Open Access
Add to BibSonomy
Abstract
All-dielectric metasurfaces have been attracting attention in the terahertz spectral range for low-loss planar optical elements such as lenses, beam splitters, waveplates, vortex plates, and magnetic mirrors. Various shapes of meta-atoms have been used in many studies; however, no systematic comparative study of each shape has been reported. The optical properties of various shapes of metasurfaces are reported in this work using finite difference time domain simulation. The phase of a pillar-type all-dielectric metasurface is mainly determined by the cross-sectional area, rather than its detailed shape. Consequently, in the square lattice geometry, the square shape meta-atom performs best in terms of full phase control at the lowest pillar height with negligible polarization dependence. Furthermore, we compare the transmission, phase, and polarization dependence of the hexagonal and square lattices. Square-shape metasurface successfully realizes subwavelength focusing metalens and vortex plate.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves, with wavelengths ranging from 300 µm and 3 mm, have attracted the interest of researchers due to their unique properties, which include spectral fingerprinting of molecular vibrations, transparency of optically opaque materials, and nonionizing photon energy. [1,2] Based on these properties, THz spectroscopy is a highly promising tool for chemical detection, material characterization, biological sensing, and medical imaging. [3–7] A compact and user-friendly THz spectral imaging system is required for the practical use of THz waves in various applications. However, typical THz systems are currently bulky due to thick lenses and large parabolic guiding mirrors. [8]
It has recently been demonstrated that metasurfaces, two-dimensional arrays of subwavelength elements, can effectively modulate the amplitude, phase, and polarization of impinging waves within a planar thin layer due to the strong interaction between the light and small nano/micro-structures. For example, Capasso et al. demonstrated in 2011 that a metasurface can spatially modulate the optical phase and achieve anomalous reflection and refraction at the interface. [9] In 2016, the same group demonstrated diffraction-limited focusing and subwavelength resolution imaging without dispersion using an ultra-thin (∼600 nm) TiO2-based metasurface. [10]
Following the success in the visible region, metasurfaces in the THz spectral range have been extensively investigated to overcome the current limitations of THz conventional optics. So far, various planar THz components such as lenses [11–14], wave plates, [15,16] and beam splitters [17] have been demonstrated. To date, most reported THz planar metasurfaces have been based on metallic micro-structures thus, exploiting plasmonic effects (interaction between light and the electrons in metals). However, such plasmonic metasurfaces suffer from low efficiency due to high Ohmic loss and low performance with limited phase modulation up to π. [18,19]
To circumvent such limitations of plasmonic metasurfaces, all-dielectric metasurfaces have recently been proposed. In addition to being free of Ohmic loss, all-dielectric metasurfaces have additional advantages such as low thermal conductivity and high melting point when compared with the metallic counterparts. Many dielectric materials have high refractive indexes in the THz spectral range. Silicon (Si), in particular, has a refractive index of approximately 3.4. With such a high index, thin dielectric micro-structures can fully control the phase of the incident THz wave. A circular shape should be used to eliminate the polarization effect. However, for subwavelength structures, the cross or square shapes also show an almost identical effect on the two orthogonal polarization states. Consequently, various shapes of metasurfaces are proposed for a lens, beam splitter, or magnetic mirror. [14,20–28] In addition, a cascade-type all-dielectric active metasurface has been recently implemented. For example, in the Ref. [29], the authors successfully demonstrate the dynamic control of THz wave fronts with two rotating cascade metasurfaces. By using square and rectangular meta-atoms, they were able to control the beam propagation direction as well as the polarization state.
Even though all-dielectric metasurfaces exhibit excellent performance, one critical issue remains unsolved: what is the best shape of the dielectric metasurface for high transmission and full phase control? To our knowledge, to date, no systematic studies have been conducted that properly compare the properties of THz dielectric metasurfaces of various shapes. In this work, we quantitatively evaluated the transmittance and phase change properties of a large set of metasurface shapes through simulation. Moreover, we compared the performance of metasurfaces with square and hexagonal lattices, to find the best arrangement for the micro-structures.
