Abstract

A planar isotropic unit cell based on Huygens’ principle is presented for achieving transmission phase control. By tailoring overlapping electric and magnetic resonances with geometry of the proposed unit cell, the transmission phase ranging from 0 − 2π is achieved with high transmittance. The proposed unit cell is then employed to design a metasurface lens with center frequency at 9.3 GHz and a square shaped patch antenna is placed at the focal point of the designed lens to perform conversion from spherical wave front of the source antenna to planar wave front. The designed lens antenna is capable to realize pencil beam radiation pattern with a gain of 19.6 dB and side lobe levels less than −15 dB in simulation. To experimentally verify the proposed design, a prototype of the metasurface lens is fabricated and measured. The measurement results well validate the proposed design and its enhanced performance.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Since the inception of radio frequency and wireless communications systems, high directive antennas are in high demand. Traditional approaches for achieving gain enhancement include antenna arrays, parabolic antennas, edge band gap structures, leaky wave antennas, horn antennas, to name a few. Recently, high directive radiation is achieved by utilizing phase correction of electromagnetic bandgap resonator antennas [1]. In the similar context, metasurface lens antenna is formed by placing the the antenna source at the focal point of the metasurface lens. According to the reciprocity principle, the arrangement will be able to realize high directive radiating antennas [2].

Recently, the utilization of metasurfaces has opened up new paradigms for plethora of applications including antenna gain enhancement [3], beam forming [4,5], OAM carrying beams [6,7] and Bessel beams [8]. Metasurfaces [9] are 2D artifical surfaces, engineered to achieve desired wave profile by stipulating either phase or impedance profile at a subwavelength scale. The desired phase profile is obtained through tailoring electric and magnetic responses [10] induced in subwavelength structures as a result of external applied fields. The functions of these metasurfaces are fixed once they are fabricated. Metasurfaces can be made reconfigurable by integrating active elements such as photosensitive materials [11], pin diodes [12] and varactor diodes [13] to name a few. There are two basic approaches to control phase i.e. through azimuthal rotation of the meta-atoms known as Pancharatnum Berry (PB) phase mechanism [1416] or by varying the geometric parameters of the meta-atoms usually known as transmit array [17,18]. In PB mechanism the half wave plate can impart additional phase to incoming circularly polarized wave which is equal to twice the rotation of half wave plate about its axis. This can be imagined from a Poincare sphere with left hand polarization on one side and right hand polarization on the opposite side of the sphere. The rotation of the waveplate makes the wave transverse its path from one pole to another pole of the sphere, hence adding an additional phase. Such a mechanism is known as space variant phase or Pancharatnum Berry phase mechanism [19]. As a result of polarization conversion, the losses in PB based metasurfaces are typically high, limiting their overall efficiency. On the other hand, transmit array does not suffer such losses. Traditionally, phase control in transmit array is obtained via cascading multiple layers [2022] of metallic patterns to obtain full $0-2\pi$ phase control. Full phase control with such meta-atoms is obtained with at least three metallic layers which increases fabrication complexity and cost.

Moreover, the implementation of traditional metasurfaces can be sufficiently optimized by extensively following the Huygens’ Principle which states that each point on the wavefront acts as a source to the secondary waves. The rigorous formulation of Huygens’ Principle was developed early in 1901 [23], which reveals later that unidirectional propagation can be achieved with crossed electric and magnetic dipoles [24,25]. Huygens’ Principle has been extensively employed to design electrically small antennas [2629]. The Huygens’ Principle was also utilized to design metasurfaces [30] in microwave domain by exploiting split ring resonators and rods to tailor both electric and magnetic resonances. Such an implementation, however, suffers due to planar incompatibility. Later, planar versions of metasurfaces [19,31,32] are also proposed, which are mostly based on multilayers. The bi-layer metasurfaces are very recently explored such as [29,33]. Both of the designs are anisotropic and can only be applied to single polarization.

Here, we propose a double layer symmetric design based on Huygens’ Principle. Phase control is obtained by utilizing two spectrally overlapped peaks satisfying Huygens’ criteria. Compared to recently proposed anisotropic bi-layer designs [29,33], the proposed unit cell is isotropic and could be applied for linear and circular polarizations equally. The proposed unit cell is then employed to design a lens of size $5.11\lambda \times 5.11 \lambda$, focusing 30 mm away from the antenna. To excite the designed lens, a linearly polarized patch antenna is placed at the focal point. According to the reciprocity principle, this setup is capable to realize high directive beams. The realized gain is 19.6 dB with side lobe level as low as $-15$ dB, resulting in an aperture efficiency of $27.8\%$ at frequency of 9.3 GHz. Up to now, the only symmetric design is by exploiting two different element groups with an aperture efficiency of 29% [34], slightly higher than the design presented here. However, compared to this design, we present a simplified design which can be controlled with only single element by just changing one dimension and thus require less computation effort to utilize the proposed design for practical applications.

2. Unit cell design

The geometry of the proposed unit cell is shown in the inset of Fig. 1. The unit cell consists of four metallic rings arranged side by side on a square substrate made of F4B with a dielectric constant of 2.65 and loss tangent of 0.001. The identical pattern is also printed on the other side of the substrate. The length of each arm, $l$, of the proposed unit cell is same and utilized to achieve the transmission phase control. The unit cell response under linear ($x$ or $y$) polarization or circular polarization is exactly the same due to symmetrical nature of the design. As shown in Fig. 1, the two peaks at 7.1 GHz and 9.87 GHz are overlapped to form a wideband high transmittance region. These peaks are utilized to achieve full phase control in transmission from $0-2\pi$ with reasonably high efficiency. Each peak can provide a phase shift of around $\pi$ to the transmitting wave. These peaks are swept through the design frequency of 9.3 GHz by varying the length $l$ of the internal arms.

 figure: Fig. 1.

Fig. 1. Transmission response of the unit cell as shown in the inset. Geometrical parameters are $w=0.4$ mm, $l=4.8$ mm, $p=14$ mm, $g=0.4$ mm, $a=0.2$ mm, and $h=1.5$ mm.

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The transmission peaks at two resonant frequencies can be explained with the help of Huygens’ resonances. The incident fields induces electric ($J_s$) and magnetic currents $M_s$. These fictious currents bridge the discontinuities between incident and transmitted fields. These electric and magnetic currents can be characterized by impedances ($Z_{\mathrm {ms}}$) and admittances $Y_{\mathrm {es}}$ which can be related to the s-parameters of the meta-atom as [30]:

$$Y_{\mathrm{es}} = \frac{2(1-S_{21}-S_{11})}{\eta_0(1+S_{21}+S_{11})}$$
$$Z_\mathrm{ms} = \frac{2\eta_0(1-S_{21}+S_{11})}{(1+S_{21}-S_{11})},$$
where $\eta _0$ is the free space impedance and $S_{21}$ is the transmission coefficient while $S_{11}$ is the reflection coefficient. Here, $\eta _0$ basically is the constant to balance electric and magnetic fields analogous to the ohmic equation.

The surface impedance and admittance for unit cell shown in Fig. 1 are plotted in Fig. 2. Huygens’ criteria requires equal contribution of electric and magnetic response to achieve unity transmission implying that $\eta _0Y_{\mathrm {es}}=Z_{\mathrm {ms}}/\eta _0$ and are purely imaginary. It is clear from the Fig. 2 that the Huygens’ criteria is fulfilled at the two frequencies around 7.1 GHz and 9.87 GHz as a result of resonating response of the proposed unit cell. The two transmission peaks form the pass band response with phase shift ranging between 2$\pi$. This could then be effectively utilized to design metasurfaces operating at a particular frequency by varying the geometric parameters.

 figure: Fig. 2.

