Abstract

We propose an all-dielectric metamaterial composed of bi-layered silicon structures orthogonally arranged on the sandwiched silica substrate, which exhibits giant dual-band asymmetric transmission of linearly polarized wave in the near-infrared regime, with one band working for the x-polarization and the other one for y-polarization. The dual-band AT phenomenon is explained by the distributions of electric field. In addition, the affection of the geometric parameters and incident angles to the AT parameters has been analyzed. Such an AT metamaterial has potential applications in polarization converters, switches and integrated photonic circuits.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The asymmetric transmission (AT) effect, which means different transmission between the forward and backward polarized light under normal illumination, has wide applications in polarization transformers, rotators, isolators, diode-like devices and polarizers. The traditional method to achieve asymmetric transmission is utilizing non-reciprocity obtained via nonlinear media or magneto-optical media [13]. Due to the drawbacks such as single function, low conversion efficiency, difficult for miniaturization, asymmetric transmission metamaterials are proposed to overcome the shortcomings [49]. Broken the mirror symmetry either in the perpendicular or along the propagation direction, the metamaterials can manipulate the polarization of electromagnetic waves to achieve the asymmetric transmission.

Asymmetric transmission of circularly polarized wave can be obtained because of the intrinsic or extrinsic chirality [10,11]. Such AT metamaterials usually consist of single-layer meta-atoms [1217], in which in-plane mirror symmetries are broken. Introducing symmetry broken along the propagation direction, AT metamaterials of linear polarization can be attained. Thus, linear AT metamaterials are mostly multilayered structures, for instance, multilayered anisotropic chiral metamaterials [1825], twisted gratings [26,27], and nonsymmetrical grating [2833]. Furthermore, metamaterials consisting of three-dimensional meta-atoms behave AT for both linear and circular polarization simultaneously [4,5]. However, most asymmetric transmission metamaterials are composed of metal structures, whose ohmic loss greatly limits the AT efficiency. On contrary, anisotropic dielectric nanostructures exhibiting the ability to increase the refractive index contrast of the orthogonal polarizations offers an effective way to construct AT metamaterials. Therefore, increasing attention has been paid to develop all-dielectric AT metamaterials [34]. Till now, AT metamaterials of circularly polarized wave [3537] and linearly polarized wave [3840] have been proposed, but there are still some problems to be improved, such as multi-function and high efficiency.

In this article, we design an all-dielectric metamaterial to realize giant dual-band asymmetric transmission of linearly polarized wave in the near-infrared region, one band working for the x-polarization and the other one for y-polarization, respectively. The physical mechanism of this phenomenon is explained through the distributions of electric field. Besides, we also analyze the influence of the geometric parameters on the AT phenomenon. Moreover, the AT parameters of this structure are sensitive to the incident angle, which can be applied to develop sensors.

2. Structure design and theoretical analysis

Figure 1 illustrates the schematic of the all-dielectric AT metamaterial for linearly polarized wave, including two silicon structures on both sides of the sandwiched silica substrate. In order to minimize the AT for the circularly polarized light, the bottom silicon structure is achieved by rotating the mirror structure of the top one 90 degrees around the z-axis. Hence, the top silicon structure is a half-swastika pattern and the bottom one is a half-gammadion pattern, with the same parameters a=250 nm, b=400 nm, c=100 nm and h1=1000 nm. The thickness of the silica substrate is h2=200 nm, and the period is 500 nm in both the x- and y-directions. In simulation, the boundary conditions in both the x- and y-directions are periodic, and that in the z-direction is perfectly matched layer. The refractive indexes of silicon and silica are set as 3.7 [41] and 1.5 [37] in the near-infrared band, respectively.

 figure: Fig. 1.

Fig. 1. Schematic of the designed structure: (a) perspective view, (b) top view, (c) bottom view and (d) side view.

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To theoretically understand the asymmetric transmission for linearly polarized wave, Jones matrix T [5,42] can be utilized to describe the transmission of electromagnetic waves. Considering the incident field propagating along the -z direction, the relationship between the transmitted and the incident waves can be expressed by

$$\left( {\begin{array}{{c}} {{T_x}}\\ {{T_y}} \end{array}} \right) = \left( {\begin{array}{{cc}} {T_{xx}^f}&{T_{xy}^f}\\ {T_{yx}^f}&{T_{yy}^f} \end{array}} \right)\left( {\begin{array}{{c}} {{I_x}}\\ {{I_y}} \end{array}} \right) = {T^f}\left( {\begin{array}{{c}} {{I_x}}\\ {{I_y}} \end{array}} \right).$$

