Abstract

The holographic technique is a promising way to manipulate light distribution and wave-front in the optical regime. In recent years, many researchers have extended this concept to microwave regime to manipulate phase, amplitude, and polarization of waves in a convenient way revealing diverse intriguing applications. Unlike the previous studies with optimization-based schemes, in this paper, we propose a simple route to design dual frequency dual-polarization holographic metasurfaces with negligible interference between the operating (lower and upper) frequencies. For this purpose, a Jerusalem-shape unit-cell is used to realize two distinct impedance distributions which yield two decoupled field profiles over the aperture of the metasurface at each frequency band. Consequently, the proposed metasurface radiator can operate in two frequency bands, independently. Each set of horizontal (vertical) cross-bars of the Jerusalem-shape unit-cell is illuminated by a vertical (horizontal) feeding network from one side of the metasurface. Side feeding has a null-free advantage, this undesired null emerges in central feeding metasurfaces and leads to an undesirable rabbit’s ears phenomenon. As the proof-of-concept, a prototype of the metasurface radiator for operating at 11.5 GHz and 14 GHz is fabricated and measured. The experimental results depict a good agreement with the full-wave simulations.

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

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2020 (3)

2019 (12)

M. Faenzi, G. Minatti, D. Gonzalez-Ovejero, F. Caminita, E. Martini, C. D. Giovampaola, and S. Maci, “Metasurface antennas: New models, applications and realizations,” Sci. Rep. 9(1), 10178 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Holographic-inspired multiple circularly polarized vortex-beam generation with flexible topological charges and beam directions,” Phys. Rev. Appl. 11(5), 054027 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Shaping electromagnetic waves with flexible and continuous control of the beam directions using holography and convolution theorem,” Sci. Rep. 9(1), 11825 (2019).
[Crossref]

K. Zhang, Y. Yuan, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “High-efficiency metalenses with switchable functionalities in microwave region,” ACS Appl. Mater. Interfaces 11(31), 28423–28430 (2019).
[Crossref]

Y. Yuan, K. Zhang, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “Complementary transmissive ultra-thin meta-deflectors for broadband polarization-independent refractions in the microwave region,” Photonics Res. 7(1), 80 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Broadband, dual-band reflectarray with dual orthogonal polarisation for single and multi-beam patterns,” IET Microwaves, Antennas & Propag. 13(12), 2037–2045 (2019).
[Crossref]

A. Abdolali, A. Momeni, H. Rajabalipanah, and K. Achouri, “Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities,” New J. Phys. 21(11), 113048 (2019).
[Crossref]

A. Momeni, H. Rajabalipanah, A. Abdolali, and K. Achouri, “Generalized optical signal processing based on multioperator metasurfaces synthesized by susceptibility tensors,” Phys. Rev. Appl. 11(6), 064042 (2019).
[Crossref]

R. Feng, B. Ratni, J. Yi, A. de Lustrac, H. Zhang, and S. Burokur, “Electronically-engineered metasurface for directional beaming of electromagnetic waves through a subwavelength aperture,” Opt. Express 27(24), 35774 (2019).
[Crossref]

M. Moeini, H. Oraizi, and A. Amini, “Collimating cylindrical surface leaky waves for highly improved radiation characteristics of holograms,” Phys. Rev. Appl. 11(4), 044006 (2019).
[Crossref]

M. Moeini, H. Oraizi, A. Amini, and V. Nayyeri, “Wide-band beam-scanning by surface wave confinement on leaky wave holograms,” Sci. Rep. 9(1), 13227 (2019).
[Crossref]

M. Movahhedi, M. Karimipour, and N. Komjani, “Multibeam bidirectional wideband/wide scanning angle holographic leaky wave antenna,” Antennas Wirel. Propag. Lett. 18(7), 1507–1511 (2019).
[Crossref]

2018 (5)

A. Momeni, K. Rouhi, H. Rajabalipanah, and A. Abdolali, “An information theory-inspired strategy for design of re-programmable encrypted graphene-based coding metasurfaces at terahertz frequencies,” Sci. Rep. 8(1), 6200 (2018).
[Crossref]

M. Karimipour and N. Komjani, “Holographic-inspired multibeam reflectarray with linear polarization,” IEEE Trans. Antennas Propag. 66(6), 2870–2882 (2018).
[Crossref]

M. Karimipour and N. Komjani, “Realization of multiple concurrent beams with independent circular polarizations by holographic reflectarray,” IEEE Trans. Antennas Propag. 66(9), 4627–4640 (2018).
[Crossref]

Y. Li, A. Li, T. Cui, and D. Sievenpiper, “Multiwavelength multiplexing hologram designed using impedance metasurfaces,” IEEE Trans. Antennas Propag. 66(11), 6408–6413 (2018).
[Crossref]

H. Oraizi, A. Amini, A. Abdolali, and A. Karimimehr, “Design of wideband leaky-wave antenna using sinusoidally modulated impedance surface based on the holography theory,” Antennas Wirel. Propag. Lett. 17(10), 1807–1811 (2018).
[Crossref]

2016 (4)

M. Casaletti, M. Smierzchalski, M. Ettorre, R. Sauleau, and N. Capet, “Polarized beams using scalar metasurfaces,” IEEE Trans. Antennas Propag. 66(8), 3391–3400 (2016).
[Crossref]