2. Method
The commercial finite difference time domain (Ansys Lumerical FDTD Solutions) simulation was used to calculate the transmission and phase. The Si resonator pillars were placed on the same Si substrate with a refractive index of 3.4. The target frequency was 1 THz (300-µm-wavelength). The incident THz beam was assumed to be a plane wave propagating along the z-axis (axial direction of the pillars). To calculate the transmission and phase of each meta-atom, a single unit cell was defined and the periodic boundary condition was applied along the x and y-axis. Because the metasurface lacked a periodic structure, the perfect matched layer (PML) boundary condition was used instead. Mesh sizes in the in-plane direction (xy plane) were set at 1 µm for a periodic single meta-atom and 5 µm for the metasurfaces, respectively. The metasurface’s relatively large in-plane mesh size is due to the non-periodic millimeter size calculation area. The mesh size was 10 µm along the z-axis, and the PML boundary condition was used for both the unit meta-atom and the metasurface calculation to eliminate the artificial reflection at the boundary.
3. Results and discussions
3.1 Polygon type meta-atom with square lattice
Our all-dielectric metasurfaces comprised columns of various cross-sectional shapes, including equilateral triangles, squares, regular pentagons, regular hexagons, regular octagons, circles, and crosses (Fig. 1). All polygons, except for circles and crosses, were designed to be of the regular type to minimize the polarization effect. Consequently, a polygon can be determined when the length of one side is given. To ensure a fair comparison, the transmittance and phase were calculated while keeping the cross-sectional area of each polygon or the circle constant. Furthermore, because crosses have significantly more design parameters than polygons, an optimization design technique was introduced and will be addressed separately later.
Fig. 1. Various shapes of meta-atom studied in this work. (From the left) equilateral triangles, squares, regular pentagons, regular hexagons, regular octagons, circles, and crosses
We changed the height and period of the metasurface from 50 to 150 µm in 5 µm steps to determine the optimal height and period. At each height and period condition, the transmission and phase were calculated by changing the area ratio (cross-sectional area of the pillar per unit cell area). The square type metasurface was used in these calculations to save calculation time, and the optimal conditions were selected by considering the following three criteria:
- 1. Full phase modulation from 0 to 360° when changing the area ratio.
- 2. Lowest standard deviation of the transmittance when changing area ratio.
- 3. Least height
The third criterion is important because the lower the height, the easier it is to fabricate an all-dielectric metasurface. Based on the criteria, we discovered that the optimal height and period were 120 and 100 µm, respectively.
Figures 2 (a) and (b) show the transmission and phase as a function of the area ratio at the optimal height and period for various meta-atom shapes (triangle, square, pentagon, hexagon, octagon, and circle). The maximum value of the area ratio varies depending on the shape of the cross-sectional area because the overlap between the adjacent meta-atoms was not allowed in our calculation. Table 1 summarizes the maximum area ratio of each meta-atom under the square lattice geometry. The black lines represent the unit cell of the square lattice, and the red lines are a schematic of the maximally inscribed polygons, respectively. The maximum area ratio denotes the maximum cross-sectional area versus the period before meta-atoms overlap. As can be seen, the transmission and phase versus area ratios do not differ significantly depending on the shapes of the meta-atoms. What matters is the area ratio: regardless of the shapes of each meta-atom, the phase change is almost directly proportional to the area ratio. Since the square shape meta-atom has a maximum area ratio of one, when compared to other polygons, it reaches the highest phase modulation up to 355°. In other words, higher pillars are needed for other shapes of meta-atoms to achieve full phase modulation, implying that a more laborious fabrication process is required. As a result, we can conclude that the square shape meta-atom is the best choice for an all-dielectric metasurface in the case of the square lattice structure due to its maximum filling factors.
Fig. 2. (a) Transmission and (b) phase as a function of area ratio (cross sectional area of meta-atom per period square) for various shapes of meta-atoms.
Table 1. Various shapes of meta-atoms and the area ratio of the maximum inscribed polygons with square lattice
Now, we investigate the polarization dependence of our circular and square shape meta-atoms. The polarization angle (the angle between the x-axis and the direction of the electric field) was changed from 0° to 90° at 10° intervals. When the polarization angle is 0° (90°), the electric field of the incident beam is parallel to the x-axis (y-axis). Transmission and phase were calculated for each area ratio by changing the polarization angles and the standard deviations were calculated. Figures 3 (a) and (b) show the standard deviations of the transmission and phase at each area ratio for the square (black squares) and circular (red circles) meta-atoms. Ideally, the circular shape metasurface should have zero standard deviations along the polarization angles. The standard deviations of transmission and phase are zero in most area ratios, according to our calculations (red circles in Fig. 3 (a) and (b)). However, at certain area ratios, the standard deviations are negligibly small but have finite positive values. The largest standard deviations of the transmission and phase are $1.6 \times {10^{ - 4}}$ and $1.35 \times {10^{ - 3}}$°, respectively, in the case of a 0.3 area ratio. These non-zero values may have resulted from the FDTD simulation’s imperfect description of the circular shape and/or numerical errors. Due to the finite mesh size (1 µm), the circles can only be described as a polygon with dozens of sides, which might cause a non-zero polarization dependence. In fact, we verified that the polarization dependency slightly depends on the mesh size as well.
Fig. 3. The standard deviations (STD) of (a) transmission and (b) phases according to polarization angles for square (black square dots) and circle shapes (red circle dots) meta-atom. STDs were calculated at each area ratio.
Surprisingly, the square shape meta-atoms have negligibly small standard deviations. The calculated orders of magnitude for both transmission and phase are about ${10^{ - 4}}$. Considering the variations of the transmission according to the area ratio (about 0.15 in Fig. 2 (a)), the ${10^{ - 4}}$ order deviation is an extremely small value. Furthermore, the ${10^{ - 4}}$ degree phase deviation has little effect on metasurface performance because most metasurfaces use the entire phase range from 0° to 360°. Since the phase profile is proportional to the area ratio (Fig. 2 (b)), it can be considered that the ${10^{ - 4}}$ degree phase corresponds to approximately ${10^{ - 6}}$ change of the area ratio (∼${10^{ - 4}}/360$) or ${10^{ - 3}}$ length ratio. Alternatively, the polarization dependency (${10^{ - 4}}$ degree phase) can be regarded as a 0.1% fabrication margin. In this study, a margin of 0.1% would result in an error of 50 nm when creating a $50\mathrm{\;\ \mu m}$ long square metasurface, which is negligible considering that the wavelength is $300\mathrm{\;\ \mu m}$. Generally, lenses or mirrors are isotropic; there is no preferred polarization direction. As a result, it is necessary to create meta-lenses or meta-mirrors that are not polarization-dependent. To apply the metasurface to unpolarized light, the polarization dependency of the meta-atom should be minimized, i.e., the transmission and phase must remain constant while the incident beam polarization changes. Consequently, a circular-shaped metasurface has been preferred thus far. However, due to their neglible polarization dependence, we can expect that square shape meta-atoms can be used to construct polarization-free metasurfaces based on our calculations.
The difficulties of design and fabrication will vary depending on the meta-atom shape. Based on our calculation, the square shape meta-atom would be better than the circular shape because of full phase control at the lowest height with negligibly small polarization dependence. However, the square meta-atom can be harder to fabricate than the circular one due to the sharp vertices at the corners. In order to verify such ‘trade-off’, it is necessary to investigate the effect of the sharpness of the vertices in square shape meta-atom. The sharpness of the vertices has a significant impact on the performance of a metallic metasurface because free charges are highly concentrated at the sharp point in the metal. Consequently, it is important to maintain the razor-sharp vertices during the fabrication process for metal-based meta-atoms, which is quite difficult. Alternatively, it is expected that the sharpness of the vertices is not expected to be as important to the all-dielectric metasurface as the metallic counterpart since no charge accumulation occurs for the dielectric meta-atom. To verify the sharpness vertex effect, we performed an additional simulation to compare the performance of the square and rounded-square metasurfaces. The sharp and rounded meta-atoms are depicted schematically in the inset of Fig. 4 (b). Both meta-atoms have 120-$\mathrm{\mu m}$-height and 100-$\mathrm{\mu m}$-period and the radius of a rounded corner for a rounded meta-atom was defined as 10% of its side. The calculated transmission and phase have been calculated as a function of the area ratio, as depicted in Fig. 4 (sky blue squares for sharp squares and red circles for rounded squares). As can be seen, there is no significant difference in the performance of the two meta-atoms, implying that the sharpness of the vertex is not important for our all-dielectric metasurface. This indicates that the fabrication tolerance of the all-dielectric metasurface could be substantially larger than the metallic counterpart.
Fig. 4. (a) Transmission and (b) phase as a function of area ratio for squares having sharp edge (sky-blue square dots) and rounded edge (red circle dots)
To summarize the preceding discussion, it appears that the square shape meta-atom is the best choice under the square lattice geometry because of i) full phase control at the lowest height meta-atom, ii) negligibly small polarization dependence for isotropic metasurfaces, and iii) large fabrication tolerance (do not need to make razor-sharp vertices during the fabrication). Another advantage of the square shape meta-atom for fabrication is that it is much easier to prepare the photo-mask than the circular shape; the circular shape requires more than 100 points to define a single meta-atom, whereas only two points (upper right and lower left) are enough to draw a square. Since the metasurface lacks a periodic structure, the metasurface based on the circular meta-atom requires a much larger design drawing file size than the metasurface based on the square meta-atom.
3.2 Cross shape meta-atom with square lattice
We also investigated the characteristics of the cross shape meta-atom, which has been widely studied. To minimize the polarization effect, our cross shape has equal arm lengths along the x and y axes. Unlike the polygons, the cross can take on a wide range of shapes; the lengths a and b can be independently varied from 0 to period (inset in Fig. 5). Consequently, an optimization algorithm was unsed to reduce the design effort. Among the various optimization algorithm, we choose the ‘particle swarm’ method, which has been widely used to find the optimal metasurface. The target phase ranged from 30° to 330° with a 30° step size. At every target phase, we ran the optimization algorithm to determine the best parameters (a and b values in the inset of Fig. 5) of the cross shape meta-atom. The maximum number of generations and the generation size were set to 50 and 20, respectively. To account for the fabrication process, the maximum value of ‘a’ was limited to 90 µm, whereas the minimum value of b was 10 µm. The optimization algorithm is designed to select the structure with the highest transmittance when the phase is within ±3° of the target phase. Table 2 displays the optimized values of a and b at 160-$\mathrm{\mu m}$-height and 100-$\mathrm{\mu m}$-period condition. As shown in the fourth column of Table 2, the differences between the target phase and the calculated phases are less than 3°, indicating that our optimization algorithm works well. The second and the third columns represent the optimized structure parameters of cross meta-atoms and the final column contains a schematic of the optimized cross shapes. Unlike polygons, where the shape simply increases as the target phase value increases, the optimized cross meta-atom does not appear to correlate with phase and shape. However, as shown in Fig. 5 (b), there is a strong correlation between the phase and the area of the optimized cross meta-atom. The area ratio refers to the ratio between the area of the cross and the period square (area of the unit cell). The strong correlation implies that regardless of the shape of the cross, the area plays a significant role in the phase change; the detailed shape of the cross can alter the transmission, but not the phase if the areas of the crosses are the same. For example, the best parameters for the target phase 210 ° were found at a = 63.6 $\mathrm{\mu m}$ and b = 62.0 $\mathrm{\mu m}$ with the transmission of 60.0%. Changing the parameters to a = 44.5 $\mathrm{\mu m}$ and b = 67.3 $\mathrm{\mu m}$ resulted in a slight decrease in transmittance to 57.6%. The transmission change was not so large because the cross-sectional area must be maintained to achieve the specific target phase (in this case 210 °) as discussed earlier (Fig. 2).
Fig. 5. (a) Transmission and (b) phase as a function of area ratio for cross shape meta-atom. At each point, optimization algorism was employed to find the best shapes.
Table 2. The optimized design parameters of the cross shaped meta-atoms at each target phase.
The corresponding transmission as a function of the area ratio is depicted in Fig. 5 (a), with an average transmission of 0.71, which is slightly lower than the polygon shapes (Fig. 2 (a)). The main difference between the polygons and the cross structure is the height; 120-$\mathrm{\mu m}$-tall was used for the polygons, while the height of the cross was 160-$\mathrm{\mu m}$. The difference in transmittance is caused by the height difference. Higher pillars were used for the cross-shaped meta-atoms to provide more space for the design parameters (lengths a and b); if the height is too low, the optimized structure would be the simple square shape mainly for the large target phase.
3.3 Hexagonal lattice vs square lattice
Recently, hexagonal lattices have been widely studied to make meta-lens because of their slightly higher isotropy compared to square lattices. The schematic diagrams for the hexagonal and square lattices investigated in this study are shown in Figs. 6 (a) and (b), respectively. As previously discussed, in the square lattice structure, the square meta-atom exhibits full phase control at the lowest height due to the highest possible area ratio compared with other shapes. Similarly, we can anticipate that the hexagonal structure will perform best with the hexagonal lattice. To find the optimal hexagonal shape meta-atom design, we calculated the transmission and phase at each area ratio by independently changing the height and period from 50 $\mathrm{\mu m}$ to 150 $\mathrm{\mu m}$ with a 5 $\mathrm{\mu m}$ step size. The optimal height (120 $\mathrm{\mu m}$) and period ($110\mathrm{\;\ \mu m}$) were selected as the conditions that resulted in the highest transmittance with the minimum standard deviation while satisfying full phase control. The transmission and phase results at the optimal condition for hexagonal lattice-hexagonal shape are displayed in Figs. 6 (c) and (d) (red hexagonal dots), respectively. For ease of comparison, the square lattice-square shape results were plotted again (sky blue square dots) in the same figures. The average transmission (hexagonal: 0.745, square: 0.744) and the phase profile showed no significant difference. However, the hexagonal lattice shows a slightly better uniformity in transmission. The standard deviation of the transmission for hexagonal was 0.027, whereas a 0.037 standard deviation was recorded for the square lattice.
Fig. 6. Schematic of (a) hexagonal lattice and (b) square lattice. (c) Transmission and (d) phase as a function of area ratio for hexagonal lattice-hexagonal meta-atom (red hexagonal dots) and square lattice-square meta-atom (sky-blue square dots)
The polarization dependence of the hexagonal lattice-hexagonal shape was also investigated as displayed in Figs. 7 (a) and (b). The standard deviation of the transmission and phase were calculated in the same manner as the square meta-atom. The standard deviation of the transmission for the hexagonal lattice was slightly greater than that for the square lattice, but the order of magnitude was the same (∼${10^{ - 4}}\mathrm{\;\ \mu m}$). Moreover, the average standard deviation of the phase was about 0.1°, which was still small, but it was 100 times greater than the value for the square lattice (Fig. 3 (b)). This means that although a hexagonal lattice appears more isotropic than a square lattice, it may not be. Since the 0.1° deviation may be significant in some applications, the hexagonal lattice is recommended to be used with caution for unpolarized light.
Fig. 7. The standard deviations (STD) of (a) transmission and (b) phases according to the polarization angles for the hexagonal lattice. STDs were calculated at each area ratio.
3.4 Application
Finally, we constructed metasurfaces for beam focusing (Fig. 8) and vortex beam (Fig. 9) based on the square lattice-square shaped meta-atom. The metalens was designed with a diameter of 2.0 mm and a focal length of 1.0 mm in mind. The calculated electric field intensities at the xz plane (y = 0 mm) and the focal plane (z = 0.96 mm) are depicted in Figs. 8 (a) and 8 (b), respectively. To see the focal length and the focal spot size clearly, the intensity profiles along the z-axis (x = y = 0) and the x axis (y = 0, z = 0.96 mm) are plotted in Figs. 8 (c) and 8 (d). As expected, our square shape all-dielectric metalens works very well as a focusing lens with focal length of 0.96 mm (Fig. 8(c)), which is slightly shorter than the design mainly due to the finite discretization of the continuous phase profile. The full width at half-maximum (FWHM) of the focal spot (Fig. 8 (d)) was estimated to be 235 $\mathrm{\mu m}$, demonstrating the metalens’ subwavelength focusing ability. Vortex beams have recently gained popularity due to the optical angular momentum they carry. To generate a vortex beam, a complicated spatial phase profile is required, which is difficult to implement with conventional optics. As a result, metasurfaces are widely used to generate and manipulate vortex beams. Using our square shape all-dielectric metasurface, we created a vortex beam with an angular momentum quantum number $l = 1$. The metasurface was divided into eight regions, with a phase difference of 45° between them. Figure 9 (a) depicts the detailed distributions of meta-atoms and the generated $l = 1$ vortex beam is displayed in Fig. 9 (b). As can be seen, the signature donut shape (circular ring shape distributions of the electric fields) of the $l = 1$ vortex beam is demonstrated. The inhomogeneous intensity distribution of the vortex beam may be attributed from the fluctuation of the transmission. Further studies are needed to find meta-atoms that provide uniform transmittance to improve the quality of the vortex beam.
Fig. 8. The electric field intensity distributions in (a) xz plane (y = 0 mm) and (b) xy plane at the focal spot (z = 0.96 mm). The intensity profile along the z-axis (x = y = 0) and the x-axis (y = 0, z = 0.96 mm).
Fig. 9. (a) Distributions of meta-atoms for $l = 1$ vortex plate. (b) Generated $l = 1$ vortex beam (electric field intensity).
4. Conclusion
In conclusion, we have investigated the shape dependence of the all-dielectric metasurface in the THz spectral range. The material of the meta-atom is assumed to be silicon with a refractive index of 3.4. The transmission and phase in the same area are compared for various cross-sectional shapes such as triangles, squares, pentagons, hexagons, octagons, circles, and crosses. The area is important in determining the phase; the phase profile is approximately proportional to the cross-sectional area of the meta-atom, and is not closely related to the detailed shapes. Consequently, for square lattice structures, the square type meta-atom may be the best choice because the full phase modulation can be realized at the pillar’s lowest height. Furthermore, the square meta-atom exhibits a negligibly small polarization dependence. We also compared the hexagonal and square lattices. Compared to the square lattice, the hexagonal lattice with hexagonal meta-atom show a slightly smaller standard deviation of transmission, whereas, the polarization dependence of the phase is greatly enhanced. Lastly, the metalens and vortex beam plate are realized through the square lattice-square meta-atom combination. Recently, coupled mode theory (CMT) has been studied to investigate the transmissive THz metasurface system. [30–32] The CMT based model together with the FDTD simulation may be helpful in revealing the underlying physics of shape dependence of meta-atoms in future studies. We believe that our work paves the way for the efficient design of low-loss all-dielectric metasurfaces for a planar lens, magnetic mirror, and vortex plate in THz communication. Unlike our all-dielectric meta-atom, the plasmonic meta-atoms show quite different behaviors for different shapes. [33–37] Therefore, we expect that the study of shape dependence of plasmonic meta-atoms would also be a very interesting research topic.
Funding
Dankook University (Research-Focused Department Promotion Project); National Research Foundation of Korea (2009-0082580, 2022K1A3A1A73080783, NRF-2020R1F1A1074832, NRF-2021R1F1A1058307, NRF-2022R1A2C2006379).
Acknowledgement
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (NRF-2020R1F1A1074832, NRF-2021R1F1A1058307, NRF-2022R1A2C2006379). This research has been done by the author(s) working at the Department of Physics of Dankook University. Department of Physics was supported by the Research-Focused Department Promotion Project as a part of the University Innovation Support Program 2020 to Dankook University. This research was supported by the International Research & Development Program of the National Research Foundation of Korea(NRF) funded by the Ministry of Science and ICT(Grant number: 2022K1A3A1A73080783). This research was supported by Nano·Material Technology Development Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning. (2009-0082580) Project number: K210309005
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. S. Mitryukovskiy, D. E. P. Vanpoucke, Y. Bai, T. Hannotte, M. Lavancier, D. Hourlier, G. Roos, and R. Peretti, “On the influence of water on THz vibrational spectral features of molecular crystals,” Phys. Chem. Chem. Phys. 24(10), 6107–6125 (2022). [CrossRef]