Fig. 2. Surface impedance and admittance for unit cell with geometrical parameters: $w=0.4$ mm, $l=4.8$ mm, $p=14$ mm, $g=0.4$ mm, $a=0.2$ mm, and $h=1.5$ mm.

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To clarify further, the electric and magnetic fields are plotted under $x$-polarized incidence for the frequency points at which Huygens’ criteria meets in Fig. 3. It can be clearly seen from the figure that vertically aligned electric dipole while horizontally aligned magnetic dipoles form at both the frequency points. These dipoles can be controlled with length $l$, keeping the strength of the electric and magnetic fields equal in both the modes and thus resulting in Huygens’ resonances [3537].

 figure: Fig. 3.

Fig. 3. simulate electric and magnetic dipoles under $x$-polarized incidence.

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Having understood the mechanism of the proposed unit cell, the full phase control of $0-2\pi$ is obtained at the desired frequency. We have use the commercial package CST microwave studio to simulate the unit cell using two sets of perfectly absorbing boundaries along longitudinal sides and a set of Floquat ports along lateral side. The arm length $l$ is then optimized for each phase from $0-360^\circ$ in a step of $15^\circ$. The phases and amplitudes of the unit cells at the designed frequency of 9.3 GHz against the arm lengths are shown in Fig. 4.

 figure: Fig. 4.

Fig. 4. Amplitude and phase response of the co-polarized transmitted waves.

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The unit cell is further characterized under incident angle variations as shown in Fig. 5. It can be seen that the unit cell is nearly stable up to $45^\circ$. The variations will increase afterwards. Only the second mode is affected by the variations of the incident angles, whereas the first mode is utilized for higher incident angles, i.e., outer circles of the metasurface. Therefore, this issue will result in only small deterioration from the optimal point as can be observed from the aperture efficiency.

 figure: Fig. 5.

Fig. 5. Unit cell response under different incident angles.

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3. Lens design

The proposed unit cell is further utilized to construct a metasurface lens for the focusing of incident plane waves. The focusing effect can be achieved by utilizing the phase distribution of lens as follows:

$$\phi(x, y)= \frac{2\pi}{\lambda}(\sqrt{x^2+y^2+f^2}-f),$$
where $\phi (x,y)$ is the discrete phase distribution over the 2D surface, $f$ is the focal point, and ($x,y$) is the actual position on the metasurface. The focal length $f$ is selected as 30 mm. The constructed lens consists of $12\times 12$ unit cells covering an area of 168 mm$\times$168 mm. These unit cells over the lens are arranged according to the phase distribution calculated by Eq. (3), considering $x =mp$ and $y = np$ with $p$ being the periodicity and $m$, $n$ are the numbers of the unit cells along the $x$-axis and $y$-axis. The constructed lens is shown in Fig. 6(a). An $x$-polarized plane wave is used to excite the lens. The $E_x$ field distribution at the focusing plane $z=30$ mm and two cut plane along propagation directions are shown in Fig. 6(b-d). It can be seen clearly that the point focusing is achieved along the $xy$ plane, which can also be confirmed from the $xoz$ and $yoz$ planes indicating peak amplitude near 30 mm away from the lens. The asymmetric side lobes are because of interference of the plane waves. As the incident field is linearly polarized ($x$-polarized), that is why asymmetric side lobes are observed. Moreover, for orthogonal polarization, these side lobes switch perpendicularly. There may be two possible causes for such response 1) non-ideal behaviour of the unit cell, and 2) finite size of the metasurface. This validates the functionality of proposed design as a focusing lens.

 figure: Fig. 6.

Fig. 6. Simulated results (a) Designed lens. $E_x$ distribution along (b) $xy$-plane at $z=30$ mm, (c) $xoz$ plane, and (d) $yoz$ plane.

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4. High gain antenna application

The demonstrated lens in the previous section is then utilized in conjunction with a quasi-point source antenna. The source antenna employed here is a simple patch antenna working at 9.3 GHz as the central frequency. The patch is placed on one side of substrate made of F4B with permittivity of 2.65 and thickness of 1.5 mm. The other side of the substrate was covered with a large ground plane for better performance. Although this arrangement resembles to the resonant cavity antennas employed in previous works [3840], however, here instead of placing an antenna between the cavity, the ground plane under the patch is extended to provide physical support for metasurface and antenna assembly. Usually the cavity antenna utilized in the past such as [38] require $\lambda$/4 distance of the antenna from both walls. Here, the distance is only decided by the focal spot of the lens and physical size of the antenna for its optimal operation which is 30 mm, slightly smaller than $\lambda$. The distance between antenna and metasurface are basically decided based on the spot size which can be controlled by metasurface numerical aperture and the antenna physical dimension. The focal depth selected here is 30 mm for optimal response. At the focal point, the width of the high intensity region is nearly 10 mm. Since the patch antenna maximum dimension is $s=9.3$ mm, therefore it would perform optimally at this frequency. Moreover, the large ground plane plays role in the reduction of side lobes. The measured S-parameters for antenna with and without the metasurface lens are shown in Fig. 7. The operating frequency range is slightly reduced with the lens.

 figure: Fig. 7.

Fig. 7. Simulated far-filed pattern on left at 9.3 GHz and measured $S_{11}$ with/without lens on right along with patch antenna in the inset with $s=9.3$ mm.

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To further gain insight into the mechanism of achieving high directive beams, the metasurface lens antenna is simulated by utilizing commercially available CST Microwave studio. The boundaries set to analyze metasurface lens antenna are perfectly absorbing boundaries. The distance of the absorbing boundaries from the structure is kept several wavelengths, which should be larger than $\lambda$/4 ideally. The $E_x$ field distributions are plotted in Fig. 8 for the cases with and without lens at both $xoz$ and $yoz$ planes. The conversion of the spherical beam as emitted from the patch antenna can be clearly observed from the figure. Another observation can be made as without lens, the beam power reduces rapidly as waves travel away from the source, as compared to the case with lens. The impedance bandwidth of the lens antenna is from 9–9.4 GHz. The antenna gain for two frequency points at $f=9.1$ GHz and $f=9.4$ GHz in the band is plotted in Fig. 9 which is still in 3 dB bandwidth limit of the peak gain. This indicates the optimal performance in the antenna band of operation, keeping in view the narrow band operation of previously proposed metasurfaces [34].

 figure: Fig. 8.

Fig. 8. Simulated electric field distribution without Lens (left) and with lens (right) for $yoz$ plane (top) and $xoz$ plane (bottom).

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 figure: Fig. 9.

Fig. 9. Simulated far-field patterns at 9.1 GHz (left) and 9.4 GHz (right).

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Finally, the antenna and the metasurface lens are fabricated using printed circuit board technology as shown in Fig. 10. The 2D radiation patterns of the fabricated antenna with and without lens are measured for two cut planes as shown in Fig. 11. The directionality improvement with the lens is around 14 dB for E-plane and around 12.5 dB for H-plane. Side lobe levels are significantly reduced and are 20 dB lower for E plane and around 15 dB lower for H-plane. The aperture efficiency of the proposed design at 9.3 GHz is achieved to be $27.8\%$, obtained using $\lambda ^2G/4\pi A_p$, where $G$ is gain, $\lambda$ is operational wavelength and $A_p$ is physical area. The evaluated aperture efficiency is nearly the same as achieved with [38], while providing simplified design approach with low computation and fabrication costs. Moreover, compared to previously reported lens antennas [34,38], the proposed design offers high gain with lowest side lobe level, while having the metasurface thickness as thin as around $0.045\lambda$, which is the lowest achieved so far. Moreover, the low profile source, i.e., patch antenna, as compared to previously used horn antennas could add to the compatibility for device integration. With these unique features, the proposed antenna could be a promising candidate for remote wireless communication based applications.

 figure: Fig. 10.