Y. Li, B. Cai, Q. Cheng, and T. Cui, “Isotropic holographic metasurfaces for dual-functional radiations without mutual interferences,” Adv. Funct. Mater. 26(1), 29–35 (2016).
[Crossref]

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

E. Arbabi, A. Arbabi, S. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6(1), 32803 (2016).
[Crossref]

2015 (4)

Y. Li, X. Wan, B. Cai, Q. Cheng, and T. Cui, “Frequency-controls of electromagnetic multi-beam scanning by metasurfaces,” Sci. Rep. 4(1), 6921 (2015).
[Crossref]

J. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alú, “Dual-polarized reduction of dipole antenna blockage using mantle cloaks,” IEEE Trans. Antennas Propag. 63(11), 4827–4834 (2015).
[Crossref]

C. Argyropoulos, “Enhanced transmission modulation based on dielectric metasurfaces loaded with graphene,” Opt. Express 23(18), 23787 (2015).
[Crossref]

Y. Liu, Y. Hao, K. Li, and S. Gong, “Wideband and polarization-independent radar cross section reduction using holographic metasurface,” Antennas Wirel. Propag. Lett. 15, 1028–1031 (2015).
[Crossref]

2013 (2)

C. Argyropoulos, N. Estakhri, F. Monticone, and A. Alú, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21(12), 15037 (2013).
[Crossref]

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

2011 (2)

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

A. Patel and A. Grbic, “A printed leaky-wave antenna based on a sinusoidally-modulated reactance surface,” IEEE Trans. Antennas Propag. 59(6), 2087–2096 (2011).
[Crossref]

2010 (2)

B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58(10), 3212–3221 (2010).
[Crossref]

H. Wang, D. Fang, B. Zhang, and W. Che, “Dielectric loaded substrate integrated waveguide (siw) H-plane horn antennas,” IEEE Trans. Antennas Propag. 58(3), 640–647 (2010).
[Crossref]

Abdolali, A.

M. Kiani, M. Tayarani, A. Momeni, H. Rajabalipanah, and A. Abdolali, “Self-biased tri-state power-multiplexed digital metasurface operating at microwave frequencies,” Opt. Express 28(4), 5410 (2020).
[Crossref]

A. Momeni, H. Rajabalipanah, A. Abdolali, and K. Achouri, “Generalized optical signal processing based on multioperator metasurfaces synthesized by susceptibility tensors,” Phys. Rev. Appl. 11(6), 064042 (2019).
[Crossref]

A. Abdolali, A. Momeni, H. Rajabalipanah, and K. Achouri, “Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities,” New J. Phys. 21(11), 113048 (2019).
[Crossref]

A. Momeni, K. Rouhi, H. Rajabalipanah, and A. Abdolali, “An information theory-inspired strategy for design of re-programmable encrypted graphene-based coding metasurfaces at terahertz frequencies,” Sci. Rep. 8(1), 6200 (2018).
[Crossref]

H. Oraizi, A. Amini, A. Abdolali, and A. Karimimehr, “Design of wideband leaky-wave antenna using sinusoidally modulated impedance surface based on the holography theory,” Antennas Wirel. Propag. Lett. 17(10), 1807–1811 (2018).
[Crossref]

Achouri, K.

A. Momeni, H. Rajabalipanah, A. Abdolali, and K. Achouri, “Generalized optical signal processing based on multioperator metasurfaces synthesized by susceptibility tensors,” Phys. Rev. Appl. 11(6), 064042 (2019).
[Crossref]

A. Abdolali, A. Momeni, H. Rajabalipanah, and K. Achouri, “Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities,” New J. Phys. 21(11), 113048 (2019).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Alu, A.

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

Alú, A.

J. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alú, “Dual-polarized reduction of dipole antenna blockage using mantle cloaks,” IEEE Trans. Antennas Propag. 63(11), 4827–4834 (2015).
[Crossref]

C. Argyropoulos, N. Estakhri, F. Monticone, and A. Alú, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21(12), 15037 (2013).
[Crossref]

Amini, A.

M. Moeini, H. Oraizi, and A. Amini, “Collimating cylindrical surface leaky waves for highly improved radiation characteristics of holograms,” Phys. Rev. Appl. 11(4), 044006 (2019).
[Crossref]

M. Moeini, H. Oraizi, A. Amini, and V. Nayyeri, “Wide-band beam-scanning by surface wave confinement on leaky wave holograms,” Sci. Rep. 9(1), 13227 (2019).
[Crossref]

H. Oraizi, A. Amini, A. Abdolali, and A. Karimimehr, “Design of wideband leaky-wave antenna using sinusoidally modulated impedance surface based on the holography theory,” Antennas Wirel. Propag. Lett. 17(10), 1807–1811 (2018).
[Crossref]

Arbabi, A.

E. Arbabi, A. Arbabi, S. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6(1), 32803 (2016).
[Crossref]

Arbabi, E.

E. Arbabi, A. Arbabi, S. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6(1), 32803 (2016).
[Crossref]

Argyropoulos, C.

Aryanian, I.

