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

1. Introduction

Because of their special spectral position in the electromagnetic spectrum, terahertz (THz) waves have a number of unique properties [1] and find important applications in spectroscopy, imaging, biomedicine, astronomy, security control, communications and other fields [24]. Being a vital device to control THz waves, beam splitters with greater flexibility and higher degrees of freedom are in great demand. However, due to the lack of suitable natural materials with the required electromagnetic response at THz frequencies, previous studies routinely use electromagnetic metamaterials to manipulate THz waves [517]. Metamaterials, with macroscopic artificial subwavelength units, enable electromagnetic responses that cannot be found in natural materials and are widely used in many fields, including wave phase modulation [1820], polarization control [2123], perfect absorption [2426], wave focusing and holography [2732].

To increase the ability to perform real-time control of electromagnetic waves and improve the construction of multifunctional devices, the method to construct “metamaterial bytes” by using “digital metamaterial bits” was proposed by Giovampaol and Engheta in 2014 [33]. In the same year, Cui et al. put forward the concept of coding metamaterials [34], where the basic unit cells are associated with digital states and a link between the physical material world is established with the digital world. Furthermore, a single metamaterial can achieve different functions through digital or programmable control, thus realizing digital and real-time control of electromagnetic waves [34]. In coding metamaterials, the function is typically achieved by designing two units with “0” and “π” phase responses to simulate the “0” and “1” digital states, and to employ digital control to realize real-time control [35,36].

In previous reports, in order to obtain higher angular degrees of freedom in beam splitting, two methods are typically adopted: The first method is to combine 1-bit coding elements according to the addition theorem and use coding elements of 2-bit or higher-bit, which can produce anomalous single-beam scattering more flexibly and enable continuous control of the beam to arbitrary directions [37,38]. In the second approach, a so-called “super unit cell” is usually adopted, which is generated by a subarray of the same basic unit cells with a size N*N [36]. The period length designed in this conventional way can only be an integer multiple of the length of a single unit cell. In addition, the number of split beams is mostly two and four, which is limited and the degrees of freedom are few. In this paper, a new design method of “offset” coding is proposed, which makes it possible to obtain more beam splitting degrees of freedom by using only the 1-bit coding elements “0” and “1”. For instance, the number of split beams can be increased to six and eight. In previous studies, the structures used are mainly of two types, “stripes” and “chessboard”. By contrast, a larger number of structures are enabled by the new coding scheme. Even with the same number of split beams, new angles different from previous designs can be obtained. Therefore, the “offset” coding arrangement provides a new strategy for designing more flexible beam splitters.

2. Theoretical analysis and element design

The beam splitting angle can be obtained according to the generalized Snell’s law [39]:

$${n_t}\sin{\theta _t} - {n_i}\sin{\theta _i} = \frac{{{\lambda _0}}}{{2\pi }}\frac{{d\phi }}{{dx}},$$
where ni (nt) is the refractive index of the incident (refraction) medium, θi (θt) represents the incident (refraction) angle, λ0 is the vacuum wavelength, and ${{\textrm{d}\phi}/{\textrm{d}x}}$ is the phase gradient along the interface between the two media.

In previous 1-bit coding scenarios [34], a “010101… /010101…” or “010101……/ 101010……” sequence is usually employed for beam splitting. The part before the stroke is the coding sequence along the x or y direction, and that after the stroke is the coding sequence of the next row or column parallel to the chosen direction. The beam splitting angle of the first coding sequence can be obtained by the formula $\theta = {\sin ^{ - 1}}({{\lambda}_0}/ {\Gamma})$ [36] derived from (1), where Γ represents the physical length of one period of the gradient phase distribution. The directions of beam splitting are the same as the directions of phase change. For the second coding sequence, the direction (θ, φ) of the anomalously reflected waves can be expressed as [40]:

$$\theta = {\sin ^{ - 1}}\left( {{\lambda_0}\sqrt {\frac{1}{{H_x^2}} + \frac{1}{{H_y^2}}} } \right),$$
$${\varphi _{1,2}} ={\pm} {\tan ^{ - 1}}\frac{{{D_x}}}{{{D_y}}},{\varphi _{3,4}} = \pi \pm {\tan ^{ - 1}}\frac{{{D_x}}}{{{D_y}}}, $$
where Hx and Hy represent the physical lengths of one period of the coding sequence along the x and y directions, respectively; Dx and Dy are the side lengths of one single coding element and in most cases are equal. φ1, φ2, φ3, φ4 are the values of φ for each split beam. Therefore, under a specific operating wavelength and with the same coding bits, how to change the period Γ becomes the key factor to increase the degrees of freedom in beam splitting.