Fig. 10. Fabricated designs: (a) antenna, (b) metasurface, and (c) metasurface antenna.

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 figure: Fig. 11.

Fig. 11. Measured radiation pattern for E-plane (top) and H-plane (bottom) at 9.3 GHz.

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5. Conclusion

In summary, a bi-layer metasurface lens has been designed, fabricated and measured. The metasurface lens has a small thickness of 0.045$\lambda$ with aperture area of 5.11$\lambda \times$5.11 $\lambda$. The peak gain achieved from the lens antenna is 19.6 dB at 9.3 GHz with aperture efficiency of 27.8$\%$ and reduced side lobe level. The unique features of easy fabrication and enhanced performance enable the proposed design to be promising candidate for remote wireless communication based applications.

Funding

National Natural Science Foundation of China (51777168, 61701303); Natural Science Foundation of Shanghai (17ZR1414300).

Disclosures

The authors declare no conflicts of interest.

References

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5. M. Chen, A. Epstein, and G. V. Eleftheriades, “Design and experimental verification of a passive huygens’ metasurface lens for gain enhancement of frequency-scanning slotted-waveguide antennas,” IEEE Trans. Antennas Propag. 67(7), 4678–4692 (2019). [CrossRef]  

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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]  

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12. P. del Hougne, M. F. Imani, A. V. Diebold, R. Horstmeyer, and D. R. Smith, “Learned integrated sensing pipeline: Reconfigurable metasurface transceivers as trainable physical layer in an artificial neural network,” Adv. Sci. 7(3), 1901913 (2020). [CrossRef]  

13. K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017). [CrossRef]  

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References

  • View by:

  1. M. U. Afzal, K. P. Esselle, and B. A. Zeb, “Dielectric phase-correcting structures for electromagnetic band gap resonator antennas,” IEEE Trans. Antennas Propag. 63(8), 3390–3399 (2015).
    [Crossref]
  2. A. H. Abdelrahman, A. Z. Elsherbeni, and F. Yang, “Transmitarray antenna design using cross-slot elements with no dielectric substrate,” IEEE Antennas Wirel. Propag. Letts. 13, 177–180 (2014).
    [Crossref]
  3. H. Li, G. Wang, H.-X. Xu, T. Cai, and J. Liang, “X-band phase-gradient metasurface for high-gain lens antenna application,” IEEE Trans. Antennas Propag. 63(11), 5144–5149 (2015).
    [Crossref]
  4. M. Jiang, Z. N. Chen, Y. Zhang, W. Hong, and X. Xuan, “Metamaterial-based thin planar lens antenna for spatial beamforming and multibeam massive mimo,” IEEE Trans. Antennas Propag. 65(2), 464–472 (2017).
    [Crossref]
  5. M. Chen, A. Epstein, and G. V. Eleftheriades, “Design and experimental verification of a passive huygens’ metasurface lens for gain enhancement of frequency-scanning slotted-waveguide antennas,” IEEE Trans. Antennas Propag. 67(7), 4678–4692 (2019).
    [Crossref]
  6. M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
    [Crossref]
  7. M. R. Akram, G. Ding, K. Chen, Y. Feng, and W. Zhu, “Ultrathin single layer metasurfaces with ultra-wideband operation for both transmission and reflection,” Adv. Mater. 32(12), 1907308 (2020).
    [Crossref]
  8. M. R. Akram, M. Q. Mehmood, T. Tauqeer, A. S. Rana, I. D. Rukhlenko, and W. Zhu, “Highly efficient generation of bessel beams with polarization insensitive metasurfaces,” Opt. Express 27(7), 9467–9480 (2019).
    [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. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Opt. Express 21(12), 14409–14429 (2013).
    [Crossref]
  11. K. Fan, J. Zhang, X. Liu, G.-F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
    [Crossref]
  12. P. del Hougne, M. F. Imani, A. V. Diebold, R. Horstmeyer, and D. R. Smith, “Learned integrated sensing pipeline: Reconfigurable metasurface transceivers as trainable physical layer in an artificial neural network,” Adv. Sci. 7(3), 1901913 (2020).
    [Crossref]
  13. K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
    [Crossref]
  14. M. R. Akram, X. Bai, R. Jin, G. A. Vandenbosch, M. Premaratne, and W. Zhu, “Photon spin hall effect based ultra-thin transmissive metasurface for efficient generation of oam waves,” IEEE Trans. Antennas Propag. 67(7), 4650–4658 (2019).
    [Crossref]
  15. M. L. Chen, L. J. Jiang, and E. Wei, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave frequencies,” IEEE Trans. Antennas Propag. 65(1), 396–400 (2017).
    [Crossref]
  16. W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin pancharatnam-berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
    [Crossref]
  17. C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102(23), 231116 (2013).
    [Crossref]
  18. F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
    [Crossref]
  19. G. Xu, S. V. Hum, and G. V. Eleftheriades, “A technique for designing multilayer multistopband frequency selective surfaces,” IEEE Trans. Antennas Propag. 66(2), 780–789 (2018).
    [Crossref]
  20. B. Rahmati and H. R. Hassani, “Low-profile slot transmitarray antenna,” IEEE Trans. Antennas Propag. 63(1), 174–181 (2015).
    [Crossref]
  21. C. G. Ryan, M. R. Chaharmir, J. Shaker, J. R. Bray, Y. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58(5), 1486–1493 (2010).
    [Crossref]
  22. C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102(23), 231116 (2013).
    [Crossref]
  23. A. E. H. Love, “I. the integration of the equations of propagation of electric waves,” Phil. Trans. Royal Soc. London. Ser. A, Cont. Pap. Math. or Phys. Charac. 197(287-299), 1–45 (1901).
    [Crossref]
  24. M. Kerker, D.-S. Wang, and C. Giles, “Electromagnetic scattering by magnetic spheres,” J. Opt. Soc. Am. 73(6), 765–767 (1983).
    [Crossref]
  25. W. Liu and Y. S. Kivshar, “Generalized kerker effects in nanophotonics and meta-optics,” Opt. Express 26(10), 13085–13105 (2018).
    [Crossref]
  26. W. Lin, R. W. Ziolkowski, and J. Huang, “Electrically small, low-profile, highly efficient, huygens dipole rectennas for wirelessly powering internet-of-things devices,” IEEE Trans. Antennas Propag. 67(6), 3670–3679 (2019).
    [Crossref]
  27. S. X. Ta, I. Park, and R. W. Ziolkowski, “Crossed dipole antennas: A review,” IEEE Antennas Propag. Mag. 57(5), 107–122 (2015).
    [Crossref]
  28. P. Jin and R. W. Ziolkowski, “Metamaterial-inspired, electrically small huygens sources,” IEEE Antennas Wirel. Propag. Letts. 9, 501–505 (2010).
    [Crossref]
  29. W. Lin and R. W. Ziolkowski, “Electrically small, low-profile, huygens circularly polarized antenna,” IEEE Trans. Antennas Propag. 66(2), 636–643 (2018).
    [Crossref]
  30. C. Pfeiffer and A. Grbic, “Metamaterial huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
    [Crossref]
  31. Z. Sun, B. Sima, J. Zhao, and Y. Feng, “Electromagnetic polarization conversion based on huygens’ metasurfaces with coupled electric and magnetic resonances,” Opt. Express 27(8), 11006–11017 (2019).
    [Crossref]
  32. J. P. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Polarization considerations for scalar huygens metasurfaces and characterization for 2-d refraction,” IEEE Trans. Microwave Theory Tech. 63(3), 913–924 (2015).
    [Crossref]
  33. L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
    [Crossref]
  34. H. Li, G. Wang, J. Liang, X. Gao, H. Hou, and X. Jia, “Single-layer focusing gradient metasurface for ultrathin planar lens antenna application,” IEEE Trans. Antennas Propag. 65(3), 1452–1457 (2017).
    [Crossref]
  35. X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
    [Crossref]
  36. A. Leitis, A. Heßler, S. Wahl, M. Wuttig, T. Taubner, A. Tittl, and H. Altug, “All-dielectric programmable huygens’ metasurfaces,” Adv. Funct. Mater.1910259 (2020).
  37. X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016).
    [Crossref]
  38. M. U. Afzal and K. P. Esselle, “A low-profile printed planar phase correcting surface to improve directive radiation characteristics of electromagnetic band gap resonator antennas,” IEEE Trans. Antennas Propag. 64(1), 276–280 (2016).
    [Crossref]
  39. A. Epstein, J. P. Wong, and G. V. Eleftheriades, “Cavity-excited huygens’ metasurface antennas for near-unity aperture illumination efficiency from arbitrarily large apertures,” Nat. Commun. 7(1), 10360 (2016).
    [Crossref]
  40. T. R. Cameron and G. V. Eleftheriades, “Experimental validation of a wideband metasurface for wide-angle scanning leaky-wave antennas,” IEEE Trans. Antennas Propag. 65(10), 5245–5256 (2017).
    [Crossref]