M. Karimipour, N. Komjani, and I. Aryanian, “Holographic-inspired multiple circularly polarized vortex-beam generation with flexible topological charges and beam directions,” Phys. Rev. Appl. 11(5), 054027 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Shaping electromagnetic waves with flexible and continuous control of the beam directions using holography and convolution theorem,” Sci. Rep. 9(1), 11825 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Broadband, dual-band reflectarray with dual orthogonal polarisation for single and multi-beam patterns,” IET Microwaves, Antennas & Propag. 13(12), 2037–2045 (2019).
[Crossref]

Bahl, I.

G. Ramesh, I. Bahl, and M. Bozzi, Microstrip lines and slotlines (Artech house, 2013).

Balanis, C. A.

C. A. Balanis, Antenna theory: analysis and design (Wiely, 2016).

Bilotti, F.

J. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alú, “Dual-polarized reduction of dipole antenna blockage using mantle cloaks,” IEEE Trans. Antennas Propag. 63(11), 4827–4834 (2015).
[Crossref]

Bozzi, M.

G. Ramesh, I. Bahl, and M. Bozzi, Microstrip lines and slotlines (Artech house, 2013).

Burokur, S.

R. Feng, B. Ratni, J. Yi, A. de Lustrac, H. Zhang, and S. Burokur, “Electronically-engineered metasurface for directional beaming of electromagnetic waves through a subwavelength aperture,” Opt. Express 27(24), 35774 (2019).
[Crossref]

Y. Yuan, K. Zhang, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “Complementary transmissive ultra-thin meta-deflectors for broadband polarization-independent refractions in the microwave region,” Photonics Res. 7(1), 80 (2019).
[Crossref]

K. Zhang, Y. Yuan, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “High-efficiency metalenses with switchable functionalities in microwave region,” ACS Appl. Mater. Interfaces 11(31), 28423–28430 (2019).
[Crossref]

Cai, B.

Y. Li, B. Cai, Q. Cheng, and T. Cui, “Isotropic holographic metasurfaces for dual-functional radiations without mutual interferences,” Adv. Funct. Mater. 26(1), 29–35 (2016).
[Crossref]

Y. Li, X. Wan, B. Cai, Q. Cheng, and T. Cui, “Frequency-controls of electromagnetic multi-beam scanning by metasurfaces,” Sci. Rep. 4(1), 6921 (2015).
[Crossref]

Caminita, F.

M. Faenzi, G. Minatti, D. Gonzalez-Ovejero, F. Caminita, E. Martini, C. D. Giovampaola, and S. Maci, “Metasurface antennas: New models, applications and realizations,” Sci. Rep. 9(1), 10178 (2019).
[Crossref]

Capasso, F.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Capet, N.

M. Casaletti, M. Smierzchalski, M. Ettorre, R. Sauleau, and N. Capet, “Polarized beams using scalar metasurfaces,” IEEE Trans. Antennas Propag. 66(8), 3391–3400 (2016).
[Crossref]

Casaletti, M.

M. Casaletti, M. Smierzchalski, M. Ettorre, R. Sauleau, and N. Capet, “Polarized beams using scalar metasurfaces,” IEEE Trans. Antennas Propag. 66(8), 3391–3400 (2016).
[Crossref]

Che, W.

H. Wang, D. Fang, B. Zhang, and W. Che, “Dielectric loaded substrate integrated waveguide (siw) H-plane horn antennas,” IEEE Trans. Antennas Propag. 58(3), 640–647 (2010).
[Crossref]

Chen, T.

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

Chen, X.

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

Cheng, Q.

Y. Li, B. Cai, Q. Cheng, and T. Cui, “Isotropic holographic metasurfaces for dual-functional radiations without mutual interferences,” Adv. Funct. Mater. 26(1), 29–35 (2016).
[Crossref]

Y. Li, X. Wan, B. Cai, Q. Cheng, and T. Cui, “Frequency-controls of electromagnetic multi-beam scanning by metasurfaces,” Sci. Rep. 4(1), 6921 (2015).
[Crossref]

Colburn, J.

B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58(10), 3212–3221 (2010).
[Crossref]

Collin, R. E.

R. E. Collin and F. J. Zucker, Antenna theory (Wiely, 1969).

Cui, T.

Y. Li, A. Li, T. Cui, and D. Sievenpiper, “Multiwavelength multiplexing hologram designed using impedance metasurfaces,” IEEE Trans. Antennas Propag. 66(11), 6408–6413 (2018).
[Crossref]

Y. Li, B. Cai, Q. Cheng, and T. Cui, “Isotropic holographic metasurfaces for dual-functional radiations without mutual interferences,” Adv. Funct. Mater. 26(1), 29–35 (2016).
[Crossref]

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

Y. Li, X. Wan, B. Cai, Q. Cheng, and T. Cui, “Frequency-controls of electromagnetic multi-beam scanning by metasurfaces,” Sci. Rep. 4(1), 6921 (2015).
[Crossref]

de Lustrac, A.

Díaz-Rubio, A.

S. Tcvetkova, D. Kwon, A. Díaz-Rubio, and S. Tretyakov, “Near-perfect conversion of a propagating plane wave into a surface wave using metasurfaces,” Phys. Rev. B 11 (2018).

Ding, X.

