Open Access
Add to BibSonomy
Abstract
Impedance mismatch generally exists upon interfaces between different media. This is especially true for TE-polarized waves with large incident angles since there is no Brewster effect. As a result, high-efficiency transmission can only be guaranteed within limited incident angle range. It is desirable that transparent windows possess robust angle-stability. In this work, we propose a strategy of realizing transparent windows with extreme angle-stability using anisotropic metasurfaces. Different from traditional isotropic materials, anisotropic metasurfaces require specific three-dimensional permittivity and permeability parameters. Theoretical formulas are derived to realize a highly efficient transmission response without angular dispersion. To validate our design concept, a two-layer cascaded electromagnetic anti-reflector is designed, and it exhibits a characteristic impedance matching for nearly all incidence angles under TE-polarization illumination. As a proof-of-concept, a prototype of extremely angle-stable transparent window is fabricated and measured. Compared with the pure dielectric plate, the reflection coefficients are on average reduced by 40% at 13.5 GHz for TE-polarized waves from 0° to 80°. Therefore, we think, anisotropic cascaded electromagnetic transparent windows are capable of tailoring the electromagnetic parameter tensors as desired, and provide more adjustable degrees of freedom for manipulating electromagnetic wavefronts, which might open up a promising way for electromagnetic antireflection and find applications in radomes, IR windows and others.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
When an electromagnetic (EM) wave impinges on an interface between two dielectrics with different refractive indices, the fundamental reflection and refraction usually occur due to the mismatched dielectric impedance [1]. As a typical example, it’s obviously noticed that for RF front-end module in wireless communication systems, a slightly deficient impedance matching network (impedance mismatch) [2,3] will affect the antenna efficiency and radiation pattern. Fortunately, some adaptive impedance tuning algorithms [4] and reconfigurable impedance systems [5–7] are proposed as a feasible improvement scheme to ensure their own information high-speed transmission fast and accurately. In the context of classical electromagnetic theory, unless the EM waves are incident at specific angle (which means Brewster’ angle) under transverse magnetic (TM)-polarization [8,9], different amounts of reflections can arise at the interface between different dielectrics. Such reflection is absolutely undesired when maximized transmission is needed, which leads to the flourish of transmission-enhancement theory [10,11] and superfluous transmission-enhancement structures. Conventional quarter-wave wavelength transmission-enhancement film [12] needs specific refractive index ${n_g} = \sqrt {{n_d}\mathrm{\ast }{n_s}} $ and the ideal thickness $\textrm{d} = \lambda /4$ (where nd, ns and λ are the refractive indices of the two dielectrics and EM wavelength of free space). Multi-layered transmission-enhancement coatings [13] require even larger thickness. However, all above coatings utilize isotropic EM parameters of general traditional materials, which might cause angular dispersion and bulky design.
Recently, with the rapid development of metasurfaces [5,7–9,11,14–34] transcending natural materials in many aspects, many phenomena for manipulating EM waves have been emerging, such as ultrathin lensing [14,15], invisibility and illusionary effects [16–18], propagating-to-evanescent wave conversion [19], antennas transmitter and decoupler [20–22], holography [23,24], photonic spin Hall effect [25] and so on, which provides an attractive way for improving transmissivity of the dielectric. Reflection-type metasurfaces can realize highly efficient reflection through additional metal substrate [26,27]. However, it’s more challengeable to achieve high-efficiency angle-stable transmission-type metasurfaces [28,29]. Many theories and structures including frequency selective surface (FSS) [30,31] and Huygens’ metasurfaces (HM) [32–34] were proposed to enhance transmittance. Among them, the EM waves propagation in anisotropic metasurfaces [35–37] is a study of wide interest. Some methods of applying cascaded photonic crystals [38] and combination of metallic rods and disk [39] were explored in terahertz domains. Other investigations were conducted in microwave frequency range as well, such as invisible metallic mesh [40], Brewster lens [41] and spatially dispersive effective medium [42]. However, these works mainly focus on the combination of pure dielectric and three-dimensional composite structures, which may bring about sophisticated fabrication technique and be not conducive to integrated design. In contrast to these, our transparent window could realize extremely angle-stable transmission while maintaining simply planar structure. Considering the differences of angular response characteristics for diffractive optics, some research works based on angle multiplex such as spin-orbit interaction [43], wide-angle metalens [44], multiplexed meta-holography [45] were developed and optimized either to broad field-of -view or enhance optical storage capacity, whose incident angle domains are relatively limited despite these unprecedented achievements.