2020 (2)

M. R. Akram, G. Ding, K. Chen, Y. Feng, and W. Zhu, “Ultrathin single layer metasurfaces with ultra-wideband operation for both transmission and reflection,” Adv. Mater. 32(12), 1907308 (2020).
[Crossref]

P. del Hougne, M. F. Imani, A. V. Diebold, R. Horstmeyer, and D. R. Smith, “Learned integrated sensing pipeline: Reconfigurable metasurface transceivers as trainable physical layer in an artificial neural network,” Adv. Sci. 7(3), 1901913 (2020).
[Crossref]

2019 (8)

M. R. Akram, X. Bai, R. Jin, G. A. Vandenbosch, M. Premaratne, and W. Zhu, “Photon spin hall effect based ultra-thin transmissive metasurface for efficient generation of oam waves,” IEEE Trans. Antennas Propag. 67(7), 4650–4658 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, T. Tauqeer, A. S. Rana, I. D. Rukhlenko, and W. Zhu, “Highly efficient generation of bessel beams with polarization insensitive metasurfaces,” Opt. Express 27(7), 9467–9480 (2019).
[Crossref]

M. Chen, A. Epstein, and G. V. Eleftheriades, “Design and experimental verification of a passive huygens’ metasurface lens for gain enhancement of frequency-scanning slotted-waveguide antennas,” IEEE Trans. Antennas Propag. 67(7), 4678–4692 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
[Crossref]

W. Lin, R. W. Ziolkowski, and J. Huang, “Electrically small, low-profile, highly efficient, huygens dipole rectennas for wirelessly powering internet-of-things devices,” IEEE Trans. Antennas Propag. 67(6), 3670–3679 (2019).
[Crossref]

Z. Sun, B. Sima, J. Zhao, and Y. Feng, “Electromagnetic polarization conversion based on huygens’ metasurfaces with coupled electric and magnetic resonances,” Opt. Express 27(8), 11006–11017 (2019).
[Crossref]

X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
[Crossref]

L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
[Crossref]

2018 (4)

W. Lin and R. W. Ziolkowski, “Electrically small, low-profile, huygens circularly polarized antenna,” IEEE Trans. Antennas Propag. 66(2), 636–643 (2018).
[Crossref]

W. Liu and Y. S. Kivshar, “Generalized kerker effects in nanophotonics and meta-optics,” Opt. Express 26(10), 13085–13105 (2018).
[Crossref]

G. Xu, S. V. Hum, and G. V. Eleftheriades, “A technique for designing multilayer multistopband frequency selective surfaces,” IEEE Trans. Antennas Propag. 66(2), 780–789 (2018).
[Crossref]

K. Fan, J. Zhang, X. Liu, G.-F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

2017 (6)

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

M. L. Chen, L. J. Jiang, and E. Wei, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave frequencies,” IEEE Trans. Antennas Propag. 65(1), 396–400 (2017).
[Crossref]

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin pancharatnam-berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
[Crossref]

M. Jiang, Z. N. Chen, Y. Zhang, W. Hong, and X. Xuan, “Metamaterial-based thin planar lens antenna for spatial beamforming and multibeam massive mimo,” IEEE Trans. Antennas Propag. 65(2), 464–472 (2017).
[Crossref]

H. Li, G. Wang, J. Liang, X. Gao, H. Hou, and X. Jia, “Single-layer focusing gradient metasurface for ultrathin planar lens antenna application,” IEEE Trans. Antennas Propag. 65(3), 1452–1457 (2017).
[Crossref]

T. R. Cameron and G. V. Eleftheriades, “Experimental validation of a wideband metasurface for wide-angle scanning leaky-wave antennas,” IEEE Trans. Antennas Propag. 65(10), 5245–5256 (2017).
[Crossref]

2016 (3)

X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016).
[Crossref]

M. U. Afzal and K. P. Esselle, “A low-profile printed planar phase correcting surface to improve directive radiation characteristics of electromagnetic band gap resonator antennas,” IEEE Trans. Antennas Propag. 64(1), 276–280 (2016).
[Crossref]

A. Epstein, J. P. Wong, and G. V. Eleftheriades, “Cavity-excited huygens’ metasurface antennas for near-unity aperture illumination efficiency from arbitrarily large apertures,” Nat. Commun. 7(1), 10360 (2016).
[Crossref]

2015 (5)

J. P. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Polarization considerations for scalar huygens metasurfaces and characterization for 2-d refraction,” IEEE Trans. Microwave Theory Tech. 63(3), 913–924 (2015).
[Crossref]

B. Rahmati and H. R. Hassani, “Low-profile slot transmitarray antenna,” IEEE Trans. Antennas Propag. 63(1), 174–181 (2015).
[Crossref]

S. X. Ta, I. Park, and R. W. Ziolkowski, “Crossed dipole antennas: A review,” IEEE Antennas Propag. Mag. 57(5), 107–122 (2015).
[Crossref]

H. Li, G. Wang, H.-X. Xu, T. Cai, and J. Liang, “X-band phase-gradient metasurface for high-gain lens antenna application,” IEEE Trans. Antennas Propag. 63(11), 5144–5149 (2015).
[Crossref]

M. U. Afzal, K. P. Esselle, and B. A. Zeb, “Dielectric phase-correcting structures for electromagnetic band gap resonator antennas,” IEEE Trans. Antennas Propag. 63(8), 3390–3399 (2015).
[Crossref]

2014 (1)

A. H. Abdelrahman, A. Z. Elsherbeni, and F. Yang, “Transmitarray antenna design using cross-slot elements with no dielectric substrate,” IEEE Antennas Wirel. Propag. Letts. 13, 177–180 (2014).
[Crossref]

2013 (5)

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102(23), 231116 (2013).
[Crossref]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Opt. Express 21(12), 14409–14429 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102(23), 231116 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Metamaterial huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
[Crossref]

2011 (1)

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]

2010 (2)

C. G. Ryan, M. R. Chaharmir, J. Shaker, J. R. Bray, Y. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58(5), 1486–1493 (2010).
[Crossref]

P. Jin and R. W. Ziolkowski, “Metamaterial-inspired, electrically small huygens sources,” IEEE Antennas Wirel. Propag. Letts. 9, 501–505 (2010).
[Crossref]

1983 (1)

1901 (1)

A. E. H. Love, “I. the integration of the equations of propagation of electric waves,” Phil. Trans. Royal Soc. London. Ser. A, Cont. Pap. Math. or Phys. Charac. 197(287-299), 1–45 (1901).
[Crossref]

Abdelrahman, A. H.

A. H. Abdelrahman, A. Z. Elsherbeni, and F. Yang, “Transmitarray antenna design using cross-slot elements with no dielectric substrate,” IEEE Antennas Wirel. Propag. Letts. 13, 177–180 (2014).
[Crossref]

Afzal, M. U.

M. U. Afzal and K. P. Esselle, “A low-profile printed planar phase correcting surface to improve directive radiation characteristics of electromagnetic band gap resonator antennas,” IEEE Trans. Antennas Propag. 64(1), 276–280 (2016).
[Crossref]

M. U. Afzal, K. P. Esselle, and B. A. Zeb, “Dielectric phase-correcting structures for electromagnetic band gap resonator antennas,” IEEE Trans. Antennas Propag. 63(8), 3390–3399 (2015).
[Crossref]

Aieta, F.

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]

Akram, M. R.

M. R. Akram, G. Ding, K. Chen, Y. Feng, and W. Zhu, “Ultrathin single layer metasurfaces with ultra-wideband operation for both transmission and reflection,” Adv. Mater. 32(12), 1907308 (2020).
[Crossref]

M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, T. Tauqeer, A. S. Rana, I. D. Rukhlenko, and W. Zhu, “Highly efficient generation of bessel beams with polarization insensitive metasurfaces,” Opt. Express 27(7), 9467–9480 (2019).
[Crossref]

M. R. Akram, X. Bai, R. Jin, G. A. Vandenbosch, M. Premaratne, and W. Zhu, “Photon spin hall effect based ultra-thin transmissive metasurface for efficient generation of oam waves,” IEEE Trans. Antennas Propag. 67(7), 4650–4658 (2019).
[Crossref]

Altug, H.

A. Leitis, A. Heßler, S. Wahl, M. Wuttig, T. Taubner, A. Tittl, and H. Altug, “All-dielectric programmable huygens’ metasurfaces,” Adv. Funct. Mater.1910259 (2020).

Alù, A.

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref]

Antar, Y. M.

C. G. Ryan, M. R. Chaharmir, J. Shaker, J. R. Bray, Y. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58(5), 1486–1493 (2010).
[Crossref]

Averitt, R. D.

X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
[Crossref]

K. Fan, J. Zhang, X. Liu, G.-F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016).
[Crossref]

Bai, X.

M. R. Akram, X. Bai, R. Jin, G. A. Vandenbosch, M. Premaratne, and W. Zhu, “Photon spin hall effect based ultra-thin transmissive metasurface for efficient generation of oam waves,” IEEE Trans. Antennas Propag. 67(7), 4650–4658 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
[Crossref]

Bray, J. R.

C. G. Ryan, M. R. Chaharmir, J. Shaker, J. R. Bray, Y. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58(5), 1486–1493 (2010).
[Crossref]

Cai, T.

H. Li, G. Wang, H.-X. Xu, T. Cai, and J. Liang, “X-band phase-gradient metasurface for high-gain lens antenna application,” IEEE Trans. Antennas Propag. 63(11), 5144–5149 (2015).
[Crossref]

Cameron, T. R.

T. R. Cameron and G. V. Eleftheriades, “Experimental validation of a wideband metasurface for wide-angle scanning leaky-wave antennas,” IEEE Trans. Antennas Propag. 65(10), 5245–5256 (2017).
[Crossref]

Capasso, F.

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]

Chaharmir, M. R.

C. G. Ryan, M. R. Chaharmir, J. Shaker, J. R. Bray, Y. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58(5), 1486–1493 (2010).
[Crossref]

Chen, K.

M. R. Akram, G. Ding, K. Chen, Y. Feng, and W. Zhu, “Ultrathin single layer metasurfaces with ultra-wideband operation for both transmission and reflection,” Adv. Mater. 32(12), 1907308 (2020).
[Crossref]

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

Chen, M.

M. Chen, A. Epstein, and G. V. Eleftheriades, “Design and experimental verification of a passive huygens’ metasurface lens for gain enhancement of frequency-scanning slotted-waveguide antennas,” IEEE Trans. Antennas Propag. 67(7), 4678–4692 (2019).
[Crossref]

Chen, M. L.

M. L. Chen, L. J. Jiang, and E. Wei, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave frequencies,” IEEE Trans. Antennas Propag. 65(1), 396–400 (2017).
[Crossref]

Chen, Z. N.

M. Jiang, Z. N. Chen, Y. Zhang, W. Hong, and X. Xuan, “Metamaterial-based thin planar lens antenna for spatial beamforming and multibeam massive mimo,” IEEE Trans. Antennas Propag. 65(2), 464–472 (2017).
[Crossref]

Cui, T. J.

L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
[Crossref]

del Hougne, P.

P. del Hougne, M. F. Imani, A. V. Diebold, R. Horstmeyer, and D. R. Smith, “Learned integrated sensing pipeline: Reconfigurable metasurface transceivers as trainable physical layer in an artificial neural network,” Adv. Sci. 7(3), 1901913 (2020).
[Crossref]

Diebold, A. V.

P. del Hougne, M. F. Imani, A. V. Diebold, R. Horstmeyer, and D. R. Smith, “Learned integrated sensing pipeline: Reconfigurable metasurface transceivers as trainable physical layer in an artificial neural network,” Adv. Sci. 7(3), 1901913 (2020).
[Crossref]

Ding, G.

M. R. Akram, G. Ding, K. Chen, Y. Feng, and W. Zhu, “Ultrathin single layer metasurfaces with ultra-wideband operation for both transmission and reflection,” Adv. Mater. 32(12), 1907308 (2020).
[Crossref]

Ding, X.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

Duan, G.

X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
[Crossref]

X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016).
[Crossref]

Eleftheriades, G. V.

M. Chen, A. Epstein, and G. V. Eleftheriades, “Design and experimental verification of a passive huygens’ metasurface lens for gain enhancement of frequency-scanning slotted-waveguide antennas,” IEEE Trans. Antennas Propag. 67(7), 4678–4692 (2019).
[Crossref]

G. Xu, S. V. Hum, and G. V. Eleftheriades, “A technique for designing multilayer multistopband frequency selective surfaces,” IEEE Trans. Antennas Propag. 66(2), 780–789 (2018).
[Crossref]

T. R. Cameron and G. V. Eleftheriades, “Experimental validation of a wideband metasurface for wide-angle scanning leaky-wave antennas,” IEEE Trans. Antennas Propag. 65(10), 5245–5256 (2017).
[Crossref]

A. Epstein, J. P. Wong, and G. V. Eleftheriades, “Cavity-excited huygens’ metasurface antennas for near-unity aperture illumination efficiency from arbitrarily large apertures,” Nat. Commun. 7(1), 10360 (2016).
[Crossref]

J. P. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Polarization considerations for scalar huygens metasurfaces and characterization for 2-d refraction,” IEEE Trans. Microwave Theory Tech. 63(3), 913–924 (2015).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Opt. Express 21(12), 14409–14429 (2013).
[Crossref]

Elsherbeni, A. Z.

A. H. Abdelrahman, A. Z. Elsherbeni, and F. Yang, “Transmitarray antenna design using cross-slot elements with no dielectric substrate,” IEEE Antennas Wirel. Propag. Letts. 13, 177–180 (2014).
[Crossref]

Epstein, A.

M. Chen, A. Epstein, and G. V. Eleftheriades, “Design and experimental verification of a passive huygens’ metasurface lens for gain enhancement of frequency-scanning slotted-waveguide antennas,” IEEE Trans. Antennas Propag. 67(7), 4678–4692 (2019).
[Crossref]

A. Epstein, J. P. Wong, and G. V. Eleftheriades, “Cavity-excited huygens’ metasurface antennas for near-unity aperture illumination efficiency from arbitrarily large apertures,” Nat. Commun. 7(1), 10360 (2016).
[Crossref]

Esselle, K. P.

M. U. Afzal and K. P. Esselle, “A low-profile printed planar phase correcting surface to improve directive radiation characteristics of electromagnetic band gap resonator antennas,” IEEE Trans. Antennas Propag. 64(1), 276–280 (2016).
[Crossref]

M. U. Afzal, K. P. Esselle, and B. A. Zeb, “Dielectric phase-correcting structures for electromagnetic band gap resonator antennas,” IEEE Trans. Antennas Propag. 63(8), 3390–3399 (2015).
[Crossref]

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F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref]

Fan, K.

X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
[Crossref]

K. Fan, J. Zhang, X. Liu, G.-F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016).
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Feng, Y.

M. R. Akram, G. Ding, K. Chen, Y. Feng, and W. Zhu, “Ultrathin single layer metasurfaces with ultra-wideband operation for both transmission and reflection,” Adv. Mater. 32(12), 1907308 (2020).
[Crossref]

Z. Sun, B. Sima, J. Zhao, and Y. Feng, “Electromagnetic polarization conversion based on huygens’ metasurfaces with coupled electric and magnetic resonances,” Opt. Express 27(8), 11006–11017 (2019).
[Crossref]

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

Gaburro, Z.

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).
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Gao, X.

L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
[Crossref]

H. Li, G. Wang, J. Liang, X. Gao, H. Hou, and X. Jia, “Single-layer focusing gradient metasurface for ultrathin planar lens antenna application,” IEEE Trans. Antennas Propag. 65(3), 1452–1457 (2017).
[Crossref]

Genevet, P.

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).
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Gou, Y.

L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
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Grbic, A.

C. Pfeiffer and A. Grbic, “Metamaterial huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102(23), 231116 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102(23), 231116 (2013).
[Crossref]

Hassani, H. R.

B. Rahmati and H. R. Hassani, “Low-profile slot transmitarray antenna,” IEEE Trans. Antennas Propag. 63(1), 174–181 (2015).
[Crossref]

He, Q.

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin pancharatnam-berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
[Crossref]

Heßler, A.

A. Leitis, A. Heßler, S. Wahl, M. Wuttig, T. Taubner, A. Tittl, and H. Altug, “All-dielectric programmable huygens’ metasurfaces,” Adv. Funct. Mater.1910259 (2020).

Hong, W.

M. Jiang, Z. N. Chen, Y. Zhang, W. Hong, and X. Xuan, “Metamaterial-based thin planar lens antenna for spatial beamforming and multibeam massive mimo,” IEEE Trans. Antennas Propag. 65(2), 464–472 (2017).
[Crossref]

Horstmeyer, R.

P. del Hougne, M. F. Imani, A. V. Diebold, R. Horstmeyer, and D. R. Smith, “Learned integrated sensing pipeline: Reconfigurable metasurface transceivers as trainable physical layer in an artificial neural network,” Adv. Sci. 7(3), 1901913 (2020).
[Crossref]

Hou, H.

H. Li, G. Wang, J. Liang, X. Gao, H. Hou, and X. Jia, “Single-layer focusing gradient metasurface for ultrathin planar lens antenna application,” IEEE Trans. Antennas Propag. 65(3), 1452–1457 (2017).
[Crossref]

Huang, J.

W. Lin, R. W. Ziolkowski, and J. Huang, “Electrically small, low-profile, highly efficient, huygens dipole rectennas for wirelessly powering internet-of-things devices,” IEEE Trans. Antennas Propag. 67(6), 3670–3679 (2019).
[Crossref]

Hum, S. V.

G. Xu, S. V. Hum, and G. V. Eleftheriades, “A technique for designing multilayer multistopband frequency selective surfaces,” IEEE Trans. Antennas Propag. 66(2), 780–789 (2018).
[Crossref]

Imani, M. F.

P. del Hougne, M. F. Imani, A. V. Diebold, R. Horstmeyer, and D. R. Smith, “Learned integrated sensing pipeline: Reconfigurable metasurface transceivers as trainable physical layer in an artificial neural network,” Adv. Sci. 7(3), 1901913 (2020).
[Crossref]

Ittipiboon, A.

C. G. Ryan, M. R. Chaharmir, J. Shaker, J. R. Bray, Y. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58(5), 1486–1493 (2010).
[Crossref]

Jia, X.

H. Li, G. Wang, J. Liang, X. Gao, H. Hou, and X. Jia, “Single-layer focusing gradient metasurface for ultrathin planar lens antenna application,” IEEE Trans. Antennas Propag. 65(3), 1452–1457 (2017).
[Crossref]

Jiang, L. J.

M. L. Chen, L. J. Jiang, and E. Wei, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave frequencies,” IEEE Trans. Antennas Propag. 65(1), 396–400 (2017).
[Crossref]

Jiang, M.

M. Jiang, Z. N. Chen, Y. Zhang, W. Hong, and X. Xuan, “Metamaterial-based thin planar lens antenna for spatial beamforming and multibeam massive mimo,” IEEE Trans. Antennas Propag. 65(2), 464–472 (2017).
[Crossref]

Jiang, T.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

Jin, P.

P. Jin and R. W. Ziolkowski, “Metamaterial-inspired, electrically small huygens sources,” IEEE Antennas Wirel. Propag. Letts. 9, 501–505 (2010).
[Crossref]

Jin, R.

M. R. Akram, X. Bai, R. Jin, G. A. Vandenbosch, M. Premaratne, and W. Zhu, “Photon spin hall effect based ultra-thin transmissive metasurface for efficient generation of oam waves,” IEEE Trans. Antennas Propag. 67(7), 4650–4658 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
[Crossref]

Kats, M. A.

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]

Keiser, G. R.

X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
[Crossref]

X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016).
[Crossref]

Kerker, M.

Kim, Y.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

Kivshar, Y. S.

Leitis, A.