K. Zhang, Y. Yuan, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “High-efficiency metalenses with switchable functionalities in microwave region,” ACS Appl. Mater. Interfaces 11(31), 28423–28430 (2019).
[Crossref]

Y. Yuan, K. Zhang, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “Complementary transmissive ultra-thin meta-deflectors for broadband polarization-independent refractions in the microwave region,” Photonics Res. 7(1), 80 (2019).
[Crossref]

Estakhri, N.

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

C. Argyropoulos, N. Estakhri, F. Monticone, and A. Alú, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21(12), 15037 (2013).
[Crossref]

Ettorre, M.

M. Casaletti, M. Smierzchalski, M. Ettorre, R. Sauleau, and N. Capet, “Polarized beams using scalar metasurfaces,” IEEE Trans. Antennas Propag. 66(8), 3391–3400 (2016).
[Crossref]

Faenzi, M.

M. Faenzi, G. Minatti, D. Gonzalez-Ovejero, F. Caminita, E. Martini, C. D. Giovampaola, and S. Maci, “Metasurface antennas: New models, applications and realizations,” Sci. Rep. 9(1), 10178 (2019).
[Crossref]

Fang, D.

H. Wang, D. Fang, B. Zhang, and W. Che, “Dielectric loaded substrate integrated waveguide (siw) H-plane horn antennas,” IEEE Trans. Antennas Propag. 58(3), 640–647 (2010).
[Crossref]

Faraon, A.

E. Arbabi, A. Arbabi, S. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6(1), 32803 (2016).
[Crossref]

Feng, R.

Fong, B.

B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58(10), 3212–3221 (2010).
[Crossref]

Gabor, D.

D. Gabor, A new microscopic principle (nature, 1948).

Gaburro, Z.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Genevet, P.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Giovampaola, C. D.

M. Faenzi, G. Minatti, D. Gonzalez-Ovejero, F. Caminita, E. Martini, C. D. Giovampaola, and S. Maci, “Metasurface antennas: New models, applications and realizations,” Sci. Rep. 9(1), 10178 (2019).
[Crossref]

Gong, S.

Y. Liu, Y. Hao, K. Li, and S. Gong, “Wideband and polarization-independent radar cross section reduction using holographic metasurface,” Antennas Wirel. Propag. Lett. 15, 1028–1031 (2015).
[Crossref]

Gonzalez-Ovejero, D.

M. Faenzi, G. Minatti, D. Gonzalez-Ovejero, F. Caminita, E. Martini, C. D. Giovampaola, and S. Maci, “Metasurface antennas: New models, applications and realizations,” Sci. Rep. 9(1), 10178 (2019).
[Crossref]

Grbic, A.

A. Patel and A. Grbic, “A printed leaky-wave antenna based on a sinusoidally-modulated reactance surface,” IEEE Trans. Antennas Propag. 59(6), 2087–2096 (2011).
[Crossref]

Hao, Y.

Y. Liu, Y. Hao, K. Li, and S. Gong, “Wideband and polarization-independent radar cross section reduction using holographic metasurface,” Antennas Wirel. Propag. Lett. 15, 1028–1031 (2015).
[Crossref]

Horie, Y.

E. Arbabi, A. Arbabi, S. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6(1), 32803 (2016).
[Crossref]

Kamali, S.

E. Arbabi, A. Arbabi, S. Kamali, Y. Horie, and A. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6(1), 32803 (2016).
[Crossref]

Kandasamy, K.

K. Rudramuni, B. Majumder, and K. Kandasamy, “Dual-band dual-polarized leaky-wave structure with forward and backward beam scanning for circular polarization-flexible antenna application,” Microw. Opt. Technol. Lett. 62(5), 2075–2084 (2020).
[Crossref]

Karimimehr, A.

H. Oraizi, A. Amini, A. Abdolali, and A. Karimimehr, “Design of wideband leaky-wave antenna using sinusoidally modulated impedance surface based on the holography theory,” Antennas Wirel. Propag. Lett. 17(10), 1807–1811 (2018).
[Crossref]

Karimipour, M.

M. Karimipour, N. Komjani, and I. Aryanian, “Broadband, dual-band reflectarray with dual orthogonal polarisation for single and multi-beam patterns,” IET Microwaves, Antennas & Propag. 13(12), 2037–2045 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Holographic-inspired multiple circularly polarized vortex-beam generation with flexible topological charges and beam directions,” Phys. Rev. Appl. 11(5), 054027 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Shaping electromagnetic waves with flexible and continuous control of the beam directions using holography and convolution theorem,” Sci. Rep. 9(1), 11825 (2019).
[Crossref]

M. Movahhedi, M. Karimipour, and N. Komjani, “Multibeam bidirectional wideband/wide scanning angle holographic leaky wave antenna,” Antennas Wirel. Propag. Lett. 18(7), 1507–1511 (2019).
[Crossref]

M. Karimipour and N. Komjani, “Holographic-inspired multibeam reflectarray with linear polarization,” IEEE Trans. Antennas Propag. 66(6), 2870–2882 (2018).
[Crossref]

M. Karimipour and N. Komjani, “Realization of multiple concurrent beams with independent circular polarizations by holographic reflectarray,” IEEE Trans. Antennas Propag. 66(9), 4627–4640 (2018).
[Crossref]

Kats, M.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Kiani, M.