In this work, we propose bi-layered embedded metasurfaces to solve the contradiction between the transmission enhancement, angular dispersion, and wide-angle domain. This design blends the elimination of angular dispersion and wide-angle transmission enhancement in a subwavelength scale. Attributed to the anisotropy of bi-layered metasurfaces, that is, different electromagnetic tensors of three dimensions, these inherently intriguing functions can be flexibly manipulated with abundant adjustable degrees of freedom, whose performance far exceeds single-layered metasurface. As a more specific demonstration, when overall EM component parameters corresponding to the material are controlled, the transmission enhancement covers the extremely wide-angle domain; when part of the corresponding EM parameters are adjusted, the bandwidth of antireflection of can be expanded. Different from the transformation optics, the impedance matching condition for anisotropic medium can be obtained based on transmission/reflection coefficients without reconstructing coordinate conditions and The cracked direction of upper and lower split resonant rings (SRRs) is designed as an inverse symmetrical structure, which compensates the transmission phase of EM waves at the two interfaces and makes them pass through the dielectric straightly. All the simulated and measured results can verify efficient integrated transmission, and concrete mechanism of principle is shown in Fig. 1. This work displays huge potential of anisotropic metasurfaces in the fields of transmission for paving the way to raise efficiency of detecting and focusing meta-devices, and can be extended to Terahertz or even optical fields.
Fig. 1. Schematic diagram of the extremely angle-stable transparent window for TE-polarized waves. The TE-polarized waves with electric field vector along y-direction is incident to ETW at different angles along the xz- plane. The rainbow-colored fan-shaped channels represent the angular domain covered by incident and refractive EM waves, while the angular domain covered by reflective EM waves are depicted by the gray fan-shaped channels. A zoom-in view of meta-atom in the upper right area denotes a basic pixel of the designed metasurface. More detailly, iridescence represents a high proportion of transmitted energy and gray represents very little reflected energy. Several arrows and break lines embedded in the fan-shaped channels depict the corresponding direction in which the EM waves propagate.
2. Theory and design
2.1 Theoretical analysis
Firstly, we demonstrate that the conflict between impedance matching between incident angle and polarization states generally exists among two different dielectric media described by the gradual impedance transformation. Without any loss of generality, we consider a linearly polarized plane wave incident from air upon a sheet of isotropic material with an incident angle θ under TE-polarization, as illustrated in Fig. 2(a). Besides, traditional ceramic-based wave transmitting materials are used in this study as typical isotropic materials. Figure 2(b) gives the z-directional characteristic impedances of air and a substrate varying with incident angle under the TE- polarized waves. The values of it for TE- incidence can be expressed as
Fig. 2. Incidence of EM waves, gradient impedance, and equivalent EM parameters model. (a) A plane wave impinging on a uniaxial material from the air at an incident angle θ under TE-polarization. (b) The z-directional characteristic impedances of air and a dielectric medium (CMC) under the incidence of TE-polarization with θ∈[0°,90°]. (c) The equivalent permittivity model (Drude-model) and equivalent permeability model (Lorentzian-model) of metamaterial.
In order to solve the conflict between incident angle, transmission enhancement and wide-angle domain, the equivalent EM parameters must be more flexibly tailored and more degrees of freedom might be introduced. In these cases, the metamaterial can no longer be approximated as isotropic medium. Previously, we note that, EM anisotropic metasurfaces with different EM parametric tensors were found to give consideration to transmission efficiency and angular dispersion affected by incident angle. Inspired by this feature of metamaterial, we explore the bi-layered inverted SRRs to achieve the high-efficiency transmission integrating extremely incident angle and angular stability. For the EM anisotropic metamaterial, in order to simplify the analysis procedure, the imaginary parts of the permittivity and permeability are ignored due to their quite small values, and all the parameters are assumed to be real. Here, the permittivity and permeability are defined as diagonal forms, which can be expressed as:
The TE- polarized reflection coefficients between the two adjacent dielectric media under boundary conditions, can be expressed as follows:
In order to achieve the high-efficiency transmission, the reflection coefficients RTE must be equal to zero. By combining the Eqs. (1), (3)–(6), the expression of reflection coefficients RTE and the condition for high-efficiency transmission are given as follows:
What’ more, the effect of angular dispersion can be eliminated while guaranteeing enhanced transmission, and the conditions that the EM parameters of anisotropic metamaterials need to satisfy the following two equations [46,47]:
For TE-polarized incidence, the unit cell of the metamaterials should possess an independently adjustable tangential and normal EM responses, which needs to control the permittivity and permeability tensors in corresponding direction. Therefore, the Drude-Lorentzian dispersion model was introduced to produce desired permittivity and permeability from negative through zero to positive values. When EM waves interact with metal layers in metamaterials, the Drude-Lorentzian dispersion model [48] can be expressed as follows:
where ω0, ω and γ are resonant frequency, angular frequency of EM waves, and loss of EM radiation.2.2 Structural design
From the point of view of transmission geometry, the highly efficient metasurfaces should be composed of embedded meta-atoms periodically arranged, so as to eliminate the reflection upon the two interfaces. Figure 3(a)i, ii, and iii show the top-, bottom-, and side-views of the designed transmission-enhancement metasurfaces, the thickness of substrate is 8 mm (t = 8 mm). Each meta-atom of the metasurfaces consists of two elements: a pair of SRRs placed in reverse, as shown in Fig. 3(b). In addition, the two elements are creatively separate-placed by the three layers of dielectric substrate (εr = 3.6, tanδ = 0.002) for phase compensation. The periods along x- and y-direction of the meta-atom are p = 6 mm and h = 6 mm, and the distances of between upper SRR and top surface, between upper SRR and lower SRR, between lower SRR and ground surface are 2 mm, 4 mm, 2 mm, respectively. The detailed structures of the unit cell are shown in Fig. 3(c) and the optimized geometrical parameters are w = 0.4 mm, g = 2.4 mm, l1 = 5.4 mm, and l2 =5.8 mm.
Fig. 3. Meta-atom of the bi-layered anisotropic metasurfaces for highly efficient transmission. (a) The configuration of the proposed metasurfaces. i, ii, and iii represent top-, bottom-, and side-views of this model, respectively. (b) Layout of the proposed meta-atom. The anisotropic double-layer metal embedded meta-atom is composed of a pair of reversely placed split resonant rings (SRRs) separated by the dielectric spacer. (c) An illustration of the structure parameters.
In the simulation, the illumination upon metal surface of EM waves induces electric or magnetic response or both to the meta-atoms. Specifically, for TE-polarized waves, the SRRs can be separated into the combination of short metal wires and double SRRs or only short metal wires. Thus, the angular dispersion and non-dispersion are controlled by the two situations. What’s more, two-layer split resonant rings are able to generate surface currents in response to incoming electric and magnetic fields. Furthermore, reverse placement is beneficial to tailor the permeability tensors through the coupling of them to produce different magnetic responses.
3. Simulation
3.1 Simulated results of the extremely angle-stable transparent window
By periodically replicating the two layers of metal patterns sandwiched inside the CMC dielectric plate, we obtain the highly efficient metasurfaces that can achieve the enhanced transmission. This meta-atom emerges different EM responses towards the illumination of the EM waves for satisfying the needs of high-efficiency transmission, as given in Eq. (6). To validate this, this meta-atom is loaded into the proposed metasurfaces, and full wave simulation are performed by Finite-Difference Time-Domain (FDTD) simulations without and with the designed metasurfaces through the Frequency Domain Solver in the Computer Simulation Technology (CST) Microwave Studio. Here, unit cell boundary is applied in x- and y- directions. Two Floquet ports are set in z-direction to calculate S-parameters.
Figure 4 depicts the reflection and transmission coefficients under TE-polarization with the varied incident angles. Firstly, it’s clearly seen that with the increase of incident angles, the transmission effect will gradually deteriorate for pure dielectric plate, as shown in Fig. 4(a), which is consistent with the analysis in Fig. 2(b). However, when loading the transmission-enhancement metasurfaces, the reflection coefficients are greatly reduced, while the red and black dotted lines in Fig. 4(b) represent the reflection valleys (less than 0.1) in different variation trend, especially the black dotted line exhibits “no-offset” angle for TE-polarization at 13.5 GHz. Compared with the pure dielectric plate, the reflection coefficients are dramatically reduced on average from 0.65 to 0.25, which reduces reflection efficiency by 40%. As described in Fig. 4(c)-(d), the transmission coefficients of this proposed ETW at 13.5 GHz also present an ultra-wide-band stable response (depicted via the black dotted line), whose values on average are 0.97, and are much higher than those of the pure CMC plate whose values on average are 0.80. Besides, the blue dotted line shown in Fig. 4(d) provides a strong dispersion transmission response for this proposed ETW, which combines the aforementioned transmission response jointly expand transmission bandwidth in Ku-band. However, considering that the proposed metasurface is not an ideal dielectric material, EM waves energy will be inevitably lost when incident at different angles, i.e., according to ${|A |^2} = 1 - {|R |^2} - {|T |^2}$ [49,50], on the one hand, when the angle of incidence is less than 60°, 5% of the energy transmitted through EM waves is absorbed by the designed ETW; on the other hand, with the increase of incidence angles from 60° to 80°, the loss of electromagnetic wave gradually increases from 5% to 25%. In spite of increasing absorption, the transmittance of electromagnetic waves relative to the pure dielectric substrate is still improved by nearly 40%, confirming the electromagnetic antireflection properties.
Fig. 4. The reflection coefficients and transmission coefficients varying against frequency with the incident angle belonging to [0°,80°]. Simulated reflection coefficients for a CMC dielectric plate without (a) and with (b) the designed transmission-enhancement metasurfaces under TE-polarized waves. Simulated transmission coefficients for a CMC dielectric plate without (c) and with (d) the designed transmission-enhancement metasurfaces under TE-polarized waves.
3.2 Anisotropic parameters analysis of the transparent window
To further explain the physical mechanism of aforementioned angular non-dispersion for TE-polarized waves, the wave impedances are calculated and the anisotropic parameters varying against the incident angle and frequency are extracted, as shown in Fig. 5. In addition, the effective characteristic wave impedance can be calculated by the ratio the integrated electric and magnetic fields outside the metasurfaces based on surface equivalent theorem [51], where the influence of near-field scattering is neglected. More specifically, the reference plane is set at two millimeters from the bottom of the dielectric under the illumination of TE-polarized waves. For a particular incident angle, the integrated electric and magnetic fields are calculated as follows:
Fig. 5. The calculated wave impedances and extracted anisotropic parameters of the extremely angle-stable transparent window for TE polarized waves. (a) The effective complex z-directional characteristic impedances of the air and the designed metasurfaces at 13.5 GHz, respectively. (b) The y-directional permittivity εyy, (c) the x-directional permeability μxx, and (d) the z-directional permeability μzz varying against the incident angle and frequency. The black dotted boxes denoting the stable values of εyy, μxx, and μzz are 3.0, 3.0 and 0.33, respectively.
Figure 5(a) shows the calculated z-directional characteristic impedance of the designed metasurfaces maintain consistent development trends with that of the air at 13.5 GHz even if the incident angle exceeds 80°. However, the imaginary part of z-directional characteristic impedance for metasurfaces is greater than that of the air, which means the loss of EM waves in metamaterial transmission. Moreover, the extracted EM parameters via scattering parameter inversion mentioned in [52] are shown in Fig. 5(b)-(d), which indicates the stable values of εyy, μxx, and μzz are 3.0, 3.0 and 0.33 at around 13.5 GHz satisfying the Eqs. (6) and (7) for variable incident angles and confirms the greatly reduced reflection coefficients in Fig. 4(b). However, the values of εyy, μxx, and μzz are no steady and varies against the incident angles. (e. g., only at the incident angle of 30°, the values of εyy, μxx, and μzz are 1.6, 1.4, and 1.1 at 14.5 GHz represented by five-pointed stars satisfying the Eq. (7) and the reflection can be eliminated). Therefore, it’s clearly indicated that both the angular dispersion and non-dispersion phenomena under TE-polarization exist.
3.3 Electromagnetic responses elaborations under TE-polarizations
The surface currents on the meta-atom are also calculated to analyze the working mechanism of the different phenomena under TE-polarized waves at the incident angle of 30°, and the simulated results are shown in Fig. 6(a)-(d). Here, for angular stability at 13.5 GHz, the currents on the surface are apparently distributed into two parts of single SRR, where one is equivalent to a magnetic dipole in a semicircle, and another is equivalent to a rectilinear electric dipole. More detailly, the antiparallel magnetic field induced by the magnetic dipole based on the Lenz's law, the induced antiparallel electric field induced by the magnetic dipole, and the reversely short metal wire currents of the two layers contribute to the adjustment of the anisotropic parameters εyy, μxx, and μzz together, as indicated in Fig. 6(a) and 6(b). This follows the Drude-Lorentzian model and works in the resonant region I, as illustrated in Fig. 2(c). On the contrary, at 14.5 GHz, Fig. 6(c) and 6(d) present that only the electric dipole plays a part in the modulating process, which cannot effectively modulate normal permeability μzz and results in the angular dispersion, which also follows the Drude-Lorentzian model and works in the resonant region I, as illustrated in Fig. 2(c). The detected different EM responses are consistent with the simulated results in Fig. 4(b).
Fig. 6. The surface currents, power flow, and 3D far-field scattering patterns under TE-polarized waves at the incident angle of 30°. (a)-(b) and (c)-(d) The surface currents of upper and lower interfaces at 13.5 GHz and 14.5 GHz, respectively. (e) The power flow through the metasurfaces at 13.5 GHz. (f) The 3D far-field scattering patterns through the metasurfaces at 13.5 GHz.
In addition, Fig. 6(e) and 6(f) respectively represents the power flow and 3D far-field scattering patterns through the metasurfaces at 13.5 GHz. The power flow upon the upper interface and the lower interface is twisted in the opposite direction, and most of the EM waves transmit through the designed metasurfaces with propagating in the same angle as the incidence, which compensates the transmission phase and verifies the theoretical analysis.
4. Experimental verification
To experimentally verify the simulated results, a prototype with a size of 1080 mm×360 mm has been fabricated as shown in Fig. 7(a). The metallic coatings are etched on substrate using the print circuit board (PCB) technique and the adjacent three dielectric layers including two pure dielectric substrates and one double-sided copper-clad dielectric layer are pasted together with 3M tape (εr = 3.0, thickness = 50 µm). During the experiment, a pair of linearly polarized antennas are separately used as the transmitter for obliquely illuminating the metasurfaces and the receiver for obtaining the transmitted EM waves. As shown in Fig. 7(b), the prototype is placed on the foam substrate, and set on the center of the rotating stage. The two antennas are connected to the two ports of the Agilent E8363B network analyzer, which is surrounded by the absorbing materials to avoid the unwanted reflections from the environment. By rotating the fixed prototype, the transmission coefficients are measured with the incident angle varying from 0° to 80°.
