Open Access
Add to BibSonomy
Abstract
Quasi-optical mode conversion technology plays a very important role in the development of high-power terahertz radiation sources. The ability of metamaterials to manipulate wave-front paves a new way in the field of quasi-optical mode conversion. In this paper, the approach for quasi-optical mode conversion by all-dielectric metalens and polarization conversion is proposed and investigated. Three metalens are designed to converter cylindrical waveguide TE01 mode to linear polarized (LP), left-hand circularly polarized (LHCP), and right-hand circularly polarized (RHCP) Gaussian beams at 350 GHz. Electromagnetic simulations show that the Gaussian mode contents of output waves from three metalens are all over 98% with high polarization contents. Furthermore, a metalens is designed for dual circularly polarized (DCP) which could convert cylindrical waveguide TE01 mode to LHCP and RHCP simultaneously. This work unveils the potential application for metalens in terahertz region.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves, also known as underdeveloped electromagnetic waves, are located in the frequency spectrum between the microwave millimeter band and the infrared optical band [1]. The special spectral location determines that terahertz technology has the advantages of both microwave and infrared waves, and shows great potential in the field of high data rate communication [2], high-resolution imaging [3], spectral analysis [4], biomedical diagnostic [5], etc. For investigation and application, the radiation source is an important component in the system. Vacuum electron devices (VEDs), as a high-power microwave radiation source, are commonly used in applications requiring high power output such as satellite communications, electronic countermeasures, and microwave heating [6]. However, as the frequency rises into the terahertz region, the high-frequency size of the VEDs decreases dramatically, limiting the devices’ power capacity and causing fabricating challenges [7]. As a result, researchers have presented using higher-order modes as operating modes to effectively address the problem of insufficient high-frequency dimensions in the high-frequency band [8,9]. For example, TM01 mode is adopted for the backward-wave oscillators [10], coaxial TEM mode is used for the magnetically insulated oscillators [11], TE0n or even higher-order TEmn mode are employed for the gyrotrons [12,13], and TEn1 mode is utilized for the full-cavity diffraction output relativistic magnetrons [14], etc. However, these modes usually have a central hollow cone shape, and most of the energy is not concentrated on the axis, which is not conducive to the transmission and application of electromagnetic waves in free space. Therefore, mode conversion is necessary to change the spatial distribution of electromagnetic energy to meet the application or transmission requirements [15,16].
Recently, electromagnetic metamaterials have been introduced into mode converter investigations. In [17], Carl et al. developed two novelty metallic metasurface prototypes of mode converters to convert linearly polarized (LP)and circularly polarized (CP) Gaussian beams into vector Bessel beams. This research is significant to illustrate that metasurfaces can be used to produce any arbitrary combination of radial and azimuthal polarizations for focus shaping or for creating tractor beams. In addition, an ultra-thin meta-waveplate [18] has been put forward for converting CP light to LP light. And Ref. [19] proposed a new plasmonic metasurface mode converter that converts high order modes into free space modes. However, as far as we know, previously published studies mainly focus on multi-layer or multi-resonant plasmonic metasurfaces. Since the plasmonic metasurface is composed of metallic periodic units, it cannot be used in high-power field because the metal surface is prone to a tip effect in the strong electromagnetic field environment, which can easily lead to breakdown discharge [20,21]. Besides, the plasmonic metasurfaces’ inherent ohmic loss restricts their transmission efficiency [22].