Different from previously reported arrangements of the periodic phase gradient change in one direction of the two-dimensional plane and repeated or fixed arrangements of the phase gradient change in the other vertical direction, the “offset” arrangement proposed here is a new arrangement in which the phase gradient changes periodically in one direction and the coding sequence is translated in the next row or column in the other direction. This will be discussed below in detail.

Figure 1(a) shows, as an example, a conventional coding sequence “000111000111……/ 000111000111……” in the x/y directions, while Fig. 1(b) is the “offset” coding sequence which is obtained by translating each previous row of the conventional coding sequence to the left by two units. By this arrangement, the period Γ is no longer restricted to being only an integer multiple of a single coding element length, thus being able to increase the degrees of freedom of the beam splitting angle. However, if the “offset” coding sequence is applied, the phase gradient direction is no longer along the x/y directions, a “saw tooth” shape is observed at the junction between the areas with different phases. Therefore, the period Γ does not completely share the same position and length (as in Fig. 1(a)) in the direction perpendicular to the phase gradients. Rather, there is offset to the right or left side with a change of the “saw tooth” shape. It can be seen that there is no formula directly corresponding to this “offset” coding scheme. Fortunately, the change of the period Γ is periodic and can be predicted. Therefore, in order to facilitate calculation, it is necessary to convert this unconventional arrangement into an equivalent conventional coding scheme. As illustrated in Fig. 1(c), the red dashed lines are used to divide different phase gradient areas as equally as possible, which makes the “offset” arrangement equivalent to the conventional arrangement. The equivalent structure is obtained as in Fig. 1(d). Thus, the angle between the direction of the equivalent structure and the y axis is angle α1, where α1 ≈ 26.6° (arctan0.5 from Fig. 1(c)). The equivalent period Γ* can then be obtained according to the Pythagorean theorem through α1 and the hypotenuse (3p in this case). Then, the results of beam splitting can be easily calculated by using the formulas described above. Figure 1(e) shows a schematic diagram for θ and φ in the Cartesian coordinate system to determine the direction of the deflected beam to be discussed later.

 figure: 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.

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In order to realize the “offset” coding sequence, the chosen medium is an all-dielectric construction of rectangular-shaped silicon pillars on a silicon substrate (nSi=3.45) [22]. The schematic of a unit cell is shown in Fig. 2(a). The all-dielectric structure is easy to process and design, and it can effectively reduce the ohmic loss associated with metallic metamaterials. The results reported below are all for transmission coding devices based on this structure. Based on the commercially available software CST Microwave Studio, numerical simulations are carried out by varying the side lengths of the pillars lx and ly, while the height of the pillar h = 200 µm and the periods px= py = p = 150 µm are fixed. Here, the target frequency in the whole work is 1.0 THz. When the incident electromagnetic wave is x-polarized, the difference in the transmission phase is obtained in Fig. 2(b), from which the following parameters are determined: for the selected “0” element, lx = 75 µm and ly = 75 µm, and for the “1” element lx= 50 µm and ly= 93.5 µm. When the incident electromagnetic wave is y-polarized, one only needs to switch the lengths of lx and ly for the “1” element.