Fig. 7. Experimental verification of the extremely angle-stable transparent window. (a) Photograph of the fabricated sample. (b) The transmission coefficients experimental setup. Under TE-polarized, the transmission coefficients of the CMC dielectric plate without (c) and with (d) fabricated metasurfaces varying against frequency and incident angles. The blue and black dotted lines depict the transmission peaks as the function of frequency and incident angle.
The tested transmission coefficients under TE-polarized waves of the prototype plate with and without the metasurfaces are shown in Fig. 7. As shown in Fig. 7(c) and 7(d), compared with the pure CMC plate, the transmission coefficient of that with the metasurfaces is significantly improved in the whole Ku-band. More specifically, through loading the high-efficiency metasurfaces, the transmittivity on average from 36% of the pure CMC plate to 80% of the prototype. The blue and black dotted lines depict the transmission peaks vary against the frequency and incident angle. According to the Fig. 4(d), the different variation trends of the transmission peaks represent the angular dispersion and non-dispersion, which coincides well with the experimental results shown in Fig. 7(d). In more detail, compared with the pure CMC plate, the fabricated EM transparent window opens two high-efficient transmission channels with ultra-wide-angle domain at 13.7 GHz and from 14.5 GHz to 15.5 GHz, respectively. However, the transmission deviations including the frequency shift and amplitude discrepancy of the designed metasurfaces are probably caused by the following reasons: (1) the dielectric properties used in the actual sample are slightly different from the values in the simulation. (2) diffraction occurring at the edges of the prototype of a finite size may introduce amplitude inaccuracies especially at extreme angles. (3) the bonding between the three dielectric layers by 3M tape introducing uncontrollable factors would lead to the frequency shift. Table 1 compares the characteristics (incident angle domain, working manner, operation bandwidth, transmission efficiency) of our proposed metadevice with other related metastructures, demonstrating our scheme has obvious advantages [53–56].
Table 1. Comparison of the characteristics of our proposed metadevice with other related metastructures
5. Conclusion
To summarize, we proposed an extremely angle-stable transparent window for TE-polarization based on metasurfaces’ anisotropy. By embedding two layers of metasurfaces composed of split resonant rings (SRRs) with opposite split directions, the high-efficiency metasurfaces can produce different EM responses to adjust the multidimensional EM parameters. The abundant adjustable degrees of freedom endowed with the bi-layered design of the meta-atoms exhibit excellent performance beyond the single-layered metasurface. Meanwhile, the transmission phase of EM waves is compensated at the two interfaces, which makes them pass through the dielectric straightly. The experimental verification is implemented at microwave frequencies and the measured results match well with the designed ones. Both the simulations and experiments demonstrated that the proposed ETW are capable of enhancing transmission efficiency by 40% in nearly Ku-band and stable angular response from 0° to 80°. For demonstration, the contradiction between the transmission enhancement, angular dispersion, and wide-angle domain is resolved simultaneously in a subwavelength scale. Such highly efficient transmission effect with simply planar structure may find applications in radomes, IR windows, and can be extended to Terahertz or even optical fields. Our discovery will open a new horizon for anisotropic metasurfaces, which will impact profoundly EM transmission responses in the future.
Funding
National Natural Science Foundation of China (61901508, 61971435); National Key Research and Development Program of China (SQ2017YFA0700201); The Graduate Scientific Research Foundation of Department of Basic Sciences..
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. L. John, Theory of Reflection of Electromagnetic and Particle Waves (Martinus Nijhoff Publishers, 1987), Chap.2.
2. M. Alibakhshikenari, B. S. Virdee, C. H. See, R. A. Abd-Alhameed, F. Falcone, and E. Limiti, “Energy Harvesting Circuit with High RF-to-DC Conversion Efficiency,” in 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting (2020 IEEE AP-S/URSI), pp. 79–86.
3. M. Alibakhshikenari, B. S. Virdee, C. H. See, R. A. Abd-Alhameed, F. Falcone, and E. Limiti, “Impedance Matching Network Based on Metasurfaces (2-D Metamaterials) for Electrically Small Antennas,” in 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting (2020 IEEE AP-S/URSI), pp.1953–1954.