In this paper, the approach for converting waveguide modes to free-space wave modes by all-dielectric metalens is proposed. All-dielectric metalens research, as far as we know, is mostly focused on imaging [23–26], polarization manipulation [27–31], vector beam generation [32,33], and holography [34–38]. Here, the application of all-dielectric metalens for quasi-optical mode conversion is attempted and investigated. Through bending the paths when the electromagnetic wave transmitted through the dielectric metalens, the mode pattern would be changed. By optimizing the meta-unit at each position, the desired mode pattern would be obtained. The investigation shows that the metalens not only could realize quasi-optical mode conversion but also could realize polarization conversion. In EM simulation, the waveguide TE01 mode at 350 GHz is converted to LP and CP Gaussian beams successfully. Furthermore, by adjusting metalens structure, left-hand circularly polarized (LHCP) and right-hand circularly polarized (RHCP) Gaussian beams could be obtained separately or simultaneously. Compared to local resonance effect of metal in plasmonic metamaterials, the all-dielectric metalens is built up by dielectric units and the electromagnetic waves in all-dielectric metalens do not couple with plasmon [39,40]. Hence, the power capability of the mode converter would be sufficiently improved and ohmic loss could be reduced.
2. Principle and theoretical model
According to Maxwell equations and boundary conditions, different electromagnetic wave modes correspond to different electric field distributions [41]. For a Gaussian beam transmitted in free space, the electric field distribution is concentrated on the transmission axis. But the electric field distribution of the electromagnetic modes in the waveguide is mostly not concentrated on the transmission axis due to the limitation of the waveguide boundary conditions. The electric field distributions of the circular waveguide TE01 mode and the free-space Gaussian beam are shown in Fig. 1, respectively [15]. The metalens has the function of focusing, and thus it is possible to focus the energy in the waveguide modes onto the transmission axis.
As shown in Fig. 2(a), cylindrical waveguide EM mode is LP at each position, and the fields of TE mode on the same wavefront are perpendicular to the transmission direction at the same phase. At the same radius on a wavefront, the $E({\rho ,\phi ,z} )={-} E({\rho ,\phi + \pi ,z} )$ when ϕ and ϕ + π, the field strength is the same, and the vector direction is positive. If the electric field at the same radius is directly reflected to the central position with the same refraction angle, it will cause coherent destructive interference in the central axis and would not generate a Gaussian beam. The electric field distribution of the ideal Gaussian mode is shown in Fig. 2(d). Thus, the vector direction rotation is a critical factor in metalens design for mode conversion. In this section, the conversion principle and a theoretical model are presented.
Fig. 2. (a) Field distribution diagram of the TE01 waveguide mode; (b) Schematic diagram of polarization conversion; (c) Schematic diagram of the all-dielectric LP Gaussian beam conversion metalens structure; (d) Vector diagram of linearly Gaussian mode.
2.1 Quasi-optical mode with linear polarization conversion
The unit of metalens is mostly built up by a pillar on a substrate. Each pillar can be viewed as a waveguide with truncated ends that functions as a Fabry-Perot resonator with a low-quality factor. Based on the Mie resonance principle [42], the high refractive index dielectric resonator units can simultaneously trigger electric and magnetic dipole responses. In the dielectric resonator mode, the electrical resonance and magnetic resonance responses can be excited inside the dielectric block with high permittivity. According to the effective medium theory, if the medium's size is bigger along a structure's symmetry axis (long side or short side direction), the effective refractive index in that direction will be larger; otherwise, it will be smaller. The larger the effective refractive index, the slower the propagation speed of the electromagnetic wave in it, and this direction is called the slow axis; correspondingly, the direction perpendicular to the slow axis is the fast axis [43]. This equivalent birefringence makes the electromagnetic wave incident along the z-direction produce different phase delays in the fast axis and slow axis directions. By adjusting the angle between the fast axis of the meta-unit and the direction of the wave vector, different strengths of the E field could be coupled on the fast axis and the slow axis of the meta-unit, respectively. Then, adjusting phase delays between the fast axis and slow axis, the polarization direction and the vector direction could be rotated. The rotation process of TE01 mode is shown in Fig. 2.