2. Y. Takida, K. Nawata, and H. Minamide, “Security screening system based on terahertz-wave spectroscopic gas detection,” Opt. Express 29(2), 2529 (2021). [CrossRef]
3. J. Kyoung, “Direct in situ observation of the percolation transition in VO2 thin film by peak-shift spectroscopy,” Opt. Mater. Express 12(3), 1065–1073 (2022). [CrossRef]
4. H. Yoshida, Y. Ogawa, Y. Kawai, S. Hayashi, A. Hayashi, C. Otani, E. Kato, F. Miyamaru, and K. Kawase, “Terahertz sensing method for protein detection using a thin metallic mesh,” Appl. Phys. Lett. 91(25), 253901 (2007). [CrossRef]
5. Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86(24), 241116 (2005). [CrossRef]
6. P. K. Poola, Y. Kumaresan, I. Krasnikov, and A. Seteikin, “Chapter 11 - Terahertz Molecular Imaging and Its Clinical Applications,” in Terahertz Biomedical and Healthcare Technologies, A. Banerjee, B. Chakraborty, H. Inokawa, and J. Nath Roy, eds. (Elsevier, 2020), pp. 195–213. [CrossRef]
7. J. Kyoung, “Anomalous blueshift of aperture resonance enabled by the loss of a thin film,” Sci. Rep. 10(1), 22100 (2020). [CrossRef]
8. J. Neu and C. A. Schmuttenmaer, “Tutorial: An introduction to terahertz time domain spectroscopy (THz-TDS),” J. Appl. Phys. 124(23), 231101 (2018). [CrossRef]
9. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef]
10. M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016). [CrossRef]
11. D. Jia, J. Xu, T. Xin, C. Zhang, and X. Yu, “Multifocal terahertz lenses realized by polarization-insensitive reflective metasurfaces,” Appl. Phys. Lett. 114(10), 101105 (2019). [CrossRef]
12. H. Zhang, X. Zhang, Q. Xu, Q. Wang, Y. Xu, M. Wei, Y. Li, J. Gu, Z. Tian, C. Ouyang, X. Zhang, C. Hu, J. Han, and W. Zhang, “Polarization-independent all-silicon dielectric metasurfaces in the terahertz regime,” Photonics Res. 6(1), 24–29 (2018). [CrossRef]
13. X.-Y. Jiang, J.-S. Ye, J.-W. He, X.-K. Wang, D. Hu, S.-F. Feng, Q. Kan, and Y. Zhang, “An ultrathin terahertz lens with axial long focal depth based on metasurfaces,” Opt. Express 21(24), 30030–30038 (2013). [CrossRef]
14. D. Jia, Y. Tian, W. Ma, X. Gong, J. Yu, G. Zhao, and X. Yu, “Transmissive terahertz metalens with full phase control based on a dielectric metasurface,” Opt. Lett. 42(21), 4494–4497 (2017). [CrossRef]
15. D. Wang, Y. Gu, Y. Gong, C.-W. Qiu, and M. Hong, “An ultrathin terahertz quarter-wave plate using planar babinet-inverted metasurface,” Opt. Express 23(9), 11114–11122 (2015). [CrossRef]
16. Y. Nakata, Y. Taira, T. Nakanishi, and F. Miyamaru, “Freestanding transparent terahertz half-wave plate using subwavelength cut-wire pairs,” Opt. Express 25(3), 2107–2114 (2017). [CrossRef]
17. T. Niu, W. Withayachumnankul, A. Upadhyay, P. Gutruf, D. Abbott, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Terahertz reflectarray as a polarizing beam splitter,” Opt. Express 22(13), 16148–16160 (2014). [CrossRef]
18. X. Liu, K. Fan, I. v Shadrivov, and W. J. Padilla, “Experimental realization of a terahertz all-dielectric metasurface absorber,” Opt. Express 25(1), 191–201 (2017). [CrossRef]
19. C. C. Nadell, B. Huang, J. M. Malof, and W. J. Padilla, “Deep learning for accelerated all-dielectric metasurface design,” Opt. Express 27(20), 27523–27535 (2019). [CrossRef]
20. S. Han, P. Pitchappa, W. Wang, Y. K. Srivastava, M. v Rybin, and R. Singh, “Extended Bound States in the Continuum with Symmetry-Broken Terahertz Dielectric Metasurfaces,” Adv. Opt. Mater. 9(7), 2002001 (2021). [CrossRef]