4. M. Alibakhshikenari, B. S. Virdee, P. Shukla, C. H. See, R. A. Abd-Alhameed, F. Falcone, and E. Limiti, “Improved adaptive impedance matching for RF front-end systems of wireless transceivers,” Sci. Rep. 10(1), 14065 (2020). [CrossRef]
5. M. Alibakhshikenari, B. S. Virdee, P. Shukla, Y. Wang, L. Azpilicueta, M. Naser-Moghadasi, C. H. See, I. Elfergani, C. Zebiri, R. A. Abd-Alhameed, I. Huynen, J. Rodriguez, T. A. Denidni, F. Falcone, and E. Limiti, “Impedance Bandwidth Improvement of a Planar Antenna Based on Metamaterial-Inspired T-Matching Network,” IEEE Access 9, 67916–67927 (2021). [CrossRef]
6. Y. W. Fan, Z. H. Zhang, M. Trinkle, A. D. Dimitrovski, J. B. Song, and H. S. Li, “A Cross-Layer Defense Mechanism Against GPS Spoofing Attacks on PMUs in Smart Grids,” IEEE. T. Smart. Grid. 6(6), 2659–2668 (2015). [CrossRef]
7. M. Alibakhshikenari, B. S. Virdee, C. H. See, R. A. Abd-Alhameed, F. Falcone, and E. Limiti, “Automated Reconfigurable Antenna Impedance for Optimum Power Transfer,” in 2019 IEEE Asia-Pacific Microwave Conference (APMC), pp. 1461–1463.
8. G. Lavigne and C. Caloz, “Generalized Brewster effect using bianisotropic metasurfaces,” Opt. Express 29(7), 11361–11370 (2021). [CrossRef]
9. J. Luo, H. Chu, R. Peng, M. Wang, J. Li, and Y. Lai, “Ultra-broadband reflectionless Brewster absorber protected by reciprocity,” Light: Sci. Appl. 10(1), 89 (2021). [CrossRef]
10. H. K. Raut, V. A. Ganesh, A. S. Nair, and S. Ramakrishna, “Anti-reflective coatings: A critical, in-depth review,” Energ. Environ. Sci. 4(10), 3779–3804 (2011). [CrossRef]
11. A. H. Dorrah, M. chen, and G. V. Eleftheriades, “Bianisotropic Huygens’ Metasurface for Wideband Impedance Matching Between Two Dielectric Media,” IEEE Trans. Antennas Propag. 66(9), 4729–4742 (2018). [CrossRef]
12. S. P. Huber, R. W. E. van de Kruijs, A. E. Yakshin, E. Zoethout, K.-J. Boller, and F. Bijkerk, “Subwavelength single layer absorption resonance antireflection coatings,” Opt. Express 22(1), 490–497 (2014). [CrossRef]
13. Y. Matsuoka, M. P. Semtsiv, S. Peters, and W. T. Masselink, “Broadband multilayer antireflection coating for quantum cascade laser facets,” Opt. Lett. 43(19), 4723–4726 (2018). [CrossRef]
14. M. Khorasaninejad, W. T. Chen, R. C. Devlin, O. Jaewon, and A. Y. Zhu, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016). [CrossRef]
15. A. She, S. Y. Zhang, S. Shian, D. R. Clarke, and F. Capasso, “Adaptive metalenses with simultaneous electrical control of focal length, astigmatism, and shift,” Sci. Adv. 4(2), e9957 (2018). [CrossRef]
16. B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B: Condens. Matter Mater. Phys. 91(19), 195444 (2015). [CrossRef]
17. H. C. Chu, L. Qi, B. B. Liu, J. Luo, S. L. Sun, Z. H. Hang, L. Zhou, and Y. Lai, “A hybrid invisibility cloak based on integration of transparent metasurfaces and zero-index materials,” Light: Sci. Appl. 7(1), 50 (2018). [CrossRef]
18. H. X. Xu, G. W. Hu, Y. Z. Wang, C. H. Wang, M. Z. Wang, S. J. Wang, Y. J. Huang, P. Genevet, W. Huang, and C. W. Qiu, “Polarization-insensitive 3D conformal-skin metasurface cloak,” Light: Sci. Appl. 10(1), 75 (2021). [CrossRef]
19. W. J. Sun, Q. He, S. L. Sun, and L. Zhou, “High-efficiency surface plasmon meta-couplers: concept and microwave-regime realizations,” Light: Sci. Appl. 5(1), e16003 (2016). [CrossRef]
20. M. Alibakhshikenari, E. M. Ali, M. Soruri, M. Dalarsson, M. Naser-Moghadasi, B. S. Virdee, C. Stefanovic, A. Pietrenko-Dabrowska, S. Koziel, S. Szczepanski, and E. Limiti, “A Comprehensive Survey on Antennas On-Chip Based on Metamaterial, Metasurface, and Substrate Integrated Waveguide Principles for Millimeter-Waves and Terahertz Integrated Circuits and Systems,” IEEE Access 10, 3668–3692 (2022). [CrossRef]
21. M. Alibakhshikenari, F. Babaeian, B. S. Virdee, S. Aïssa, L. Azp, C. H. See, A. A. Althuwayb, I. Huynen, R. A. Abd-Alhameed, F. Falcone, and E. Limiti, “A Comprehensive Survey on “Various Decoupling Mechanisms with Focus on Metamaterial and Metasurface Principles Applicable to SAR and MIMO Antenna Systems,” IEEE Access 8, 144778–144808 (2020). [CrossRef]
22. M. Alibakhshikenari, B. S. Virdee, L. Azpilicueta, M. Naser-Moghadasi, M. O. Akinsoluilicueta, C. H. See, B. Liu, R. A. Abd-Alhameed, F. Falcone, I. Huynen, T. A. Denidni, and E. Limiti, “A Comprehensive Survey of “Metamaterial Transmission-Line Based Antennas: Design, Challenges, and Applications,” IEEE Access 8, 192965–193004 (2020). [CrossRef]
23. W. W. Wan, J. Gao, and X. D. Yang, “Metasurface Holograms for Holographic Imaging,” Adv. Opt. Mater. 5(21), 1700541 (2017). [CrossRef]
24. L. W. Wei, H. F. Ma, R. Y. Wu, Q. Xiao, Y. Gou, M. Wang, Z. X. Wang, L. Bao, H. L. Wang, Y. M. Qing, and T. J. Cui, “Transmission-Reflection Controls and Polarization Controls of Electromagnetic Holograms by a Reconfigurable Anisotropic Digital Coding Metasurface,” Adv. Opt. Mater. 8(22), 2001065 (2020). [CrossRef]
25. O. Takayama, S. Johneph, M. Radu, L. Andrevi V, and P. Graciana, “Photonic spin Hall effect in hyperbolic metamaterials at visible wavelengths,” Opt. Lett. 43(19), 4602–4605 (2018). [CrossRef]
26. L. J. Yang, S. Sun, and W. E. I. Sha, “Ultra-wideband Reflection-type Metasurface for Generating Integer and Fractional Orbital Angular Momentum,” IEEE Trans. Antennas Propag. 68(3), 2166–2175 (2020). [CrossRef]
27. R. C. Zhu, T. S. Qiu, J. F. Wang, S. Sai, C. L. Hao, T. H. Liu, Y. F. Li, M. D. Feng, A. X. Zhang, C. W. Qiu, and S. B. Qu, “Phase-to-pattern inverse design paradigm for fast realization of functional metasurfaces via transfer learning,” Nat. Commun. 12(1), 2794 (2021). [CrossRef]
28. H. C. Chu, H. Y. Zhang, Y. Zhang, R. W. Peng, M. Wang, Y. Hao, and Y. Lai, “Invisible surfaces enabled by the coalescence of anti-reflection and wavefront controllability in ultrathin metasurfaces,” Nat. Commun. 12(1), 4523 (2021). [CrossRef]
29. W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninehad, Z. J. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13(3), 220–226 (2018). [CrossRef]
30. A. Kesavan, R. Karimian, and T. A. Denidni, “A novel wideband frequency selective surface for millimeter-wave applications,” IEEE Antennas Wirel. Propag. Lett. 19(12), 2428–2432 (2020). [CrossRef]
31. T. Tain, H. J. Huang, K. Cheng, Y. L. Liang, S. R. Hu, L. X. Yao, D. F. Guan, Y. L. Xu, and P. G. Liu, “Flexible and Reconfigurable Frequency Selective Surface With Wide Angular Stability Fabricated With Additive Manufacturing Procedure,” IEEE Antennas Wirel. Propag. Lett. 15, 1711–1714 (2016). [CrossRef]
32. C. Pfeiffer and A. Grbic, “Metasurface Huygens’ Surfaces: Tailoring Wave Fronts with Reflectionless Sheets,” Phys. Rev. Lett. 110(19), 197401 (2013). [CrossRef]
33. M. R. Akram, C. He, and W. R. Zhu, “Bi-layer metasurface based on Huygens’ principle for high gain antenna applications,” Opt. Express 28(11), 15844–15854 (2020). [CrossRef]
34. K. Chen, Y. J. Feng, F. Monticone, J. M. Zhao, B. Zhu, T. Jiang, Y. Kim, X. M. Ding, S. Zhang, A. Alù, and C. W. Qiu, “A Reconfigurable Active Huygens’ Metalens,” Adv. Mater. 29(17), 1606422 (2017). [CrossRef]
35. L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017). [CrossRef]
36. R. Y. Wu, L. Bao, L. W. Wu, Z. X. Wang, Q. Ma, J. W. Wu, G. D. Bai, V. Galdi, and T. J. Cui, “Independent Control of Copolarized Amplitude and Phase Responses via Anisotropic Metasurfaces,” Adv. Opt. Mater. 8(11), 1902126 (2020). [CrossRef]
37. A. Herrero-Bermello, A. Dias-Ponte, J. M. Luque-González, A. Ortega-Moñux, A. V. Velasco, P. Cheben, and R. Halir, “Experimental demonstration of metamaterial anisotropy engineering for broadband on-chip polarization beam splitting,” Opt. Express 28(11), 16385–16393 (2020). [CrossRef]
38. S. S. Li, Y. Wang, W. Y. Zhang, W. X. Lu, B. Hou, J. Luo, and Y. Lai, “Observation of wide-angle impedance matching in terahertz photonic crystals,” New J. Phys. 22(2), 023033 (2020). [CrossRef]
39. C. Wang, Z. B. Zhu, W. Z. Cui, Y. B. Yang, L. X. Ran, and D. X. Ye, “All-angle Brewster effect observed on a terahertz metasurface,” Appl. Phys. Lett. 114(19), 191902 (2019). [CrossRef]
40. D. X. Ye, L. Lu, J. D. Joannopoulos, M. Soljačić, and L. X. Ran, “Invisible metallic mesh,” Proc. Natl. Acad. Sci. U. S. A. 113(10), 2568–2572 (2016). [CrossRef]
41. H. Huang and Z. X. Sheng, “Brewster lens with perfect wave refraction,” IEEE Trans. Antennas Propag. 68(8), 6204–6213 (2020). [CrossRef]
42. J. Luo, Y. T. Yang, Z. Q. Yao, W. X. Lu, B. Hou, Z. H. Hang, C. T. Chan, and Y. Lai, “Ultratransparent Media and Transformation Optics with Shifted Spatial Dispersions,” Phys. Rev. Lett. 117(22), 223901 (2016). [CrossRef]
43. M. B. Po, Y. H. Guo, X. Li, X. L. Ma, and X. G. Luo, “Revisitation of Extraordinary Young’s Interference from Catenary Optical Fields to Spin–Orbit Interaction in Metasurfaces,” ACS Photonics 5(8), 3198–3204 (2018). [CrossRef]
44. Y. H. Gui, X. L. Ma, M. B. Pu, X. Li, Z. Y. Zhao, and X. G. Luo, “High-efficiency and wide-angle beam steering based on catenary optical fields in ultrathin metalens,” Adv. Opt. Mater. 6(19), 1800592 (2018). [CrossRef]
45. H. Gao, X. H. Fan, W. Xiong, and M. H. Hong, “Recent advances in optical dynamic meta-holography,” Opto-Electron. Adv. 4(11), 210030 (2021). [CrossRef]
46. Y. Lai, H. H. Zheng, Z. Q. Zhang, and C. T. Chan, “Manipulating sources using transformation optics with ‘folded geometry’,” J. Opt. 13(2), 024009 (2011). [CrossRef]
47. V. Popov, S. Tretyakov, and A. Novitsky, “Brewster effect when approaching exceptional points of degeneracy: Epsilon-near-zero behavior,” Phys. Rev. B 99(4), 045146 (2019). [CrossRef]
48. M. A. Van de haar, R. Maas, H. Schokker, and A. Polman, “Experimental Realization of a Polarization-Independent Ultraviolet/Visible Coaxial Plasmonic Metamaterial,” Nano Lett. 14(11), 6356–6360 (2014). [CrossRef]
49. J. Zhang, Z. F. Li, H. Wang, L. D. Shao, L. Zheng, and W. R. Zhu, “Dynamical absorption manipulation in a graphene-based optically transparent and flexible metasurface,” Carbon 176, 374–382 (2021). [CrossRef]
50. H. J. Jeong, D. H. Le, D. Lim, R. Phon, and S. Lim, “Reconfigurable Metasurfaces for Frequency Selective Absorption,” Adv. Opt. Mater. 8(13), 1902182 (2020). [CrossRef]
51. Z. L. Lu and D. W. Prather, “Calculation of effective permittivity, permeability, and surface impedance of negative-refraction photonic crystals,” Opt. Express 15(13), 8340–8345 (2007). [CrossRef]
52. Y. C. He and G. V. Eleftheriades, “Magnetoelectric uniaxial metamaterials as wide-angle polarization-insensitive matching layers,” Phys. Rev. B 98(20), 205404 (2018). [CrossRef]
53. H. Bai, M. B. Yan, H. Wang, F. J. Wang, L. Zheng, C. C. Li, and S. B. Qu, “Active meta-device for angular dispersion elimination of dual-polarized transmission windows,” Opt. Express 29(17), 26598–26607 (2021). [CrossRef]
54. X. Y. Zhang, Q. Li, F. F. Liu, M. Qiu, S. L. Sun, Q. He, and L. Zhou, “Controlling angular dispersions in optical metasurfaces,” Light: Sci. Appl. 9(1), 76 (2020). [CrossRef]
55. D. Z. Zhu, M. D. Gregory, P. L. Werner, and D. H. Werner, “Fabrication and Characterization of Multiband Polarization Independent 3-D-Printed Frequency Selective Structures With UltraWide Fields of View,” IEEE Trans. Antennas Propag. 66(11), 6096–6105 (2018). [CrossRef]
56. C. Jin, Q. H. Lv, B. C. Zhang, J. L. Liu, S. N. An, Z. X. He, and Z. X. Shen, “Ultra-Wide-Angle Bandpass Frequency Selective,” IEEE Trans. Antennas Propag. 69(9), 5673–5681 (2021). [CrossRef]