Here, the subscripts of the matrix elements correspond to the direction of the linear polarization, and the superscript of Tf denotes the forward propagation along -z direction. Meanwhile, the backward transmission matrix Tb along the + z direction can be obtained by applying the four-port systems reciprocity theorem [5] since the medium is composed of reciprocal materials, which is

$${T^b} = \left( {\begin{array}{{cc}} {T_{xx}^b}&{ - T_{yx}^b}\\ { - T_{xy}^b}&{T_{yy}^b} \end{array}} \right).$$

In order to clearly value the asymmetric transmission, the AT parameter Δ is defined as the followings,

$$\begin{array}{l} {\Delta ^x} = {|{T_{xx}^f} |^2} + {|{T_{yx}^f} |^2} - {|{T_{xx}^b} |^2} - {|{T_{xy}^f} |^2} = {|{T_{yx}^f} |^2} - {|{T_{xy}^f} |^2},\\ {\Delta ^y} = {|{T_{yy}^f} |^2} + {|{T_{xy}^f} |^2} - {|{T_{yy}^b} |^2} - {|{T_{yx}^f} |^2} = {|{T_{xy}^f} |^2} - {|{T_{yx}^f} |^2}. \end{array}$$

According to Eq. (3), the AT parameter of x-polarized light Δx is opposite to that of y-polarized light Δy. Therefore, the discussion of the x- and y-polarized waves can be simplified to the discussion of x-polarization only.

3. Results and discussion

The transmission coefficients of the all-dielectric metamaterial under forward and backward illuminations are shown in Figs. 2(a) and 2(b), respectively. The cross-polarization transmission coefficient $\textrm{|}T_{yx}^f\textrm{|}$ reaches the maximum of 0.99 at λ1=957 nm, where the incident x-polarized wave is almost completely converted to y-polarized wave. Meanwhile, another cross-polarization peak of $\textrm{|}T_{xy}^f\textrm{|}$ reaches the maximum of 0.93 at λ2=949 nm, indicating polarization conversion from y- to x-polarization. The co-polarized transmission coefficient |Txx| is in good agreement with the |Tyy| for both the forward and backward propagation, ensuring no AT effect of the circularly polarized wave.

 figure: Fig. 2.

Fig. 2. The transmission coefficients of linearly polarized waves for (a) the forward (-z) and (b) the backward (+z) propagations. (c) The cross-polarized transmission coefficients and (d) the AT parameters.

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As shown in Fig. 2(c), $|T_{yx}^f|= |T_{xy}^b|$ can be observed, implying that the structure follows the four-port systems reciprocity theorem, which is consistent with the theoretical analysis above. Most importantly, two independent pass bands appear, which exhibit remarkable optical rotation corresponding to the y- to x-polarization and x- to y-polarization rotations, respectively. Consequently, different polarization conversions can be achieved at different bands. Figure 2(d) shows the AT parameters according to Eq. (3), in which the Δx and Δy are opposite to each other. The AT parameter Δx possesses a dip of −0.78 and a peak of 0.94 at the wavelengths of 949 nm and 957 nm, respectively. Apparently, the all-dielectric metamaterial behaves the dual-band unidirectional transmission of linear polarization, one band working for the x-polarization and the other one for y-polarization.

To explore the physical mechanism of the dual-band AT phenomenon, we calculate the distributions of the electric field under forward illumination, including the vector and amplitude. For the x-polarized incidence at λ1, the results are shown in Figs. 3(a) and (b), in which both the top and bottom silicon structures are greatly excited, indicating the strong coupling between the structures and the incident wave. The structures provide a channel to convert the field direction because of the high index of silicon. As a result, the total equivalent electric field induced by those in the top and bottom silicon structures is schematically shown in Fig. 3(c), which is strong enough to convert the incident light from x- to y-polarization, leading to the large $|T_{yx}^f|$ and small $|T_{xx}^f|$. Figures 3(d) –3(f) display the corresponding results under y-polarization. Although the total equivalent electric field in Fig. 3(f) can lead to the y-to-x polarization conversion, the strength is too weak due to the weak coupling between the silicon structures and the incident light, which results in the block of the y-polarized incident wave, related to the small $|T_{xy}^f|$ and $|T_{yy}^f|$. Consequently, AT occurs at λ1 with the large Δx. Similar mechanism can be found for the forward propagating light at λ2, as shown in Fig. 4. The silicon structures hardly couple with the x-polarized incident light but strongly couple with the y-polarized light, resulting in the large Δy.

 figure: Fig. 3.

Fig. 3. In the forward propagation at λ1 = 957 nm, the distributions of electric field vector (white arrow) and intensity (color map) in the (a) top silicon and (b) bottom silicon in the x-y plane under x-polarization, and (c) shows the equivalent electric field distributions with the black arrow indicating the total field. (d) - (f) show the corresponding results under y-polarization. The scales of these maps are the same.

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 figure: Fig. 4.

Fig. 4. In the forward propagation at λ2 = 949 nm, the distributions of electric field vector (white arrow) and intensity (color map) in the (a) top silicon and (b) bottom silicon in the x-y plane under x-polarization, and (c) shows the equivalent electric field distributions with the black arrow indicating the total field. (d) - (f) show the corresponding results under y-polarization. The scales of these maps are the same.

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Next, we discuss the important geometric parameters having great impact on the dual-band AT phenomenon. As the AT effect is sensitive to the geometric symmetry of the metamaterial, a is a significant parameter to affect the Δx (and Δy), as shown in Fig. 5(a). The structure possesses mirror symmetry along both x- and y-axes when a=100nm, leading to symmetric transmission. With the increase of a, the mirror symmetry is broken and the AT effect gradually appears. The dual-band AT effect reaches the optimization under the condition of a=250nm. Besides, we also calculate the AT parameter related to the thickness of the silicon structures and silica, as displayed in Figs. 5(b) and 5(c), respectively. The AT parameter varies greatly with the thickness of silicon, and the optimized two-band AT effect is achieved when h1 is 1000 nm. On the other hand, the dual-band AT phenomenon is absent when the silica is too thin, where h2=100 nm. The amplitude of the AT parameter increases and then decreases as the thickness of the silica increasing from 150 nm to 300 nm, with the red-shift of the working wavelength. As a result, the dual-band AT effect reaches its best when h2=200 nm.

 figure: Fig. 5.

Fig. 5. The AT parameter Δx varies with the geometric parameters (a) a, (b) h1 and (c) h2.

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Then, we check the sensitivity of the all-dielectric metamaterial to the incident angle θ, and the variation of the AT parameter Δx related to the incident angle and wavelength are given in Figs. 6(a) and 6(b). Increasing the incident angle, the amplitudes of the Δx at both λ1 and λ2 decrease and gradually vanish to zero while the angle exceeding 25°, with the working wavelength maintaining. As shown in Figs. 6(c) and 6(d), the amplitudes of the AT parameters are sensitive to the incident angle, with the variation close to linear. Defining the figure of merit (FOM) as FOM = ΔΔxθ to quantify the sensitivity, it reaches 0.032 at λ1 and −0.025 at λ2. Consequently, this metamaterial can be applied to develop sensors and detectors.

 figure: Fig. 6.

Fig. 6. (a) 3D colormap and (b) the projection of the Δx varying with the incident angle. The variation of Δx with the fitting line at (c) λ1 and (d) λ2.

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Finally, we compare the function of our design with the other work based on all-dielectric metamaterials in the near-infrared band, as shown in Table 1. Different from the previous work, our design can simultaneously achieve multi-band, multi-function and high efficiency for linear-polarization.

Tables Icon

Table 1. The comparison between references and our work.

4. Conclusion

In summary, we propose an all-dielectric AT metamaterial constructed by the orthogonally arranged silicon structures. The metamaterial exhibits giant dual-band AT effect of linearly polarized wave, one band working for x-polarization and the other one for y-polarization. Analyzing the distributions of the electric field, the physical mechanism of the dual-band AT effect has been explained. Moreover, the affection of the geometric parameters and incident angles to the AT parameters has been discussed. Such an all-dielectric AT metamaterial with dual-band and large AT parameters may have potential applications in the polarization converters, switches and integrated photonic circuits.

Funding

National Natural Science Foundation of China (11804178); Natural Science Foundation of Shandong Province (ZR2018BA027); National Laboratory of Solid State Microstructures, Nanjing University (M34009).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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4. C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010). [CrossRef]  

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7. J. Liu, Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “High-efficiency mutual dual-Band asymmetric transmission of circularly polarized waves with few-layer anisotropic metasurfaces,” Adv. Opt. Mater. 4(12), 2028–2034 (2016). [CrossRef]  

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10. L. Wu, Z. Yang, Y. Cheng, Z. Lu, P. Zhang, M. Zhao, R. Gong, X. Yuan, Y. Zheng, and J. Duan, “Electromagnetic manifestation of chirality in layer-by-layer chiral metamaterials,” Opt. Express 21(5), 5239–5246 (2013). [CrossRef]  

11. H. Jiang, W. Zhao, and Y. Jiang, “High-efficiency tunable circular asymmetric transmission using dielectric metasurface integrated with graphene sheet,” Opt. Express 25(17), 19732–19739 (2017). [CrossRef]  

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13. R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, and N. I. Zheludev, “Terahertz metamaterial with asymmetric transmission,” Phys. Rev. B 80(15), 153104 (2009). [CrossRef]  

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References

  • View by:

  1. L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
    [Crossref]
  2. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
    [Crossref]
  3. M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
    [Crossref]
  4. C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
    [Crossref]
  5. C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced Jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82(5), 053811 (2010).
    [Crossref]
  6. E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93(19), 191911 (2008).
    [Crossref]
  7. J. Liu, Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “High-efficiency mutual dual-Band asymmetric transmission of circularly polarized waves with few-layer anisotropic metasurfaces,” Adv. Opt. Mater. 4(12), 2028–2034 (2016).
    [Crossref]
  8. D. Liu, L. Yao, X. Zhai, M. Li, and J. Dong, “Diode-like asymmetric transmission of circularly polarized waves,” Appl. Phys. A 116(1), 9–13 (2014).
    [Crossref]
  9. S. Zhang, F. Liu, T. Zentgraf, and J. Li, “Interference-induced asymmetric transmission through a monolayer of anisotropic chiral metamolecules,” Phys. Rev. A 88(2), 023823 (2013).
    [Crossref]
  10. L. Wu, Z. Yang, Y. Cheng, Z. Lu, P. Zhang, M. Zhao, R. Gong, X. Yuan, Y. Zheng, and J. Duan, “Electromagnetic manifestation of chirality in layer-by-layer chiral metamaterials,” Opt. Express 21(5), 5239–5246 (2013).
    [Crossref]
  11. H. Jiang, W. Zhao, and Y. Jiang, “High-efficiency tunable circular asymmetric transmission using dielectric metasurface integrated with graphene sheet,” Opt. Express 25(17), 19732–19739 (2017).
    [Crossref]
  12. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
    [Crossref]
  13. R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, and N. I. Zheludev, “Terahertz metamaterial with asymmetric transmission,” Phys. Rev. B 80(15), 153104 (2009).
    [Crossref]
  14. E. Plum, V. A. Fedotov, and N. I. Zheludev, “Planar metamaterial with transmission and reflection that depend on the direction of incidence,” Appl. Phys. Lett. 94(13), 131901 (2009).
    [Crossref]
  15. E. Plum, V. A. Fedotov, and N. I. Zheludev, “Asymmetric transmission: a generic property of two-dimensional periodic patterns,” J. Opt. 13(2), 024006 (2011).
    [Crossref]
  16. A. V. Novitsky, V. M. Galynsky, and S. V. Zhukovsky, “Asymmetric transmission in planar chiral split-ring metamaterials: Microscopic Lorentz-theory approach,” Phys. Rev. B 86(7), 075138 (2012).
    [Crossref]
  17. Z. Li, M. Gokkavas, and E. Ozbay, “Manipulation of Asymmetric Transmission in planar chiral nanostructures by anisotropic loss,” Adv. Opt. Mater. 1(7), 482–488 (2013).
    [Crossref]
  18. M. Kang, J. Chen, H. X. Cui, Y. N. Li, and H. T. Wang, “Asymmetric transmission for linearly polarized electromagnetic radiation,” Opt. Express 19(9), 8347–8356 (2011).
    [Crossref]
  19. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
    [Crossref]
  20. J. Han, H. Li, Y. Fan, Z. Wei, C. Wu, Y. Cao, X. Yu, F. Li, and Z. Wang, “An ultrathin twist-structure polarization transformer based on fish-scale metallic wires,” Appl. Phys. Lett. 98(15), 151908 (2011).
    [Crossref]
  21. C. Huang, Y. Feng, J. Zhao, Z. Wang, and T. Jiang, “Asymmetric electromagnetic wave transmission of linear polarization via polarization conversion through chiral metamaterial structures,” Phys. Rev. B 85(19), 195131 (2012).
    [Crossref]
  22. J. H. Shi, X. C. Liu, S. W. Yu, T. T. Lv, Z. Zhu, H. F. Ma, and T. J. Cui, “Dual-band asymmetric transmission of linear polarization in bilayered chiral metamaterial,” Appl. Phys. Lett. 102(19), 191905 (2013).
    [Crossref]
  23. L. Wu, Z. Y. Yang, Y. Z. Cheng, M. Zhao, R. Z. Gong, Y. Zheng, J. Duan, and X. H. Yuan, “Giant asymmetric transmission of circular polarization in layer-by-layer chiral metamaterials,” Appl. Phys. Lett. 103(2), 021903 (2013).
    [Crossref]
  24. L. Wang, S. Liu, H. Zhang, Y. Wen, and X. Shi, “Asymmetric transmission and absorption generated with three-dimensional metamaterials at oblique incidence,” Opt. Mater. Express 9(3), 965–975 (2019).
    [Crossref]
  25. J. Zhao, J. Song, T. Xu, T. Yang, and J. Zhou, “Controllable linear asymmetric transmission and perfect polarization conversion in a terahertz hybrid metal-graphene metasurface,” Opt. Express 27(7), 9773–9781 (2019).
    [Crossref]
  26. W. M. Ye, X. D. Yuan, and C. Zeng, “Unidirectional transmission realized by two nonparallel gratings made of isotropic media,” Opt. Lett. 36(15), 2842 (2011).
    [Crossref]
  27. Z. H. Zhu, K. Liu, W. Xu, Z. Luo, C. C. Guo, B. Yang, T. Ma, X. D. Yuan, and W. M. Ye, “One-way transmission of linearly polarized light in plasmonic subwavelength metallic grating cascaded with dielectric grating,” Opt. Lett. 37(19), 4008–4010 (2012).
    [Crossref]
  28. A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B 80(15), 155117 (2009).
    [Crossref]
  29. S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “One-way transmission through the subwavelength slit in nonsymmetric metallic gratings,” Opt. Lett. 35(15), 2597–2599 (2010).
    [Crossref]
  30. W. M. Ye, X. D. Yuan, C. C. Guo, and C. Zen, “Unidirectional transmission in non-symmetric gratings made of isotropic material,” Opt. Express 18(8), 7590–7595 (2010).
    [Crossref]
  31. S. Cakmakyapan, H. Caglayan, A. E. Serebryannikov, and E. Ozbay, “Experimental validation of strong directional selectivity in nonsymmetric metallic gratings with a subwavelength slit,” Appl. Phys. Lett. 98(5), 051103 (2011).
    [Crossref]
  32. M. Stolarek, D. Yavorskiy, R. Kotynski, C. J. Zapata Rodriguez, J. Lusakowski, and T. Szoplik, “Asymmetric transmission of terahertz radiation through a double grating,” Opt. Lett. 38(6), 839–841 (2013).
    [Crossref]
  33. E. Battal, T. A. Yogurt, and A. K. Okyay, “Ultrahigh contrast one-way optical transmission through a subwavelength slit,” Plasmonics 8(2), 509–513 (2013).
    [Crossref]
  34. Y. Hu, X. Wang, X. Luo, X. Ou, L. Li, Y. Chen, S. Wang, and H. Duan, “All-dielectric metasurfaces for polarization manipulation: principles and emerging applications,” Nanophotonics 9(12), 3755–3780 (2020).
    [Crossref]
  35. F. Zhang, M. Pu, X. Li, P. Gao, X. Ma, J. Luo, H. Yu, and X. Luo, “All-Dielectric metasurfaces for simultaneous giant circular asymmetric transmission and wavefront shaping based on asymmetric photonic spin-orbit interactions,” Adv. Funct. Mater. 27(47), 1704295 (2017).
    [Crossref]
  36. Z. Ma, Y. Li, Y. Li, Y. Gong, S. A. Maier, and M. Hong, “All-dielectric planar chiral metasurface with gradient geometric phase,” Opt. Express 26(5), 6067–6078 (2018).
    [Crossref]
  37. D. Ma, Z. Li, Y. Zhang, W. Liu, H. Cheng, S. Chen, and J. Tian, “Giant spin-selective asymmetric transmission in multipolar-modulated metasurfaces,” Opt. Lett. 44(15), 3805–3808 (2019).
    [Crossref]
  38. N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “The origin and limit of asymmetric transmission in chiral resonators,” ACS Photonics 4(4), 884–890 (2017).
    [Crossref]
  39. Y. Rao, L. Pan, C. Ouyang, Q. Xu, L. Liu, Y. Li, J. Gu, Z. Tian, J. Han, and W. Zhang, “Asymmetric transmission of linearly polarized waves based on Mie resonance in all-dielectric terahertz metamaterials,” Opt. Express 28(20), 29855–29864 (2020).
    [Crossref]
  40. L. Zinkiewicz, M. Nawrot, J. Haberko, and P. Wasylczyk, “Polarization-independent asymmetric light transmission in all-dielectric photonic structures,” Opt. Mater. 73, 484–488 (2017).
    [Crossref]
  41. