Abstract

Terahertz waves have attracted considerable research interest in recent years because of their potential applications in diverse fields. As an important device to control terahertz waves, beam splitters with greater flexibility and higher degrees of freedom are highly desirable. In order to obtain higher degrees of freedom in beam splitting, 2-bit or higher-bit coding elements are usually introduced into metamaterial beam splitters based on the coding theory. In this work, a new “offset” coding scheme using only the 1-bit coding elements of “0” and “1” is presented, and the period of coding for beam splitting can be a non-integer multiple of the length of a single unit rather than only its integer multiples. Therefore, more beam-splitting degrees of freedom can be obtained, and the design strategy is experimentally verified. We believe that the new coding scheme will also be of significance in radar cross section reduction and flexible wave control.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

P. C. Huo, S. Zhang, Y. Z. Liang, Y. Q. Lu, and T. Xu, “Hyperbolic metamaterials and metasurfaces: fundamentals and applications,” Adv. Opt. Mater. 7(14), 1970054 (2019).
[Crossref]

2018 (3)

Y. Kivshar, “All-dielectric meta-optics and non-linear nanophotonics,” Natl. Sci. Rev. 5(2), 144–158 (2018).
[Crossref]

R. Y. Wu, C. B. Shi, S. Liu, W. Wu, and T. J. Cui, “Addition theorem for digital coding metamaterials,” Adv. Opt. Mater. 6(5), 1701236 (2018).
[Crossref]

M. C. Feng, Y. F. Li, J. F. Wang, Q. Q. Zheng, S. Sui, C. Wang, H. Y. Chen, H. Ma, S. B. Qu, and J. M. Zhang, “Ultra-wideband and high-efficiency transparent coding metasurface,” Appl. Phys. A 124(9), 630 (2018).
[Crossref]

2017 (7)

M. G. Wei, Q. Xu, Q. Wang, X. Q. Zhang, Y. F. Li, J. Q. Gu, Z. Tian, X. X. Zhang, J. G. Han, and W. L. Zhang, “Broadband non-polarizing terahertz beam splitters with variable split ratio,” Appl. Phys. Lett. 111(7), 071101 (2017).
[Crossref]

M. R. Hashemi, S. Cakmakyapan, and M. Jarrahi, “Reconfigurable metamaterials for terahertz wave manipulation,” Rep. Prog. Phys. 80(9), 094501 (2017).
[Crossref]

Q. L. Yang, J. Q. Gu, Y. H. Xu, X. Q. Zhang, Y. F. Li, C. M. Ouyang, Z. Tian, J. G. Han, and W. L. Zhang, “Broadband and robust metalens with nonlinear phase profiles for efficient terahertz wave control,” Adv. Opt. Mater. 5(10), 1601084 (2017).
[Crossref]

J. Zhao, Q. Cheng, T. Q. Wang, W. Yuan, and T. J. Cui, “Fast design of broadband terahertz diffusion metasurfaces,” Opt. Express 25(2), 1050–1061 (2017).
[Crossref]

J. S. Li, Z. J. Zhao, and J. Q. Yao, “Flexible manipulation of terahertz wave reflection using polarization insensitive coding metasurfaces,” Opt. Express 25(24), 29983–29992 (2017).
[Crossref]

S. Liu and T. J. Cui, “Flexible controls of terahertz waves using coding and programmable metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–12 (2017).
[Crossref]

J. Park, J. Kang, S. J. Kim, X. G. Liu, and M. L. Brongersma, “Dynamic reflection phase and polarization control in metasurfaces,” Nano Lett. 17(1), 407–413 (2017).
[Crossref]

2016 (7)

V. Asadchy, M. Albooyeh, S. Tcvetkova, A. Diaz-Rubio, Y. Radi, and S. A. Tretyakov, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94(7), 075142 (2016).
[Crossref]

P. Su, Y. J. Zhao, S. L. Jia, W. W. Shi, and H. L. Wang, “An ultra-wideband and polarization-independent metasurface for RCS reduction,” Sci. Rep. 6(1), 20387 (2016).
[Crossref]