As shown in Fig. 2(b), the vector direction of the incident wave is in the U-direction, and the vector direction of the target outgoing wave is in the V-direction. For vector direction rotation, it can be simplified to rotate the direction of the LP wave at the same phase. A local coordinate is established, with the meta-unit's center serving as its origin, the Y1 axis serving as its slow axis and the X1 axis serving as its fast axis. To rotate the vector direction from the U-direction to the V-direction, the angle θ1 between the Y1 axis and U-direction and the angle θ2 between the Y1 axis and V-direction should be the same as θ1 = θ2. Then, the incident wave $\vec{E}_u^i$ would be coupled to the meta-unit as
Meanwhile, the phase delays between the fast axis and the slow axis could be adjusted as
Arranging the axes direction of the meta-unit based on the vector direction of the E field at each position, an anisotropic metalens could be built up to rotate the vector direction of waveguide mode at each position to the same polarization direction.
2.2 Quasi-optical mode with circular polarization conversion
In this investigation, two stages are taken to convert the waveguide mode to a CP Gaussian beam, as depicted in Fig. 3. First, the waveguide mode in the waveguide is converted to a LP wave according to the above process. Second, convert the LP wave to a CP Gaussian beam. Then, the conversion from the waveguide mode to a CP Gaussian beam is achieved. As this principle, the proposed array structure contains two layers, which are located on the top and bottom surface of the substrate, respectively. The outgoing wave from the top layer $\vec{E}_{v1}^o$ could be the incident wave of the bottom layer $\vec{E}_{v2}^i$, and a local coordinate system for circular polarization can be defined as above, in which origin is the center of the meta-unit, the Y2 axis is the meta-unit's slow axis, and the X2 axis is the meta-unit's fast axis. To convert linear polarization to circular polarization, the angle θ'1 between the Y2 axis and V-direction is set to θ'1 = π/4. Then the incident wave $\vec{E}_{v2}^i$ can be decomposed to two orthogonal electric field vectors of $\vec{E}_{{x_2}}^i$ and $\vec{E}_{{y_2}}^i$ in X2 axis and Y2 axis, respectively and equally. The expression is
Fig. 3. The all-dielectric metalens based on double-layer structure. (a) Schematic diagram of the structure; (b) Definition of the structural parameters of the top layer element; (c) Definition of the structural parameters of the bottom layer element.
3. Metalens design and simulation
To demonstrate the proposed conversion principle, four quasi-optical mode converters based on metalens have been designed to convert the waveguide TE01 mode at 350 GHz to LP, LHCP, RHCP, DCP Gaussian beams, respectively. The electromagnetic simulation is done by a commercial finite element method solver High Frequency Structure Simulator (HFSS), and the following are the detailed designs.
3.1 Metalens design
In this investigation, the employed unit is an elliptical cylindrical-shaped pillar on a substrate, which is depicted in Fig. 4(e). To get high permittivity and reduce structure size, high purity alumina ceramic with a high dielectric constant (ɛr = 9.9) was adopted as pillar materials, and quartz (SiO2 ɛr = 4) was adopted as substrate. To achieve polarization-dependent wavefront control, the transmission characteristics of EM waves along the fast axis and slow axis of the meta-unit have been down. For 350 GHz terahertz wave, the pillar height H is 0.88 mm, and each unit size is about 0.42 mm × 0.42 mm (corresponding to 0.5λ of 350 GHz). The magnitudes and phases of the S21 parameters of $\vec{E}$ field along the fast axis and the slow axis are presented in Fig. 4(a)–(d). Due to the adoption of axisymmetric elliptic cylindrical design, both the phase shift and transmission amplitude distributions are symmetric in response to the line D = d. By adjusting the length of D and d carefully, a combination of high transmission amplitudes with almost arbitrary phase shifts in the fast axis and the slow axis from 0 to 2π can be obtained simultaneously. Through optimizing the diameters of the elliptical pillar D and d, the desired phase shift would be gotten with low loss. In this design, the unit structure of D1 = 0.282 mm, d1 = 0.104 mm is adopted for linear conversation, in which the phase difference between the fast axis and slow axis is about π. The unit structure of D2 = 0.226 mm, d2 = 0.104 mm is adopted for circular conversation, in which the phase difference between the fast axis and slow axis is about ±π/2. By arranging the pillar directions in the bottom layer, the LHCP and RHCP can be obtained. Figure 5(a)–(d) show the obtained LHCP E field, in which the electric field rotates in the counterclockwise direction as the phase changes, and Fig. 5(e)–(h) show the obtained RHCP E field, in which the electric field rotates in the clockwise direction as the phase changes.