A. Leitis, A. Heßler, S. Wahl, M. Wuttig, T. Taubner, A. Tittl, and H. Altug, “All-dielectric programmable huygens’ metasurfaces,” Adv. Funct. Mater.1910259 (2020).

Li, H.

H. Li, G. Wang, J. Liang, X. Gao, H. Hou, and X. Jia, “Single-layer focusing gradient metasurface for ultrathin planar lens antenna application,” IEEE Trans. Antennas Propag. 65(3), 1452–1457 (2017).
[Crossref]

H. Li, G. Wang, H.-X. Xu, T. Cai, and J. Liang, “X-band phase-gradient metasurface for high-gain lens antenna application,” IEEE Trans. Antennas Propag. 63(11), 5144–5149 (2015).
[Crossref]

Liang, J.

H. Li, G. Wang, J. Liang, X. Gao, H. Hou, and X. Jia, “Single-layer focusing gradient metasurface for ultrathin planar lens antenna application,” IEEE Trans. Antennas Propag. 65(3), 1452–1457 (2017).
[Crossref]

H. Li, G. Wang, H.-X. Xu, T. Cai, and J. Liang, “X-band phase-gradient metasurface for high-gain lens antenna application,” IEEE Trans. Antennas Propag. 63(11), 5144–5149 (2015).
[Crossref]

Lin, W.

W. Lin, R. W. Ziolkowski, and J. Huang, “Electrically small, low-profile, highly efficient, huygens dipole rectennas for wirelessly powering internet-of-things devices,” IEEE Trans. Antennas Propag. 67(6), 3670–3679 (2019).
[Crossref]

W. Lin and R. W. Ziolkowski, “Electrically small, low-profile, huygens circularly polarized antenna,” IEEE Trans. Antennas Propag. 66(2), 636–643 (2018).
[Crossref]

Liu, W.

Liu, X.

K. Fan, J. Zhang, X. Liu, G.-F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

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A. E. H. Love, “I. the integration of the equations of propagation of electric waves,” Phil. Trans. Royal Soc. London. Ser. A, Cont. Pap. Math. or Phys. Charac. 197(287-299), 1–45 (1901).
[Crossref]

Luo, W.

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin pancharatnam-berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
[Crossref]

Ma, H. F.

L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
[Crossref]

Mehmood, M. Q.

M. R. Akram, M. Q. Mehmood, T. Tauqeer, A. S. Rana, I. D. Rukhlenko, and W. Zhu, “Highly efficient generation of bessel beams with polarization insensitive metasurfaces,” Opt. Express 27(7), 9467–9480 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
[Crossref]

Monticone, F.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

F. Monticone, N. M. Estakhri, and A. Alù, “Full control of nanoscale optical transmission with a composite metascreen,” Phys. Rev. Lett. 110(20), 203903 (2013).
[Crossref]

Padilla, W. J.

K. Fan, J. Zhang, X. Liu, G.-F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

Park, I.

S. X. Ta, I. Park, and R. W. Ziolkowski, “Crossed dipole antennas: A review,” IEEE Antennas Propag. Mag. 57(5), 107–122 (2015).
[Crossref]

Pfeiffer, C.

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102(23), 231116 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102(23), 231116 (2013).
[Crossref]

C. Pfeiffer and A. Grbic, “Metamaterial huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110(19), 197401 (2013).
[Crossref]

Premaratne, M.

M. R. Akram, X. Bai, R. Jin, G. A. Vandenbosch, M. Premaratne, and W. Zhu, “Photon spin hall effect based ultra-thin transmissive metasurface for efficient generation of oam waves,” IEEE Trans. Antennas Propag. 67(7), 4650–4658 (2019).
[Crossref]

M. R. Akram, M. Q. Mehmood, X. Bai, R. Jin, M. Premaratne, and W. Zhu, “High efficiency ultrathin transmissive metasurfaces,” Adv. Opt. Mater. 7(11), 1801628 (2019).
[Crossref]

Rahmati, B.

B. Rahmati and H. R. Hassani, “Low-profile slot transmitarray antenna,” IEEE Trans. Antennas Propag. 63(1), 174–181 (2015).
[Crossref]

Rana, A. S.

Rukhlenko, I. D.

Ryan, C. G.

C. G. Ryan, M. R. Chaharmir, J. Shaker, J. R. Bray, Y. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58(5), 1486–1493 (2010).
[Crossref]

Schalch, J.

X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
[Crossref]

Selvanayagam, M.

J. P. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Polarization considerations for scalar huygens metasurfaces and characterization for 2-d refraction,” IEEE Trans. Microwave Theory Tech. 63(3), 913–924 (2015).
[Crossref]

M. Selvanayagam and G. V. Eleftheriades, “Discontinuous electromagnetic fields using orthogonal electric and magnetic currents for wavefront manipulation,” Opt. Express 21(12), 14409–14429 (2013).
[Crossref]

Shaker, J.

C. G. Ryan, M. R. Chaharmir, J. Shaker, J. R. Bray, Y. M. Antar, and A. Ittipiboon, “A wideband transmitarray using dual-resonant double square rings,” IEEE Trans. Antennas Propag. 58(5), 1486–1493 (2010).
[Crossref]

Sima, B.

Smith, D. R.

P. del Hougne, M. F. Imani, A. V. Diebold, R. Horstmeyer, and D. R. Smith, “Learned integrated sensing pipeline: Reconfigurable metasurface transceivers as trainable physical layer in an artificial neural network,” Adv. Sci. 7(3), 1901913 (2020).
[Crossref]

Sun, S.

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin pancharatnam-berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
[Crossref]

Sun, Z.

Ta, S. X.

S. X. Ta, I. Park, and R. W. Ziolkowski, “Crossed dipole antennas: A review,” IEEE Antennas Propag. Mag. 57(5), 107–122 (2015).
[Crossref]

Taubner, T.

A. Leitis, A. Heßler, S. Wahl, M. Wuttig, T. Taubner, A. Tittl, and H. Altug, “All-dielectric programmable huygens’ metasurfaces,” Adv. Funct. Mater.1910259 (2020).

Tauqeer, T.

Tetienne, J.-P.

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]

Tittl, A.

A. Leitis, A. Heßler, S. Wahl, M. Wuttig, T. Taubner, A. Tittl, and H. Altug, “All-dielectric programmable huygens’ metasurfaces,” Adv. Funct. Mater.1910259 (2020).

Vandenbosch, G. A.

M. R. Akram, X. Bai, R. Jin, G. A. Vandenbosch, M. Premaratne, and W. Zhu, “Photon spin hall effect based ultra-thin transmissive metasurface for efficient generation of oam waves,” IEEE Trans. Antennas Propag. 67(7), 4650–4658 (2019).
[Crossref]

Wahl, S.

A. Leitis, A. Heßler, S. Wahl, M. Wuttig, T. Taubner, A. Tittl, and H. Altug, “All-dielectric programmable huygens’ metasurfaces,” Adv. Funct. Mater.1910259 (2020).

Wang, D.-S.

Wang, G.

H. Li, G. Wang, J. Liang, X. Gao, H. Hou, and X. Jia, “Single-layer focusing gradient metasurface for ultrathin planar lens antenna application,” IEEE Trans. Antennas Propag. 65(3), 1452–1457 (2017).
[Crossref]

H. Li, G. Wang, H.-X. Xu, T. Cai, and J. Liang, “X-band phase-gradient metasurface for high-gain lens antenna application,” IEEE Trans. Antennas Propag. 63(11), 5144–5149 (2015).
[Crossref]

Wang, M.