B. Wang, F. L. Dong, Q. T. Li, D. Yang, C. W. Sun, J. J. Chen, Z. W. Song, L. H. Xu, W. G. Chu, Y. F. Xiao, Q. H. Gong, and Y. Li, “Visible-frequency dielectric metasurfaces for multiwavelength achromatic and highly dispersive holograms,” Nano Lett. 16(8), 5235–5240 (2016).
[Crossref]

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. L. Du, X. Wan, W. X. Tang, C. M. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. G. Han, W. L. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light: Sci. Appl. 5(5), e16076 (2016).
[Crossref]

S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Q. Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution operations on coding metasurface to reach flexible and continuous controls of terahertz beams,” Adv. Sci. 3(10), 1600156 (2016).
[Crossref]

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

A. Baron, A. Aradian, V. Ponsinet, and P. Barois, “Self-assembled optical metamaterials,” Opt. Laser Technol. 82, 94–100 (2016).
[Crossref]

2015 (4)

P. Genevet and F. Capasso, “Holographic optical metasurfaces: a review of current progress,” Rep. Prog. Phys. 78(2), 024401 (2015).
[Crossref]

G. X. Zheng, H. Mühlenbernd, M. Kenney, G. X. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

2014 (5)

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

P. R. West, J. L. Stewart, A. V. Kildishev, V. M. Shalaev, V. Shkunov, F. Strohkendl, Y. Zakharenkov, R. K. Dodds, and R. Byren, “All-dielectric subwavelength metasurface focusing lens,” Opt. Express 22(21), 26212–26221 (2014).
[Crossref]

C. D. Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
[Crossref]

T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light: Sci. Appl. 3(10), e218 (2014).
[Crossref]

L. X. Liu, X. Q. Zhang, M. Kenney, X. Q. Su, N. N. Xu, C. M. Ouyang, Y. L. Shi, J. G. Han, W. L. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
[Crossref]

2013 (5)

B. O. Zhu, J. M. Zhao, and Y. J. Feng, “Active impedance metasurface with full 360° reflection phase tuning,” Sci. Rep. 3(1), 3059 (2013).
[Crossref]

A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21(22), 27438–27451 (2013).
[Crossref]

X. J. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013).
[Crossref]

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref]

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

2012 (3)

2011 (2)

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5(9), 523–530 (2011).
[Crossref]

N. F. 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]

2007 (2)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
[Crossref]

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, and T. Kürner, “Short-range ultra-broadband terahertz communications: concepts and perspectives,” IEEE Antennas Propag. Mag. 49(6), 24–39 (2007).
[Crossref]

2004 (1)

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microwave Theory Tech. 52(10), 2438–2447 (2004).
[Crossref]

2002 (1)

B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
[Crossref]

Aieta, F.

N. F. 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]

Alaee, R.

Albooyeh, M.

V. Asadchy, M. Albooyeh, S. Tcvetkova, A. Diaz-Rubio, Y. Radi, and S. A. Tretyakov, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94(7), 075142 (2016).
[Crossref]

Aradian, A.

A. Baron, A. Aradian, V. Ponsinet, and P. Barois, “Self-assembled optical metamaterials,” Opt. Laser Technol. 82, 94–100 (2016).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

Asadchy, V.

V. Asadchy, M. Albooyeh, S. Tcvetkova, A. Diaz-Rubio, Y. Radi, and S. A. Tretyakov, “Perfect control of reflection and refraction using spatially dispersive metasurfaces,” Phys. Rev. B 94(7), 075142 (2016).
[Crossref]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10(11), 937–943 (2015).
[Crossref]

Bao, D.

S. Liu, T. J. Cui, Q. Xu, D. Bao, L. L. Du, X. Wan, W. X. Tang, C. M. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. G. Han, W. L. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light: Sci. Appl. 5(5), e16076 (2016).
[Crossref]

Barois, P.

A. Baron, A. Aradian, V. Ponsinet, and P. Barois, “Self-assembled optical metamaterials,” Opt. Laser Technol. 82, 94–100 (2016).
[Crossref]

Baron, A.

A. Baron, A. Aradian, V. Ponsinet, and P. Barois, “Self-assembled optical metamaterials,” Opt. Laser Technol. 82, 94–100 (2016).
[Crossref]

Belov, P. A.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: from microwaves to visible,” Phys. Rep. 634, 1–72 (2016).
[Crossref]

Bozhevolnyi, S. I.