Fig. 4. Simulation results of the proposed elliptical cylinder-shaped unit cell. (a)–(b). Transmission amplitude ${t_f}$ and phase shift ${\varphi _f}\; $ of the pillar as a function of D and d under the fast axis F-polarized incidence at 350 GHz, respectively; (c)–(d). Transmission amplitude ${t_s}$ and phase shift ${\varphi _s}$ of the pillar as a function of D and d under the slow axis S-polarized incidence at 350 GHz, respectively; (e). Schematic of the unit.
Fig. 5. With X-polarized plane wave incidence, the output vector field diagram of the designed double-layer all-dielectric unit at 350 GHz., set the counterclockwise rotation angle to a positive value. (a)–(d) Corresponding to the top layer unit cell rotation angle of ${\theta _1} = {45^\circ }$ and the bottom layer unit cell rotation angle of $\theta _1^{\prime} ={-} {45^\circ }$: (a) phase=${0^\circ }$; (b) phase =${90^\circ }$; (c) phase =${180^\circ }$; (d) phase =${270^\circ }$. (e)-(h) Corresponding to the top layer unit cell rotation angle of ${\theta _1} = {45^\circ }$ and the bottom layer unit cell rotation angle of $\theta _1^{\prime} = {45^\circ }$: (e) phase=${0^\circ }$; (f) phase =${90^\circ }$; (g) phase =${180^\circ }$; (h) phase =${270^\circ }.$
As the size of 350 GHz cylindrical waveguide TE01 mode, the aperture size of the metalens is set as 5.88 mm × 5.88 mm, which is built up by 14 × 14 meta-unit designed above. For converting TE01 mode to LP Gaussian beam, the angles of pillar set are according to the TE01 mode $\vec{E}$ field vector direction at the center of the pillar. In this design, the TE01 mode is converted to a Y-direction LP Gaussian beam, and the cross-section view of the designed anisotropic metalens is shown in Fig. 6(a).
For circular polarization metalens design, the structure in Fig. 6(a) is set as the top layer, then, the bottom layer can be designed. Due to the polarization directions of the outgoing wave from the top layer at each position are all in Y-direction, the bottom layer for circular polarization could be isotropic. Figure 6(b)–6(c) are the cross-section views of two bottom layers for left-hand circular polarization and right-hand circular polarization, respectively. Moreover, a bottom layer for dual circular polarization is designed as shown in Fig. 6(d), in which the LHCP wave would be obtained in the upper half-plane and the RHCP wave would be obtained in the lower half-plane simultaneously.
Fig. 6. The layout of the designed metalens. (a) For LP Gaussian mode conversion; (b) The bottom layout for the LHCP Gaussian mode conversion; (c) The bottom layout for the RHCP Gaussian mode conversion; (d) The bottom layout for the DCP Gaussian mode conversion; (e) The scheme of EM simulation model.
3.2 EM simulation
The scheme of EM simulation model for whole metalens is shown in Fig. 6(e). The incident wave is launched from an 8 mm length tapered cylindrical waveguide with an output port of 2.4 mm and 1 mm away from the metalens. The observed plane is 1.82 mm away from the metalens on the output side. The EM simulation of TE01 mode converted to linearly Gaussian beam is shown in Fig. (7). Figure 7(a) and 7(b) show the results of the distribution of Ex and Ey components of the outgoing wave from cylindrical waveguide on the observation plane without metalens, respectively. The total electric field distribution on the observation field is shown in Fig. 7(c). It can be observed that the output mode has a symmetric field pattern corresponding to the field pattern of the typical circular waveguide TE01 mode. Figure 7(d)–(f) illustrate the outgoing wave $\vec{E}$ field patterns from the mode conversion system with the designed metalens at the frequency 350 GHz.
