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Metamaterials or metasurfaces have been widely studied to manipulate the propagation of light by controlling the wavefront. In previous work, more and more structures were designed to study the reflected or the transmitted light. However, as far as we know, it is rarely reported how to efficiency tailor the wavefront, especially for transmitted light. Helical metamaterial, which has a relatively strong coupling effect among the helical nanowires, may provide an alternative to the wavefront control. In this study, a kind of complementary helical metamaterial with a left-handedness and a right-handedness helixes coupled to each other is proposed. The complementary helical metamaterial has a strong circular conversion dichroism, and it is expected to be a good candidate for generating phase shift and controlling wavefront with high efficiency. Using the finite-difference time-domain method, we find that this kind of helix has a high circular polarization conversion in a broadband, which often implies a high efficiency of the transmitted light. Moreover, it is also found that the structure will introduce a controllable phase shift（) between the incident and the transmitted light whose polarizations are orthogonal to each other. By calculating the surface current density of the helix, the performance of high circular polarization conversion is explained. Meanwhile, we also find that the phase shift has a linear relationship with the initial angle of the helix（), which is =2. This relationship can be explained exactly by Jones calculus. According to the generalized Snell's law, the refracted beam can have an arbitrary direction by designing a suitable constant gradient of phase discontinuity. And then, by arranging 12 helixes in an array with a constant phase gradient along the X-axis, the phenomenon of anomalous refraction with a high efficiency（64%) is observed in the near infrared range（1.0-1.4 m). The angle of the anomalous refraction is in good agreement with the theoretical value. Compared with the metasurface, the helical metamaterial has a relatively complex structure. But with the development of the nanotechnology, there are several methods that can complete the propagations of nano helical structures, such as the direct laser writing, the glancing angle deposition, and the molecular self-assembly techniques. And by carefully designing the structure parameters of the helix, this kind of complementary helical metamaterial is expected to be an ideal candidate not only for traditional optics but also for biological detection and medical science.
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[16] Gansel J K, Thiel M, Rill M S, Decker M, Bade K, Saile V, Freymann G, Linden S, Wegener M 2009 Science 325 1513
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[20] Smith D R, Mock J J, Starr A F, Schurig D 2005 Phys. Rev. E 71 036609
[21] Kabashin A V, Evans P, Pastkovsky S, Hendren W, Wurtz G A, Atkinson R, Pollard R, Podolskiy V A, Zayats A V 2009 Nat. Mater. 8 867
[22] Luo X G, Qiu T, Lu W B, Ni Z H 2013 Mater. Sci. Eng. R-Rep. 74 351
[23] Rakic A D, Djurisic A B, Elazar J M, Majewski M L 1998 Appl. Opt. 37 5271
[24] Yang Z Y, Zhao M, Lu P X, Lu Y F 2010 Opt. Lett. 35 2588
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[1] Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333
[2] Huang L, Chen X, Muehlenbernd H, Li G, Bai B, Tan Q, Jin G, Zentgraf T, Zhang S 2012 Nano Lett. 12 5750
[3] Zhao Y, Alu A 2013 Nano Lett. 13 1086
[4] Yang Y, Wang W, Moitra P, Kravchenko I I, Briggs D P, Valentine J 2014 Nano Lett. 14 1394
[5] Li Y, Liang B, Gu Z M, Zou X Y, Cheng J C 2013 Sci. Rep. 3 2546
[6] Yu N, Genevet P, Aieta F, Kats M A, Blanchard R, Aoust G, Tetienne J P, Gaburro Z, Capasso F 2013 IEEE J. Sel. Top. Quantum Electron. 19 4700423
[7] Yu N, Capasso F 2014 Nat. Mater. 13 139
[8] Blanchard R, Aoust G, Genevet P, Yu N, Kats M A, Gaburro Z, Capasso F 2012 Phys. Rev. B 85 155457
[9] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[10] Shalaev V M, Cai W S, Chettiar U K, Yuan H K, Sarychev A K, Drachev V P, Kildishev A V 2004 Science 305 788
[11] Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov D A, Bartal G, Zhang X 2008 Nature 455 376
[12] Meinzer N, Barnes W L, Hooper I R 2014 Nat. Photon. 8 889
[13] Zheng G X, Muhlenbernd H, Kenney M, Li G X, Zentgraf T, Zhang S 2015 Nat. Nanotechnol. 10 308
[14] Cheng H, Liu Z C, Chen S Q, Tian J G 2015 Adv. Mater. 27 5410
[15] Kaschke J, Blume L, Wu L, Thiel M, Bade K, Yang Z, Wegener M 2015 Adv. Opt. Mater. 3 1411
[16] Gansel J K, Thiel M, Rill M S, Decker M, Bade K, Saile V, Freymann G, Linden S, Wegener M 2009 Science 325 1513
[17] Kaschke J, Wegener M 2015 Opt. Lett. 40 3986
[18] Robbie K, Beydaghyan G, Brown T, Dean C, Adams J, Buzea C 2004 Rev. Sci. Instrum. 75 1089
[19] Kuzyk A, Schreiber R, Fan Z, Pardatscher G, Roller E M, Hoegele A, Simmel F C, Govorov A O, Liedl T 2012 Nature 483 311
[20] Smith D R, Mock J J, Starr A F, Schurig D 2005 Phys. Rev. E 71 036609
[21] Kabashin A V, Evans P, Pastkovsky S, Hendren W, Wurtz G A, Atkinson R, Pollard R, Podolskiy V A, Zayats A V 2009 Nat. Mater. 8 867
[22] Luo X G, Qiu T, Lu W B, Ni Z H 2013 Mater. Sci. Eng. R-Rep. 74 351
[23] Rakic A D, Djurisic A B, Elazar J M, Majewski M L 1998 Appl. Opt. 37 5271
[24] Yang Z Y, Zhao M, Lu P X, Lu Y F 2010 Opt. Lett. 35 2588
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