A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21(22), 27438–27451 (2013).
[Crossref]

A. Pors, M. G. Nielsen, R. L. Eriksen, and S. I. Bozhevolnyi, “Broadband focusing flat mirrors based on plasmonic gradient metasurfaces,” Nano Lett. 13(2), 829–834 (2013).
[Crossref]

Brongersma, M. L.

J. Park, J. Kang, S. J. Kim, X. G. Liu, and M. L. Brongersma, “Dynamic reflection phase and polarization control in metasurfaces,” Nano Lett. 17(1), 407–413 (2017).
[Crossref]

Byren, R.

Cai, B. G.

Cakmakyapan, S.

M. R. Hashemi, S. Cakmakyapan, and M. Jarrahi, “Reconfigurable metamaterials for terahertz wave manipulation,” Rep. Prog. Phys. 80(9), 094501 (2017).
[Crossref]

Capasso, F.

P. Genevet and F. Capasso, “Holographic optical metasurfaces: a review of current progress,” Rep. Prog. Phys. 78(2), 024401 (2015).
[Crossref]

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref]

N. F. 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]

Chen, H. B.

L. H. Gao, Q. Cheng, J. Yang, S. J. Ma, J. Zhao, S. Liu, H. B. Chen, Q. He, W. X. Jiang, H. F. Ma, Q. Y. Wen, L. J. Liang, B. B. Jin, W. W. Liu, L. Zhou, J. Q. Yao, P. H. Wu, and T. J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light: Sci. Appl. 4(9), e324 (2015).
[Crossref]

Chen, H. Y.

M. C. Feng, Y. F. Li, J. F. Wang, Q. Q. Zheng, S. Sui, C. Wang, H. Y. Chen, H. Ma, S. B. Qu, and J. M. Zhang, “Ultra-wideband and high-efficiency transparent coding metasurface,” Appl. Phys. A 124(9), 630 (2018).
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Figures (6)

Fig. 1.
Fig. 1. (a) Conventional coding “000111000111……/000111000111……” sequence, with “0” elements in blue and “1” elements in yellow. (b) Unconventional “offset” coding sequence. (c) Equivalent modeling of “offset” sequence. (d) Equivalent structure of “offset” sequence for (b). (e) Schematic diagram of θ and φ in the Cartesian coordinate system.
Fig. 2.
Fig. 2. (a) Schematic of rectangular-shaped silicon coding element. (b) Transmission phase difference corresponding to “0” and “1” elements for x-polarized incidence
Fig. 3.
Fig. 3. (a) Conventional coding sequence. (b) Simulation results of field intensity as a function of angle for the structure in Fig. 1(b) with peak values determined to be at θ = 47° and φ = 117°. (c) “Chessboard” coding sequence. (d) Novel “offset” coding sequence producing four split beams and calculation of equivalent structure. (e) 3D far-field scattering pattern of the structure in (d).
Fig. 4.
Fig. 4. (a) Anisotropic “offset” coding sequence. White elements: x-polarization→ “0” element and y-polarization→ “0” element; green elements: x-polarization→ “1” element and y-polarization→ “0” element; blue elements: x-polarization→ “0” element and y-polarization→ “1” element; red elements: x-polarization→ “1” element and y-polarization→ “1” element. (b) Simulation results for x-polarized incidence (at φ = 45°) with output peak at θ = 44° and y-polarized incidence (at φ = 135°) with output peak at θ = 43°.
Fig. 5.
Fig. 5. (a) Scanning electron microscopy image of sample. (b) Experiment results of x-polarized incidence (at φ = 45°) with peak at θ = 44°, and experiment results of y-polarized incidence (at φ = 135°) with peak at θ = 43°. The corresponding simulations are given in Fig. 4(b).
Fig. 6.
Fig. 6. (a) The “offset” coding sequence with six split beams. (b) 3D far-field scattering pattern simulation results of Fig. 6(a). (c) The “offset” coding sequence with eight split beams. (d) 3D far-field scattering pattern simulation results of Fig. 6(c).

Equations (3)

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n t sin θ t n i sin θ i = λ 0 2 π d ϕ d x ,
θ = sin 1 ( λ 0 1 H x 2 + 1 H y 2 ) ,
φ 1 , 2 = ± tan 1 D x D y , φ 3 , 4 = π ± tan 1 D x D y ,

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