21. R. Jia, Y. Gao, Q. Xu, X. Feng, Q. Wang, J. Gu, Z. Tian, C. Ouyang, J. Han, and W. Zhang, “Achromatic Dielectric Metasurface with Linear Phase Gradient in the Terahertz Domain,” Adv. Opt. Mater. 9(2), 2001403 (2021). [CrossRef]
22. Z. Ma, S. M. Hanham, P. Albella, B. Ng, H. T. Lu, Y. Gong, S. A. Maier, and M. Hong, “Terahertz All-Dielectric Magnetic Mirror Metasurfaces,” ACS Photonics 3(6), 1010–1018 (2016). [CrossRef]
23. J. Zhou, J. Wang, K. Guo, F. Shen, Q. Zhou, Zhiping Yin, and Z. Guo, “High-efficiency terahertz polarization devices based on the dielectric metasurface,” Superlattices Microstruct. 114, 75–81 (2018). [CrossRef]
24. X. Jiang, H. Chen, Z. Li, H. Yuan, L. Cao, Z. Luo, K. Zhang, Z. Zhang, Z. Wen, L. Zhu, X. Zhou, G. Liang, D. Ruan, L. Du, L. Wang, and G. Chen, “All-dielectric metalens for terahertz wave imaging,” Opt. Express 26(11), 14132–14142 (2018). [CrossRef]
25. Q. Yang, X. Chen, Q. Xu, C. Tian, Y. Xu, L. Cong, X. Zhang, Y. Li, C. Zhang, X. Zhang, J. Han, and W. Zhang, “Broadband terahertz rotator with an all-dielectric metasurface,” Photonics Res. 6(11), 1056–1061 (2018). [CrossRef]
26. J. Wang, J. Zhou, K. Guo, F. Shen, Q. Zhou, Z. yin, and Z. Guo, “High-efficiency terahertz dual-function devices based on the dielectric metasurface,” Superlattices Microstruct. 120, 759–765 (2018). [CrossRef]
27. Y.-Y. Ji, F. Fan, M. Chen, L. Yang, and S.-J. Chang, “Terahertz artificial birefringence and tunable phase shifter based on dielectric metasurface with compound lattice,” Opt. Express 25(10), 11405–11413 (2017). [CrossRef]
28. Y. Wang, D. Zhu, Z. Cui, L. Yue, X. Zhang, L. Hou, K. Zhang, and H. Hu, “Properties and Sensing Performance of All-Dielectric Metasurface THz Absorbers,” IEEE Trans. Terahertz Sci. Technol. 10(6), 599–605 (2020). [CrossRef]
29. X. Cai, R. Tang, H. Zhou, Q. Li, S. Ma, D. Wang, T. Liu, X. Ling, W. Tan, Q. He, S. Xiao, and L. Zhou, “Dynamically controlling terahertz wavefronts with cascaded metasurfaces,” Adv. Photonics 3(3), 036003 (2021). [CrossRef]
30. Y. Li, J. Lin, H. Guo, W. Sun, S. Xiao, and L. Zhou, “A Tunable Metasurface with Switchable Functionalities: From Perfect Transparency to Perfect Absorption,” Adv. Opt. Mater. 8(6), 1901548 (2020). [CrossRef]
31. Q. Li, X. Cai, T. Liu, M. Jia, Q. Wu, H. Zhou, H. Liu, Q. Wang, X. Ling, C. Chen, F. Ding, Q. He, Y. Zhang, S. Xiao, and L. Zhou, “Gate-tuned graphene meta-devices for dynamically controlling terahertz wavefronts,” 11(9), 2085–2096 (2022).
32. M. v Gorkunov, A. A. Antonov, and Y. S. Kivshar, “Metasurfaces with Maximum Chirality Empowered by Bound States in the Continuum,” Phys. Rev. Lett. 125(9), 093903 (2020). [CrossRef]
33. X. Zhang, Z. Tian, W. Yue, J. Gu, S. Zhang, J. Han, and W. Zhang, “Broadband Terahertz Wave Deflection Based on C-shape Complex Metamaterials with Phase Discontinuities,” Adv. Mater. 25(33), 4567–4572 (2013). [CrossRef]
34. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012). [CrossRef]
35. S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-Efficiency Broadband Anomalous Reflection by Gradient Meta-Surfaces,” Nano Lett. 12(12), 6223–6229 (2012). [CrossRef]
36. W. T. Chen, K.-Y. Yang, C.-M. Wang, Y.-W. Huang, G. Sun, I.-D. Chiang, C. Y. Liao, W.-L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-Efficiency Broadband Meta-Hologram with Polarization-Controlled Dual Images,” Nano Lett. 14(1), 225–230 (2014). [CrossRef]
37. S. Li, S. Dong, S. Yi, W. Pan, Y. Chen, F. Guan, H. Guo, Z. Wang, Q. He, L. Zhou, and S. Sun, “Broadband and high-efficiency spin-polarized wave engineering with PB metasurfaces,” Opt. Express 28(10), 15601–15610 (2020). [CrossRef]