Komjani, N.

M. Movahhedi, M. Karimipour, and N. Komjani, “Multibeam bidirectional wideband/wide scanning angle holographic leaky wave antenna,” Antennas Wirel. Propag. Lett. 18(7), 1507–1511 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Shaping electromagnetic waves with flexible and continuous control of the beam directions using holography and convolution theorem,” Sci. Rep. 9(1), 11825 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Holographic-inspired multiple circularly polarized vortex-beam generation with flexible topological charges and beam directions,” Phys. Rev. Appl. 11(5), 054027 (2019).
[Crossref]

M. Karimipour, N. Komjani, and I. Aryanian, “Broadband, dual-band reflectarray with dual orthogonal polarisation for single and multi-beam patterns,” IET Microwaves, Antennas & Propag. 13(12), 2037–2045 (2019).
[Crossref]

M. Karimipour and N. Komjani, “Realization of multiple concurrent beams with independent circular polarizations by holographic reflectarray,” IEEE Trans. Antennas Propag. 66(9), 4627–4640 (2018).
[Crossref]

M. Karimipour and N. Komjani, “Holographic-inspired multibeam reflectarray with linear polarization,” IEEE Trans. Antennas Propag. 66(6), 2870–2882 (2018).
[Crossref]

Kwon, D.

S. Tcvetkova, D. Kwon, A. Díaz-Rubio, and S. Tretyakov, “Near-perfect conversion of a propagating plane wave into a surface wave using metasurfaces,” Phys. Rev. B 11 (2018).

Li, A.

Y. Li, A. Li, T. Cui, and D. Sievenpiper, “Multiwavelength multiplexing hologram designed using impedance metasurfaces,” IEEE Trans. Antennas Propag. 66(11), 6408–6413 (2018).
[Crossref]

Li, K.

Y. Liu, Y. Hao, K. Li, and S. Gong, “Wideband and polarization-independent radar cross section reduction using holographic metasurface,” Antennas Wirel. Propag. Lett. 15, 1028–1031 (2015).
[Crossref]

Li, Y.

Y. Li, A. Li, T. Cui, and D. Sievenpiper, “Multiwavelength multiplexing hologram designed using impedance metasurfaces,” IEEE Trans. Antennas Propag. 66(11), 6408–6413 (2018).
[Crossref]

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

Y. Li, B. Cai, Q. Cheng, and T. Cui, “Isotropic holographic metasurfaces for dual-functional radiations without mutual interferences,” Adv. Funct. Mater. 26(1), 29–35 (2016).
[Crossref]

Y. Li, X. Wan, B. Cai, Q. Cheng, and T. Cui, “Frequency-controls of electromagnetic multi-beam scanning by metasurfaces,” Sci. Rep. 4(1), 6921 (2015).
[Crossref]

Liu, Y.

Y. Liu, Y. Hao, K. Li, and S. Gong, “Wideband and polarization-independent radar cross section reduction using holographic metasurface,” Antennas Wirel. Propag. Lett. 15, 1028–1031 (2015).
[Crossref]

Maci, S.

M. Faenzi, G. Minatti, D. Gonzalez-Ovejero, F. Caminita, E. Martini, C. D. Giovampaola, and S. Maci, “Metasurface antennas: New models, applications and realizations,” Sci. Rep. 9(1), 10178 (2019).
[Crossref]

Majumder, B.

K. Rudramuni, B. Majumder, and K. Kandasamy, “Dual-band dual-polarized leaky-wave structure with forward and backward beam scanning for circular polarization-flexible antenna application,” Microw. Opt. Technol. Lett. 62(5), 2075–2084 (2020).
[Crossref]

Martini, E.

M. Faenzi, G. Minatti, D. Gonzalez-Ovejero, F. Caminita, E. Martini, C. D. Giovampaola, and S. Maci, “Metasurface antennas: New models, applications and realizations,” Sci. Rep. 9(1), 10178 (2019).
[Crossref]

Minatti, G.

M. Faenzi, G. Minatti, D. Gonzalez-Ovejero, F. Caminita, E. Martini, C. D. Giovampaola, and S. Maci, “Metasurface antennas: New models, applications and realizations,” Sci. Rep. 9(1), 10178 (2019).
[Crossref]

Moeini, M.

M. Moeini, H. Oraizi, A. Amini, and V. Nayyeri, “Wide-band beam-scanning by surface wave confinement on leaky wave holograms,” Sci. Rep. 9(1), 13227 (2019).
[Crossref]

M. Moeini, H. Oraizi, and A. Amini, “Collimating cylindrical surface leaky waves for highly improved radiation characteristics of holograms,” Phys. Rev. Appl. 11(4), 044006 (2019).
[Crossref]

Momeni, A.