Fig. 7. Simulation results of electric field distributions for output modes with and without the proposed TE01-LP Gaussian beam conversion metalens. (a)-(c) Without the proposed metalens, the observed output mode electric field distributions; (a) Horizontal components; (b) Perpendicular components; (c) Output field pattern. (d)-(f) With the proposed metalens, the observed output mode electric field distributions: (d) Horizontal components; (e) Perpendicular components; (f) Output field pattern.
A Gaussian beam can be characterized by Gaussian mode purity [44], which is usually described by the correlation coefficient between the output beams. The scalar Gaussian mode content of the Gaussian beam can be obtained by the following formula:
The EM simulation of TE01 mode converted to CP Gaussian beam is shown in Fig. (8). Figure 8(a)–(c) show the Ex, Ey, and |E| of LHCP wave output field patterns, and Fig. 8(d)–(f) show the Ex, Ey and |E| of RHCP wave output field patterns. For the LHCP wave, the scalar Gaussian content is 98.86%. The axial ratios obtained in the axial line is 1.06 dB, according to the model from Ref. [47]. The polarization content of the Ex and Ey components are 51.31% and 48.69%, respectively. For the RHCP wave, the scalar Gaussian content is 98.15%, the axial ratios obtained in the axial line is 1.11 dB, and the polarization content of the Ex and Ey components are 52.63% and 47.37%, respectively. Figure 8(g)–(i) show the Ex, Ey, and |E| of DCP wave output field patterns. Simulation results show that the Ex component has a symmetric field pattern along the X-axis which corresponds to the design in Fig. 6(d), and the Ey component still has Gaussian-like distribution. The wave polarization pattern in the upper half-plane is consistent with Fig. 8(c), which is LHCP wave. The wave polarization pattern in the lower half-plane is consistent with Fig. 8(f), which is RHCP wave. As illustrated in Fig. 8(i), the incident waveguide TE01 mode wave is transformed into a DCP wave simultaneously.
Fig. 8. Simulation results of electric field distributions for output modes with the proposed metalens. (a)-(c) The observed output mode electric field distributions of the LHCP Gaussian mode metalens: (a) Horizontal components; (b) Perpendicular components; (c) Output field pattern. (d)-(f) The observed output mode electric field distributions of the RHCP Gaussian mode metalens: (d) Horizontal components; (e) Perpendicular components; (f) Output field pattern. (g)-(i) The observed output mode electric field distributions of the metalens with co-existence of left- and right-hand circular polarization: (g) Horizontal components; (h) Perpendicular components; (i) Output field pattern.
4. Discussion and conclusion
In summary, all-dielectric metalenses for quasi-optical mode and polarization conversion are proposed and investigated in this paper. To demonstrate the proposed conversion principle and design method. Four types of metalens are designed and electromagnetically simulated for converting cylindrical waveguide TE01 mode to LP, LHCP, RHCP, and DCP Gaussian beams at 350 GHz. The Gaussian mode contents of LP, LHCP, and RHCP output waves from metalens are all over 98% with high polarization contents. In DCP conversation, LHCP and RHCP waves are generated simultaneously and separately. The results show that the metalens for LP conversation is similar as an anisotropic half-wave plate, which could convert the polarization direction of LP wave at different position. The bottom layer of metalens for CP conversation is similar as an isotropic quarter-wave plate, which could convert the LP wave to a CP wave. Compared to traditional quasi-optical mode converter based on mirrors, the quasi-optical mode converter based on metalens proposed would generate not only LP wave, but also LHCP, RHCP, and DCP waves, and it also has the advantages of compact size, easy integration, low cost, and coaxial output. Compared to metal-surface metamaterials, all-dielectric metalens has high power capability and low internal ohmic losses, which is suitable for high power applications. This approach could extend the application of metalens, and promote the development and application of high-power VEDs in the terahertz region.
Funding
National Key Research and Development Program of China (2019YFA0210202); National Natural Science Foundation of China (61971097, 62111530054).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but maybe obtained from the authors upon reasonable request.
References
1. A. Y. Pawar, D. D. Sonawane, K. B. Erande, and D. V. Derle, “Terahertz technology and its applications,” Drug Invention Today 5(2), 157–163 (2013). [CrossRef]
2. S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nature Photon 7(12), 977–981 (2013). [CrossRef]
3. L.-M. Xu, W.-H. Fan, and J. Liu, “High-resolution reconstruction for terahertz imaging,” Appl. Opt. 53(33), 7891 (2014). [CrossRef]
4. J. El Haddad, B. Bousquet, L. Canioni, and P. Mounaix, “Review in terahertz spectral analysis,” TrAC Trends in Analytical Chemistry 44, 98–105 (2013). [CrossRef]
5. Y. Peng, J. Huang, J. Luo, Z. Yang, L. Wang, X. Wu, X. Zang, C. Yu, M. Gu, Q. Hu, X. Zhang, Y. Zhu, and S. Zhuang, “Three-step one-way model in terahertz biomedical detection,” PhotoniX 2(1), 12 (2021). [CrossRef]
6. J. H. Booske, “Plasma physics and related challenges of millimeter-wave-to-terahertz and high power microwave generation,” Phys. Plasmas 15(5), 055502 (2008). [CrossRef]
7. X. Li, J. Wang, R. Xiao, G. Wang, L. Zhang, Y. Zhang, and H. Ye, “Analysis of electromagnetic modes excited in overmoded structure terahertz source,” Phys. Plasmas 20(8), 083105 (2013). [CrossRef]
8. W. Liu, Y. Lu, Z. He, W. Li, L. Wang, and Q. Jia, “Broad-tunable terahertz source with over-mode waveguide driven by train of electron bunches,” Opt. Express 24(4), 4109 (2016). [CrossRef]
9. N. Shi, H. Wang, D. Xu, Z. Wang, Z. Lu, H. Gong, D. Liu, Z. Duan, Y. Wei, and Y. Gong, “Study of 220 GHz Dual-Beam Overmoded Photonic Crystal-Loaded Folded Waveguide TWT,” IEEE Trans. Plasma Sci. 47(6), 2971–2978 (2019). [CrossRef]
10. R. Xiao, J. Li, X. Bai, X. Zhang, Z. Song, Y. Teng, H. Ye, X. Li, J. Sun, and C. Chen, “An overmoded relativistic backward wave oscillator with efficient dual-mode operation,” Appl. Phys. Lett. 104(9), 093505 (2014). [CrossRef]
11. “A dual-mode operation overmoded coaxial millimeter-wave generator with high power capacity and pure transverse electric and magnetic mode output,” Physics of Plasmas 23(4), 043109 (2016).
12. W. Fu, X. Guan, and Y. Yan, “Generating High-Power Continuous-Frequency Tunable Sub-Terahertz Radiation From a Quasi-Optical Gyrotron With Confocal Waveguide,” IEEE Electron Device Lett. 41(4), 613–616 (2020). [CrossRef]
13. D. Lu, W. Fu, X. Guan, T. Yang, and Y. Yan, “Study on a Depressed Collector for a 75 GHz Low-Voltage Compact Gyrotron for Industrial Application,” J Infrared Milli Terahz Waves 42(2), 211–219 (2021). [CrossRef]
14. F. Qin, S. Xu, L.-R. Lei, B.-Q. Ju, and D. Wang, “A Compact Relativistic Magnetron With Lower Output Mode,” IEEE Trans. Electron Devices 66(4), 1960–1964 (2019). [CrossRef]
15. M. K. Thumm and W. Kasparek, “Passive high-power microwave components,” IEEE Trans. Plasma Sci. 30(3), 755–786 (2002). [CrossRef]
16. C.-W. Yuan, Y.-W. Fan, H.-H. Zhong, Q.-X. Liu, and B.-L. Qian, “A Novel Mode-Transducing Antenna for High-Power Microwave Application,” IEEE Trans. Antennas Propag. 54(10), 3022–3025 (2006). [CrossRef]
17. C. Pfeiffer and A. Grbic, “Controlling Vector Bessel Beams with Metasurfaces,” Phys. Rev. Applied 2(4), 044012 (2014). [CrossRef]
18. H. Yang, G. Li, X. Su, G. Cao, Z. Zhao, F. Yu, X. Chen, and W. Lu, “Annihilating optical angular momentum and realizing a meta-waveplate with anomalous functionalities,” Opt. Express 25(15), 16907 (2017). [CrossRef]
19. W. Fu, S. Hu, C. Zhang, X. Guan, and Y. Yan, “Compact quasi-optical mode converter based on anisotropic metasurfaces,” Opt. Express 29(11), 16205 (2021). [CrossRef]
20. C.-H. Liu and N. Behdad, “Investigating the Impact of Microwave Breakdown on the Responses of High-Power Microwave Metamaterials,” IEEE Trans. Plasma Sci. 41(10), 2992–3000 (2013). [CrossRef]
21. J. Xie, C. Chen, C. Chang, C. Wu, and Y. Huo, “Mechanisms of high-gradient microwave breakdown on metal surfaces in high power microwave source,” Phys. Plasmas 24(12), 123302 (2017). [CrossRef]
22. A. Boltasseva and H. A. Atwater, “Low-Loss Plasmonic Metamaterials,” Science 331(6015), 290–291 (2011). [CrossRef]
23. 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 (2018). [CrossRef]
24. X. Shi, D. Meng, Z. Qin, Q. He, S. Sun, L. Zhou, D. R. Smith, Q. H. Liu, T. Bourouina, and Z. Liang, “All-dielectric orthogonal doublet cylindrical metalens in long-wave infrared regions,” Opt. Express 29(3), 3524 (2021). [CrossRef]
25. X. Zang, H. Ding, Y. Intaravanne, L. Chen, Y. Peng, J. Xie, Q. Ke, A. V. Balakin, A. P. Shkurinov, X. Chen, Y. Zhu, and S. Zhuang, “A Multi-Foci Metalens with Polarization-Rotated Focal Points,” Laser Photonics Rev. 13(12), 1900182 (2019). [CrossRef]
26. X. Zang, W. Xu, M. Gu, B. Yao, L. Chen, Y. Peng, J. Xie, A. V. Balakin, A. P. Shkurinov, Y. Zhu, and S. Zhuang, “Polarization-Insensitive Metalens with Extended Focal Depth and Longitudinal High-Tolerance Imaging,” Adv. Optical Mater. 8(2), 1901342 (2020). [CrossRef]
27. S. Gao, C. Park, C. Zhou, S. Lee, and D. Choi, “Twofold Polarization-Selective All-Dielectric Trifoci Metalens for Linearly Polarized Visible Light,” Adv. Optical Mater. 7(21), 1900883 (2019). [CrossRef]
28. Y. Zhu, B. Lu, Z. Fan, F. Yue, X. Zang, A. V. Balakin, A. P. Shkurinov, Y. Zhu, and S. Zhuang, “Geometric metasurface for polarization synthesis and multidimensional multiplexing of terahertz converged vortices,” Photon. Res. 10(6), 1517 (2022). [CrossRef]
29. H. Yang, G. Li, G. Cao, Z. Zhao, J. Chen, K. Ou, X. Chen, and W. Lu, “Broadband polarization resolving based on dielectric metalenses in the near-infrared,” Opt. Express 26(5), 5632 (2018). [CrossRef]
30. M. Kang, Z. Zhang, T. Wu, X. Zhang, Q. Xu, A. Krasnok, J. Han, and A. Alù, “Coherent full polarization control based on bound states in the continuum,” Nat Commun 13(1), 4536 (2022). [CrossRef]
31. R. Lin and X. Li, “Multifocal metalens based on multilayer Pancharatnam–Berry phase elements architecture,” Opt. Lett. 44(11), 2819 (2019). [CrossRef]
