structures. These fine structures on the metamaterials rely on nanofabrications including lithography, deposition, and etching[9, 10, 11]. For efficient and cost-effective fabrication manufacturing, metamaterials by 3D printing technology recently have been suggested. The 3D printing technique as a rapid fabrication method forms complex structures by simply deposition of materials layer-by-layer[12, 13]. One of the most widely used 3D printing methods is fused deposition modeling (FDM), which involves melting a thermoplastic filament and extruding it through a nozzle to build the object. This method allows simple and fast printing with various filament materials[14]. However, the resolution by FDM is limited to hundreds of microns by the mechanical diameter of the nozzle for smooth extruding and die swelling of extrudate[15, 16, 17]. For better printing resolution, optical image projection to photopolymer resin can be adopted. The liquid crystal display (LCD) type 3D printer builds an object by stacking cured photopolymer by slicing UV images using LCD as a photomask. Depending on the resolution of the LCD mask, the 3D printer can achieve a better resolution than FDM[18]. In addition, each layer is cured by a single-shot UV image leading to faster printing than FDM. To make optimized THz optics by 3D printing, the effect on the optical performance of the meta-optics by a structural size error by 3D printing should be estimated to minimize the performance difference between the ideal design and the printed real meta-optics.

In this study, we analyze the performances of a 3D-printed metamaterial-based THz lens (metalens) in terms of focal length and focusing efficiency by size errors on unit cell structure. The THz metalens was designed as a square pillar array, by considering the square pixel shape of the LCD mask. Phase of incident THz waves changed by the unit cell occurred by controlling the width of pillars. To test actual structural errors, simple pillar arrays with an identical size are fabricated with pillar width that is applied to unit cells in the THz metalens. Size errors are analyzed using microscopy imaging with image processing including pattern-matching. The statistically evaluated size errors are applied to the finite-difference time-domain (FDTD) method. Focusing performances and focal length shifts of THz metalenses with and without structural errors are compared in field distributions.

The schematic diagram of the fabrication process for the metalens is shown in Fig. 1(a). The metalens consists of an array of square pillars printed on a quartz substrate using a commercial low-cost 3D printer (Anycubic Photon Mono 4K) that selectively exposes ultraviolet (UV) light through an LCD shadow mask with a resolution of several tens of microns. The metalens, designed for a target frequency of 0.2 THz (λ = 1500 μm), features a square pillar array with 2800 μm in height and 1500 μm of a period with consideration of the wavelength and diffraction efficiency. The phase of each unit cell is controlled in the range of 0–2π by controlling the width of square pillar unit cells in the range from 400 μm to 1200 μm. The refractive index of the cured photopolymer resin, which is composed of epoxy resin (60%), (1-methyl, 2-ethanediyl)bis[oxy(methyl-2,1 ethanediyl)]diacrylate (35%), and hydroxycyclohexyl phenyl ketone (5%), are 1.74 at 0.2 THz, respectively[19]. Printing errors are measured using simple 4 × 4 square pillar arrays with identical width as shown in Fig. 1(c). Actual pillar widths are extracted from optical microscopy images using image processing including a pattern-matching algorithm as shown in Fig. 1(d). The blue line indicates the accurate size of the printed pillar array. In the range of 400 μm to 1200 μm corresponding to the pillar width for the metalens, printed actual pillars show good correlation with target widths. These pillars have under 5% of errors and 20 μm of standard deviations, which is sufficiently smaller than 35 μm of the pixel size of the LCD mask (Fig. 1(e)).

Figure 1. (Color online) (a) Schematic of 3D printing metalens manufacturing process. (b) Design of the unit cell. (c) A optical microscopy image of 3D printed square pillar arrays. (d) Measured pillar width. (e) Average and standard deviation of errors.

Based on the measured size error, the phase and transmittance of the unit cells with size errors are calculated using FDTD calculation. For simple calculation, the absorption of the resin was negligible due to its sufficiently low absorption coefficient of 3.78 cm​-1. The pillars showed a gradually changed phase in the range of 0–2π by pillar width (Fig. 2(a)). The blue line indicates phase changes by pillars with ideal width. In contrast, the transmittance for pillars is almost constant with a small deviation of under 6% (Fig. 2(b)). Thus, we can design the metalens by arranging the pillars in sufficient radial positions for the required phase change. The lens was designed for focusing optics with 50 mm of the radius and 50 mm of the focal length for THz waves of 0.2 THz using the following equation:

Figure 2. (Color online) Simulated (a) phase shift and (b) transmittance with and without size errors. (c) Pillar width and phase shift by target position. (d) A schematic of metalens.

where φ is the phase shift, λ is the wavelength, r is the distance from the lens center, and f is the focal length[20]. Because the required phase change for the lens with a large diameter is larger than 2π, the phase is wrapped as shown in Fig. 2(c). Pillars are arranged to satisfy the calculated phase. The red and blue lines indicate phase change and pillar width by radial position, respectively. Thus, the metalens is a rectangular unit cell array on the circular substrate as shown in Fig. 2(d).

The focusing performance of a metalens with an accurate focal length of 50 mm is shown in Fig. 3(a). The metalens with average error also show almost identical focusing performance to the metalens with the ideal structure. In addition, the focusing performances of the metalenses with additional size errors of the printed actual pillars show field distributions without significant deviations as shown in Fig. 3(b–d).

Figure 3. (Color online) (a) Simulated focusing performance with no error, (b) with average error, (c) with average minus standard deviation, (d) with average plus standard deviation.

To compare the shift of focal length directly, field intensities at the center of propagation direction are summarized in Fig. 4. The metalens of the ideal design shows the maximum intensity at 50 mm, which is the target focal length. The metalenses with structural errors also show almost identical intensity distributions despite their unit cell having size errors up to 6%. Thus we can fabricate accurate and robust focusing optics based on the all-dielectric metamaterial using 3D printing.

Figure 4. (Color online) The comparison of the normalized intensity distribution of the metalens with no error, average error, average minus standard deviation, and average plus standard deviation.

We investigated the focusing performance of the 3D printed metalens by structural size errors of unit cells due to the LCD mask resolution of an LCD-type 3D printer on the performance of a metalens, including its focal length and focusing performance. Based on the characteristics of the photopolymer resin used in the 3D printer, we determined the parameters (period, height) of square pillars, which serve as the unit cell of the metalens, for operating at the target frequency of 0.2 THz. Additionally, we adjusted the width of the square pillars from 400 μm to 1200 μm to achieve a phase shift from 0 to 2π. To measure structural errors, we printed 4 × 4 arrays for each pillar width, captured microscope images, and utilized pattern-matching in image processing to measure individual errors. Including the measured errors into the square pillars, we calculated the phase shift and transmittance using the finite-difference time-domain (FDTD) method. The simulation results showed differences of less than 6% between cases with and without errors. Furthermore, we applied the square pillars with errors directly to simulate a metalens with a focal length of 50 mm. The results demonstrated minimal differences between the case with errors and the ideal case. This finding indicates that structural imperfections in the unit cell structure produced via 3D printing may not critically affect their focusing functionality of THz waves. We also hope this research contributes to expanding the 3D-printed meta-optics application fields.

This research was supported by Kumoh National Institute of Technology (2021).