M. Kiani, M. Tayarani, A. Momeni, H. Rajabalipanah, and A. Abdolali, “Self-biased tri-state power-multiplexed digital metasurface operating at microwave frequencies,” Opt. Express 28(4), 5410 (2020).
[Crossref]

A. Momeni, H. Rajabalipanah, A. Abdolali, and K. Achouri, “Generalized optical signal processing based on multioperator metasurfaces synthesized by susceptibility tensors,” Phys. Rev. Appl. 11(6), 064042 (2019).
[Crossref]

A. Abdolali, A. Momeni, H. Rajabalipanah, and K. Achouri, “Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities,” New J. Phys. 21(11), 113048 (2019).
[Crossref]

A. Momeni, K. Rouhi, H. Rajabalipanah, and A. Abdolali, “An information theory-inspired strategy for design of re-programmable encrypted graphene-based coding metasurfaces at terahertz frequencies,” Sci. Rep. 8(1), 6200 (2018).
[Crossref]

Monti, A.

J. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alú, “Dual-polarized reduction of dipole antenna blockage using mantle cloaks,” IEEE Trans. Antennas Propag. 63(11), 4827–4834 (2015).
[Crossref]

Monticone, F.

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

C. Argyropoulos, N. Estakhri, F. Monticone, and A. Alú, “Negative refraction, gain and nonlinear effects in hyperbolic metamaterials,” Opt. Express 21(12), 15037 (2013).
[Crossref]

Movahhedi, M.

M. Movahhedi, M. Karimipour, and N. Komjani, “Multibeam bidirectional wideband/wide scanning angle holographic leaky wave antenna,” Antennas Wirel. Propag. Lett. 18(7), 1507–1511 (2019).
[Crossref]

Nayyeri, V.

M. Moeini, H. Oraizi, A. Amini, and V. Nayyeri, “Wide-band beam-scanning by surface wave confinement on leaky wave holograms,” Sci. Rep. 9(1), 13227 (2019).
[Crossref]

Oraizi, H.

M. Moeini, H. Oraizi, A. Amini, and V. Nayyeri, “Wide-band beam-scanning by surface wave confinement on leaky wave holograms,” Sci. Rep. 9(1), 13227 (2019).
[Crossref]

M. Moeini, H. Oraizi, and A. Amini, “Collimating cylindrical surface leaky waves for highly improved radiation characteristics of holograms,” Phys. Rev. Appl. 11(4), 044006 (2019).
[Crossref]

H. Oraizi, A. Amini, A. Abdolali, and A. Karimimehr, “Design of wideband leaky-wave antenna using sinusoidally modulated impedance surface based on the holography theory,” Antennas Wirel. Propag. Lett. 17(10), 1807–1811 (2018).
[Crossref]

Ottusch, J.

B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58(10), 3212–3221 (2010).
[Crossref]

Patel, A.

A. Patel and A. Grbic, “A printed leaky-wave antenna based on a sinusoidally-modulated reactance surface,” IEEE Trans. Antennas Propag. 59(6), 2087–2096 (2011).
[Crossref]

Rajabalipanah, H.

M. Kiani, M. Tayarani, A. Momeni, H. Rajabalipanah, and A. Abdolali, “Self-biased tri-state power-multiplexed digital metasurface operating at microwave frequencies,” Opt. Express 28(4), 5410 (2020).
[Crossref]

A. Momeni, H. Rajabalipanah, A. Abdolali, and K. Achouri, “Generalized optical signal processing based on multioperator metasurfaces synthesized by susceptibility tensors,” Phys. Rev. Appl. 11(6), 064042 (2019).
[Crossref]

A. Abdolali, A. Momeni, H. Rajabalipanah, and K. Achouri, “Parallel integro-differential equation solving via multi-channel reciprocal bianisotropic metasurface augmented by normal susceptibilities,” New J. Phys. 21(11), 113048 (2019).
[Crossref]

A. Momeni, K. Rouhi, H. Rajabalipanah, and A. Abdolali, “An information theory-inspired strategy for design of re-programmable encrypted graphene-based coding metasurfaces at terahertz frequencies,” Sci. Rep. 8(1), 6200 (2018).
[Crossref]

Ramesh, G.

G. Ramesh, I. Bahl, and M. Bozzi, Microstrip lines and slotlines (Artech house, 2013).

Ratni, B.

R. Feng, B. Ratni, J. Yi, A. de Lustrac, H. Zhang, and S. Burokur, “Electronically-engineered metasurface for directional beaming of electromagnetic waves through a subwavelength aperture,” Opt. Express 27(24), 35774 (2019).
[Crossref]

Y. Yuan, K. Zhang, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “Complementary transmissive ultra-thin meta-deflectors for broadband polarization-independent refractions in the microwave region,” Photonics Res. 7(1), 80 (2019).
[Crossref]

K. Zhang, Y. Yuan, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “High-efficiency metalenses with switchable functionalities in microwave region,” ACS Appl. Mater. Interfaces 11(31), 28423–28430 (2019).
[Crossref]

Rouhi, K.

A. Momeni, K. Rouhi, H. Rajabalipanah, and A. Abdolali, “An information theory-inspired strategy for design of re-programmable encrypted graphene-based coding metasurfaces at terahertz frequencies,” Sci. Rep. 8(1), 6200 (2018).
[Crossref]

Rudramuni, K.

K. Rudramuni, B. Majumder, and K. Kandasamy, “Dual-band dual-polarized leaky-wave structure with forward and backward beam scanning for circular polarization-flexible antenna application,” Microw. Opt. Technol. Lett. 62(5), 2075–2084 (2020).
[Crossref]

Saifullah, Y.

Sauleau, R.

M. Casaletti, M. Smierzchalski, M. Ettorre, R. Sauleau, and N. Capet, “Polarized beams using scalar metasurfaces,” IEEE Trans. Antennas Propag. 66(8), 3391–3400 (2016).
[Crossref]

Sievenpiper, D.

Y. Li, A. Li, T. Cui, and D. Sievenpiper, “Multiwavelength multiplexing hologram designed using impedance metasurfaces,” IEEE Trans. Antennas Propag. 66(11), 6408–6413 (2018).
[Crossref]

B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58(10), 3212–3221 (2010).
[Crossref]

Smierzchalski, M.

M. Casaletti, M. Smierzchalski, M. Ettorre, R. Sauleau, and N. Capet, “Polarized beams using scalar metasurfaces,” IEEE Trans. Antennas Propag. 66(8), 3391–3400 (2016).
[Crossref]

Soric, J.

J. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alú, “Dual-polarized reduction of dipole antenna blockage using mantle cloaks,” IEEE Trans. Antennas Propag. 63(11), 4827–4834 (2015).
[Crossref]

Tao, Z.

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

Tayarani, M.

Tcvetkova, S.

S. Tcvetkova, D. Kwon, A. Díaz-Rubio, and S. Tretyakov, “Near-perfect conversion of a propagating plane wave into a surface wave using metasurfaces,” Phys. Rev. B 11 (2018).

Tetienne, J.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Toscano, A.

J. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alú, “Dual-polarized reduction of dipole antenna blockage using mantle cloaks,” IEEE Trans. Antennas Propag. 63(11), 4827–4834 (2015).
[Crossref]

Tretyakov, S.

S. Tcvetkova, D. Kwon, A. Díaz-Rubio, and S. Tretyakov, “Near-perfect conversion of a propagating plane wave into a surface wave using metasurfaces,” Phys. Rev. B 11 (2018).

Visher, J.

B. Fong, J. Colburn, J. Ottusch, J. Visher, and D. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antennas Propag. 58(10), 3212–3221 (2010).
[Crossref]

Wan, X.

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

Y. Li, X. Wan, B. Cai, Q. Cheng, and T. Cui, “Frequency-controls of electromagnetic multi-beam scanning by metasurfaces,” Sci. Rep. 4(1), 6921 (2015).
[Crossref]

Wang, H.

H. Wang, D. Fang, B. Zhang, and W. Che, “Dielectric loaded substrate integrated waveguide (siw) H-plane horn antennas,” IEEE Trans. Antennas Propag. 58(3), 640–647 (2010).
[Crossref]

Waqas, A.

Wu, Q.

Y. Yuan, K. Zhang, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “Complementary transmissive ultra-thin meta-deflectors for broadband polarization-independent refractions in the microwave region,” Photonics Res. 7(1), 80 (2019).
[Crossref]

K. Zhang, Y. Yuan, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “High-efficiency metalenses with switchable functionalities in microwave region,” ACS Appl. Mater. Interfaces 11(31), 28423–28430 (2019).
[Crossref]

Xu, F.

Yang, G.

Yi, J.

Yin, J.

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

Yu, N.

N. Yu, P. Genevet, M. Kats, F. Aieta, J. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref]

Yuan, Y.

K. Zhang, Y. Yuan, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “High-efficiency metalenses with switchable functionalities in microwave region,” ACS Appl. Mater. Interfaces 11(31), 28423–28430 (2019).
[Crossref]

Y. Yuan, K. Zhang, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “Complementary transmissive ultra-thin meta-deflectors for broadband polarization-independent refractions in the microwave region,” Photonics Res. 7(1), 80 (2019).
[Crossref]

Zhang, B.

H. Wang, D. Fang, B. Zhang, and W. Che, “Dielectric loaded substrate integrated waveguide (siw) H-plane horn antennas,” IEEE Trans. Antennas Propag. 58(3), 640–647 (2010).
[Crossref]

Zhang, H.

Zhang, K.

Y. Yuan, K. Zhang, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “Complementary transmissive ultra-thin meta-deflectors for broadband polarization-independent refractions in the microwave region,” Photonics Res. 7(1), 80 (2019).
[Crossref]

K. Zhang, Y. Yuan, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “High-efficiency metalenses with switchable functionalities in microwave region,” ACS Appl. Mater. Interfaces 11(31), 28423–28430 (2019).
[Crossref]

Zhang, L.

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

Zhang, Q.

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
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Zucker, F. J.

R. E. Collin and F. J. Zucker, Antenna theory (Wiely, 1969).

ACS Appl. Mater. Interfaces (1)

K. Zhang, Y. Yuan, X. Ding, B. Ratni, S. Burokur, and Q. Wu, “High-efficiency metalenses with switchable functionalities in microwave region,” ACS Appl. Mater. Interfaces 11(31), 28423–28430 (2019).
[Crossref]

Adv. Funct. Mater. (2)

Y. Li, B. Cai, Q. Cheng, and T. Cui, “Isotropic holographic metasurfaces for dual-functional radiations without mutual interferences,” Adv. Funct. Mater. 26(1), 29–35 (2016).
[Crossref]

X. Wan, T. Chen, Q. Zhang, J. Yin, Z. Tao, L. Zhang, X. Chen, Y. Li, and T. Cui, “Manipulations of dual beams with dual polarizations by full-tensor metasurfaces,” Adv. Funct. Mater. 4(10), 1567–1572 (2016).
[Crossref]

Antennas Wirel. Propag. Lett. (3)

M. Movahhedi, M. Karimipour, and N. Komjani, “Multibeam bidirectional wideband/wide scanning angle holographic leaky wave antenna,” Antennas Wirel. Propag. Lett. 18(7), 1507–1511 (2019).
[Crossref]

Y. Liu, Y. Hao, K. Li, and S. Gong, “Wideband and polarization-independent radar cross section reduction using holographic metasurface,” Antennas Wirel. Propag. Lett. 15, 1028–1031 (2015).
[Crossref]

H. Oraizi, A. Amini, A. Abdolali, and A. Karimimehr, “Design of wideband leaky-wave antenna using sinusoidally modulated impedance surface based on the holography theory,” Antennas Wirel. Propag. Lett. 17(10), 1807–1811 (2018).
[Crossref]

IEEE Trans. Antennas Propag. (8)

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IET Microwaves, Antennas & Propag. (1)

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Figures (8)

Fig. 1.
Fig. 1. General schematic of the proposed holographic metasurface. In each frequency a perfect flat wave-front as a reference wave excites the metasurface from one sides and then one sets of the modulated cross-bars radiate the power in the form of spatial wave for forming the desired object wave with specific polarization.
Fig. 2.
Fig. 2. Concepts of leaky-type metasurface (a) Brillouin diagram and its specific regions,(b) Definition of rabbits ears phenomenon.
Fig. 3.
Fig. 3. Proposed JC-AMC pixel (a) Details of the pixel in 3D view,(b) Its dimensions (Dimensions are $p=4mm$, $d=1.44mm$, $W_{ind}=0.2mm$, $W_{cap}=0.2mm$. Also the substrate is Rogers 4003C with the 60mil thickness). (c) and (d) Show surface impedance distribution by sweeping length $L_1$ and $L_2$ of JC-AMC in lower and upper band, respectively. (e) Depicts the density of surface current distribution.
Fig. 4.
Fig. 4. (a) and (c) show the surface impedance distribution needed for broadside direction in lower and upper band respectively, Also (b) and (d) depict predicted far-field pattern for the lower and upper band respectively.
Fig. 5.
Fig. 5. (a) and (b) depict the full structure configuration, excitation direction and the 3D far-field pattern for lower and upper band, respectively. (c) and (d) show Cartesian normalized pattern in lower and upper bands respectively.
Fig. 6.
Fig. 6. (a) SIW power splitter in the feeding network configuration and its dimensions($L_1=16mm$, $L_2=6.89mm$, $W_1=W_2=W_3=W_4=W_5=W_6=W_7=9mm$, $W_8=6.38mm$, $W_9=4.93mm$, $W_{10}=5.26mm$, $W_{11}=36mm$, $W_{12}=18mm$ ) for the lower band. All dimensions are same for upper band except $W_8=3.62mm$, $W_9=2.60mm$, $W_{10}=2.69mm$. Also, scattering parameters results of the power splitter in (b) lower band,(c) upper band, respectively.
Fig. 7.
Fig. 7. (a) Proposed SIW horn structure in 3D perspective, (b) scattering parameters result. The inset picture shows the back-to-back configuration for the calculation of scattering parameters ($W_1=9mm$ and $W_2=17mm$). (c) and (d ) show the electric field distribution inside and in front of the horn arrays which is provided for exciting the metasurface.
Fig. 8.
Fig. 8. Psrototype located in anechoic chamber. Also, the insets show the zoom picture of components of the structure. (b) and (c) clarify the normalized measurement far-field pattern and compare it with the simulation result in lower and upper band, respectively, in the polar coordination.

Tables (1)

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Table 1. Performance comparison between the proposed metasurfce with same works

Equations (11)

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X s ¯ ¯ . k t ^ = j X 0 [ k t ^ + 2 I m { E a k t ^ . H t | z = 0 + } ]
X s = j X 0 ( 1 + M × R e { ψ r e f ψ o b j } )
K t = K t 0 + 2 π p d = K t 0 u p + Δ K + 2 π p d
E F ( r , θ , ϕ ) j k e j k r 2 π r [ F θ ( θ , ϕ ) θ ^ + F ϕ ( θ , ϕ ) ϕ ^ ]
F θ ( θ , ϕ ) = f x cos ϕ + f y sin ϕ
F ϕ ( θ , ϕ ) = cos θ ( f x sin ϕ + f y cos ϕ )
f x ( k x , k y ) = a p E a x ( x , y , z = 0 ) e j ( k x x + k y y ) d x d y
f y ( k x , k y ) = a p E a y ( x , y , z = 0 ) e j ( k x x + k y y ) d x d y
X s = j X 01 2 ( 1 + M 1 × R e { ψ r e f 1 ψ o b j 1 } ) + j X 02 2 ( 1 + M 2 × R e { ψ r e f 2 ψ o b j 2 } )
X s x = j X 0 x ( 1 + M x × R e { ψ r e f x ψ o b j x } )
X s y = j X 0 y ( 1 + M y × R e { ψ r e f y ψ o b j y } )

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