32. Y. Xu, H. Zhang, Q. Li, X. Zhang, Q. Xu, W. Zhang, C. Hu, X. Zhang, J. Han, and W. Zhang, “Generation of terahertz vector beams using dielectric metasurfaces via spin-decoupled phase control,” Nanophotonics 9(10), 3393–3402 (2020). [CrossRef]
33. T. Wu, H. Zhang, S. Kumaran, Y. Xu, Q. Wang, W. Michailow, X. Zhang, H. E. Beere, D. A. Ritchie, and J. Han, “All dielectric metasurfaces for spin-dependent terahertz wavefront control,” Photonics Res. 10(7), 1695 (2022). [CrossRef]
34. H. Zhou, L. Huang, X. Li, X. Li, G. Geng, K. An, Z. Li, and Y. Wang, “All-dielectric bifocal isotropic metalens for a single-shot hologram generation device,” Opt. Express 28(15), 21549 (2020). [CrossRef]
35. X. Zang, B. Yao, L. Chen, J. Xie, X. Guo, A. V. Balakin, A. P. Shkurinov, and S. Zhuang, “Metasurfaces for manipulating terahertz waves,” gxjzz 2(2), 148 (2021). [CrossRef]
36. T. Wu, X. Zhang, Q. Xu, E. Plum, K. Chen, Y. Xu, Y. Lu, H. Zhang, Z. Zhang, X. Chen, G. Ren, L. Niu, Z. Tian, J. Han, and W. Zhang, “Dielectric Metasurfaces for Complete Control of Phase, Amplitude, and Polarization,” Adv. Opt. Mater. 10(1), 2101223 (2022). [CrossRef]
37. Q. Wei, B. Sain, Y. Wang, B. Reineke, X. Li, L. Huang, and T. Zentgraf, “Simultaneous Spectral and Spatial Modulation for Color Printing and Holography Using All-Dielectric Metasurfaces,” Nano Lett. 19(12), 8964–8971 (2019). [CrossRef]
38. B. Wang, F. Dong, D. Yang, Z. Song, L. Xu, W. Chu, Q. Gong, and Y. Li, “Polarization-controlled color-tunable holograms with dielectric metasurfaces,” Optica 4(11), 1368 (2017). [CrossRef]
39. P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser & Photon. Rev. 4(6), 795–808 (2010). [CrossRef]
40. L. Zhang, S. Mei, K. Huang, and C.-W. Qiu, “Advances in Full Control of Electromagnetic Waves with Metasurfaces,” Adv. Opt. Mater. 4(6), 818–833 (2016). [CrossRef]
41. P. F. Goldsmith, “Quasi-optical techniques,” Proc. IEEE 80(11), 1729–1747 (1992). [CrossRef]
42. M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High-Efficiency Dielectric Huygens’ Surfaces,” Adv. Opt. Mater. 3(6), 813–820 (2015). [CrossRef]
43. A. Kabiri, E. Girgis, and F. Capasso, “Metasurface-based half-wave plate,” in 2013 IEEE Antennas and Propagation Society International Symposium (APSURSI) (IEEE, 2013), pp. 322–323.
44. J. Jin, B. Piosczyk, M. Thumm, T. Rzesnicki, and S. Zhang, “Quasi-Optical Mode Converter/Mirror System for a High-Power Coaxial-Cavity Gyrotron,” IEEE Trans. Plasma Sci. 34(4), 1508–1515 (2006). [CrossRef]
45. R. Martínez-Herrero, P. M. Mejías, G. Piquero, and V. Ramírez-Sánchez, “Global parameters for characterizing the radial and azimuthal polarization content of totally polarized beams,” Opt. Commun. 281(8), 1976–1980 (2008). [CrossRef]
46. Y. Ma and R. Wu, “Characterizing polarization properties of radially polarized beams,” Opt. Rev. 21(1), 4–8 (2014). [CrossRef]
47. D.-G. Fang, Antenna Theory and Microstrip Antennas (CRC Press, 2017).