 figure: 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

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3. Results and discussion

3.1 Increase of angular degrees of freedom for beam splitting

When we design beam splitters based on the coding metamaterial theory, how to achieve higher angular degrees of freedom in beam splitting is a crucial point. In Fig. 3(a), a conventional beam splitting coding scheme is illustrated. Given the formula $\theta = {\sin ^{ - 1}}({{\lambda_0}/\Gamma } )$, when the wavelength λ0 is kept constant, there is a one-to-one correspondence between the beam splitting angle θ and the period length Γ. In previous research, e.g. [38], normally n = m is presumed, and the values of Γ are restricted to 2p, 4p, 6p…, where p is the length of a single unit. Thus, the period Γ can only be an even multiple of the length of a single unit. When nm, similar conclusions can be drawn. For example, if the sequence is “001001001……/001001001……”, then the values of Γ are 3p, 5p, 7p…, odd multiples of the unit length. All the analysis shows that for the conventional beam splitting method, the period length Γ can only be an integer multiple of the length of a single unit p. However, if an “offset” sequence is made, as shown in Fig. 1(b), ${{\Gamma }^{\ast }} = \frac{{6\sqrt 5 }}{5}p$, which is $3p\cos {\alpha _1}$ as determined from Fig. 1(d), and the theoretical value of θ is 48.2°, while the theoretical value of φ is 116.6°. CST Microwave Studio is used to verify the theory. The incident wave is selected as x-polarization and the propagation direction is + z. This setting is used in all the following simulations. The result of far-field beam splitting is shown in Fig. 3(b), where the derivation of the calculated angles of θ and φ from the theoretical ones is about 1°, fully corroborating our analysis. Other similar coding sequences can also be manipulated with a corresponding “offset” scheme.

 figure: 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).

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When the number of the split beams needed is four, the traditional way is to use the “chessboard” structure (Fig. 3(c)) for the two-dimensional coding. Accordingly, the value range of Γ is limited. A novel construction based on the “offset” arrangement outlined above is illustrated in the upper panel of Fig. 3(d). As can be seen, the structure consists of four coding areas with mirror symmetry with respect to the x and y axes. The fourth quadrant is used to illustrate how to calculate the equivalent period Γ* in the lower panel of Fig. 3(d). Here, the angle between the direction of the equivalent structure and the y axis is angle α2, where α2= 45°. The equivalent period can be obtained as ${{\Gamma}^{\ast}} = 3p \cos {\alpha_2} = \frac{{{3}\sqrt{2}p}}2$ and the theoretical value of θ is 70.5°. The other three quadrants share the same Γ* and θ. The simulation results of the 3D far-field scattering patterns of the structure are shown in Fig. 3(e), where θ ≈ 69°. The central lobe is due to the directly transmitted wave.

Because of polarization sensitivity of the chosen all-dielectric construction of rectangular-shaped silicon pillars on a silicon substrate, different sequence arrangements of the sequence “001100110011……/001100110011……” under x and y polarizations with different offset directions can be combined as an anisotropic two-dimensional coding structure, as schematically illustrated in Fig. 4(a). The anisotropic structure can be used to verify the feasibility of the new “offset” arrangement. Basic coding elements with polarization sensitivity are obtained by changing the lengths of lx and ly. For a “0/0” element (where the first letter stands for x polarization and the latter for y polarization), lx = 75 µm and ly = 75 µm. For a “1/0” element, lx = 50 µm and ly = 93.5 µm. For a “0/1” element, lx = 93.5 µm and ly = 50 µm. For a “1/1” element, lx = 57.5 µm and ly = 57.5 µm. The simulated far-field beam splitting results are shown in Fig. 4(b). Given the fact that the experiment system used to verify our design cannot measure all the variables at the same time, for comparison purposes the simulation here is to keep φ fixed and obtain the relative intensity as a function of θ.

 figure: 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°.

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Metamaterial samples for beam splitting based on the new coding scheme are fabricated by optical lithography followed by deep reactive ion etching. The scanning electron microscopy image of one structure corresponding to Fig. 4(a) is shown in Fig. 5(a). A fiber laser-based THz time-domain spectroscopy system [41] is utilized to characterize the samples. The splitting angles θ of the sample are measured for different parameters φ of x- or y-polarized THz wave. The THz signal is measured in the time domain and converted into the frequency domain by fast Fourier transform. Figure 5(b) shows the measured results for x- and y-polarized incidence. The measured angles are in good agreement with calculated values based on the measured sample parameters. The difference between the measured intensity distribution and the simulation can be attributed to the fabrication error in the sample parameters.

 figure: 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).

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3.2 Increase of the number of beam splitting

Increase of the angular degrees of freedom in beam splitting is not the only advantage that the “offset” coding scheme can offer. One can envisage the design of beam splitting devices with new functions by rearranging and combining the “offset” sequence and the conventional sequence or one “offset” sequence with another “offset” sequence.

For the design with six split beams (Fig. 6(a)), we consider using structures with different “offset” directions in area 1 or 2 so that two split beams can be obtained in different diagonal directions for each structure individually. Then, by combining areas 1 and 2 alternatively along the direction of the y axis, the structure can be seen as a conventional coding sequence in the x direction and thus two addition split beams are obtained in this direction. With the four split beams in the diagonal directions, there are six split beams in total. Similarly, for the design with eight split beams (Fig. 6(c)), we consider obtaining four split beams in the axis directions by using areas 1 and 2 and obtaining another four split beams in the diagonal directions by using areas 3 and 4. In total, eight split beams are obtained. The simulation results of 3D far-field scattering patterns of the two structures are given in Figs. 6(b) and 6(d), respectively. The angles of each beam splitting structure can be obtained by the equivalent method described above. In Fig. 6(a), the actual size of the structure used in the simulation is 32*32, while it is 31*31 in Fig. 6(c).

 figure: 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).

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4. Conclusion

A novel “offset” coding arrangement for metamaterial devices is proposed and demonstrated. The period length in the new coding scheme is no longer restricted to be an integer multiple of the unit length, enabling the design of beam splitters with more flexibility and higher degrees of freedom. Furthermore, the new designed “offset” coding scheme provides strategies for devices from which a larger number of beam splitting can be obtained and shows significant advantages in reducing RCS and manipulating the THz waves.

Funding

National Key Research and Development Program of China (2017YFA0701004); Tianjin Municipal Fund for Distinguished Young Scholars (18JCJQJC45600); National Natural Science Foundation of China (61420106006, 61422509, 61427814, 61505146, 61735012, 61775159); King Abdullah University of Science and Technology (CRF-2016-2950-CRG5, URF/1/2950).

Acknowledgments

We thank Dr. Quanlong Yang for illuminating discussions.

Disclosures

The authors declare no conflicts of interest.

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References

  • View by:

  1. B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002).
    [Crossref]
  2. M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1(2), 97–105 (2007).
    [Crossref]
  3. 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]
  4. P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microwave Theory Tech. 52(10), 2438–2447 (2004).
    [Crossref]
  5. 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]
  6. 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]
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    [Crossref]
  8. 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).
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  10. Y. Kivshar, “All-dielectric meta-optics and non-linear nanophotonics,” Natl. Sci. Rev. 5(2), 144–158 (2018).
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  11. M. R. Hashemi, S. Cakmakyapan, and M. Jarrahi, “Reconfigurable metamaterials for terahertz wave manipulation,” Rep. Prog. Phys. 80(9), 094501 (2017).
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    [Crossref]
  14. A. Baron, A. Aradian, V. Ponsinet, and P. Barois, “Self-assembled optical metamaterials,” Opt. Laser Technol. 82, 94–100 (2016).
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  15. 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).
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  16. N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11(11), 917–924 (2012).
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  17. 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).
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  18. 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).
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  19. A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21(22), 27438–27451 (2013).
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  20. 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).
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  21. C. Pfeiffer and A. Grbic, “Cascaded metasurfaces for complete phase and polarization control,” Appl. Phys. Lett. 102(23), 231116 (2013).
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    [Crossref]
  23. 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).
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  26. 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).
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  27. X. Li, S. Y. Xiao, B. G. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett. 37(23), 4940–4942 (2012).
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  29. 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).
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  30. X. J. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013).
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  31. 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).
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  32. 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).
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  33. C. D. Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014).
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  34. 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).
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  35. 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]
  36. 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]
  37. 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).
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  38. 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).
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  39. 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).
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  40. 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]
  41. 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).
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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).
[Crossref]

Chen, J. J.

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]

Cheng, Q.

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]

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. 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]

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]

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]

Chu, W. G.

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]

Cui, T. J.

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]

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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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