L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
[Crossref]

Wang, Z. X.

L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
[Crossref]

Wei, E.

M. L. Chen, L. J. Jiang, and E. Wei, “Ultrathin complementary metasurface for orbital angular momentum generation at microwave frequencies,” IEEE Trans. Antennas Propag. 65(1), 396–400 (2017).
[Crossref]

Wong, J. P.

A. Epstein, J. P. Wong, and G. V. Eleftheriades, “Cavity-excited huygens’ metasurface antennas for near-unity aperture illumination efficiency from arbitrarily large apertures,” Nat. Commun. 7(1), 10360 (2016).
[Crossref]

J. P. Wong, M. Selvanayagam, and G. V. Eleftheriades, “Polarization considerations for scalar huygens metasurfaces and characterization for 2-d refraction,” IEEE Trans. Microwave Theory Tech. 63(3), 913–924 (2015).
[Crossref]

Wu, L. W.

L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
[Crossref]

Wu, R. Y.

L. W. Wu, H. F. Ma, Y. Gou, R. Y. Wu, Z. X. Wang, M. Wang, X. Gao, and T. J. Cui, “High-transmission ultrathin huygens’ metasurface with 360 phase control by using double-layer transmitarray elements,” Phys. Rev. Appl. 12(2), 024012 (2019).
[Crossref]

Wuttig, M.

A. Leitis, A. Heßler, S. Wahl, M. Wuttig, T. Taubner, A. Tittl, and H. Altug, “All-dielectric programmable huygens’ metasurfaces,” Adv. Funct. Mater.1910259 (2020).

Xu, G.

G. Xu, S. V. Hum, and G. V. Eleftheriades, “A technique for designing multilayer multistopband frequency selective surfaces,” IEEE Trans. Antennas Propag. 66(2), 780–789 (2018).
[Crossref]

Xu, H.-X.

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin pancharatnam-berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
[Crossref]

H. Li, G. Wang, H.-X. Xu, T. Cai, and J. Liang, “X-band phase-gradient metasurface for high-gain lens antenna application,” IEEE Trans. Antennas Propag. 63(11), 5144–5149 (2015).
[Crossref]

Xuan, X.

M. Jiang, Z. N. Chen, Y. Zhang, W. Hong, and X. Xuan, “Metamaterial-based thin planar lens antenna for spatial beamforming and multibeam massive mimo,” IEEE Trans. Antennas Propag. 65(2), 464–472 (2017).
[Crossref]

Yang, F.

A. H. Abdelrahman, A. Z. Elsherbeni, and F. Yang, “Transmitarray antenna design using cross-slot elements with no dielectric substrate,” IEEE Antennas Wirel. Propag. Letts. 13, 177–180 (2014).
[Crossref]

Yu, N.

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]

Zeb, B. A.

M. U. Afzal, K. P. Esselle, and B. A. Zeb, “Dielectric phase-correcting structures for electromagnetic band gap resonator antennas,” IEEE Trans. Antennas Propag. 63(8), 3390–3399 (2015).
[Crossref]

Zhang, G.-F.

K. Fan, J. Zhang, X. Liu, G.-F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

Zhang, J.

X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
[Crossref]

K. Fan, J. Zhang, X. Liu, G.-F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016).
[Crossref]

Zhang, L.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

Zhang, S.

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

Zhang, X.

X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
[Crossref]

X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016).
[Crossref]

Zhang, Y.

M. Jiang, Z. N. Chen, Y. Zhang, W. Hong, and X. Xuan, “Metamaterial-based thin planar lens antenna for spatial beamforming and multibeam massive mimo,” IEEE Trans. Antennas Propag. 65(2), 464–472 (2017).
[Crossref]

Zhao, J.

Z. Sun, B. Sima, J. Zhao, and Y. Feng, “Electromagnetic polarization conversion based on huygens’ metasurfaces with coupled electric and magnetic resonances,” Opt. Express 27(8), 11006–11017 (2019).
[Crossref]

K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
[Crossref]

Zhao, X.

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[Crossref]

X. Zhao, K. Fan, J. Zhang, G. R. Keiser, G. Duan, R. D. Averitt, and X. Zhang, “Voltage-tunable dual-layer terahertz metamaterials,” Microsyst. Nanoeng. 2(1), 16025 (2016).
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Zhou, L.

W. Luo, S. Sun, H.-X. Xu, Q. He, and L. Zhou, “Transmissive ultrathin pancharatnam-berry metasurfaces with nearly 100% efficiency,” Phys. Rev. Appl. 7(4), 044033 (2017).
[Crossref]

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K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, and S. Zhang, “A reconfigurable active huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017).
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P. Jin and R. W. Ziolkowski, “Metamaterial-inspired, electrically small huygens sources,” IEEE Antennas Wirel. Propag. Letts. 9, 501–505 (2010).
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W. Lin, R. W. Ziolkowski, and J. Huang, “Electrically small, low-profile, highly efficient, huygens dipole rectennas for wirelessly powering internet-of-things devices,” IEEE Trans. Antennas Propag. 67(6), 3670–3679 (2019).
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[Crossref]

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X. Zhao, J. Zhang, K. Fan, G. Duan, J. Schalch, G. R. Keiser, R. D. Averitt, and X. Zhang, “Real-time tunable phase response and group delay in broadside coupled split-ring resonators,” Phys. Rev. B 99(24), 245111 (2019).
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Figures (11)

Fig. 1.
Fig. 1. Transmission response of the unit cell as shown in the inset. Geometrical parameters are $w=0.4$ mm, $l=4.8$ mm, $p=14$ mm, $g=0.4$ mm, $a=0.2$ mm, and $h=1.5$ mm.
Fig. 2.
Fig. 2. Surface impedance and admittance for unit cell with geometrical parameters: $w=0.4$ mm, $l=4.8$ mm, $p=14$ mm, $g=0.4$ mm, $a=0.2$ mm, and $h=1.5$ mm.
Fig. 3.
Fig. 3. simulate electric and magnetic dipoles under $x$-polarized incidence.
Fig. 4.
Fig. 4. Amplitude and phase response of the co-polarized transmitted waves.
Fig. 5.
Fig. 5. Unit cell response under different incident angles.
Fig. 6.
Fig. 6. Simulated results (a) Designed lens. $E_x$ distribution along (b) $xy$-plane at $z=30$ mm, (c) $xoz$ plane, and (d) $yoz$ plane.
Fig. 7.
Fig. 7. Simulated far-filed pattern on left at 9.3 GHz and measured $S_{11}$ with/without lens on right along with patch antenna in the inset with $s=9.3$ mm.
Fig. 8.
Fig. 8. Simulated electric field distribution without Lens (left) and with lens (right) for $yoz$ plane (top) and $xoz$ plane (bottom).
Fig. 9.
Fig. 9. Simulated far-field patterns at 9.1 GHz (left) and 9.4 GHz (right).
Fig. 10.
Fig. 10. Fabricated designs: (a) antenna, (b) metasurface, and (c) metasurface antenna.
Fig. 11.
Fig. 11. Measured radiation pattern for E-plane (top) and H-plane (bottom) at 9.3 GHz.

Equations (3)

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Y e s = 2 ( 1 S 21 S 11 ) η 0 ( 1 + S 21 + S 11 )
Z m s = 2 η 0 ( 1 S 21 + S 11 ) ( 1 + S 21 S 11 ) ,
ϕ ( x , y ) = 2 π λ ( x 2 + y 2 + f 2 f ) ,

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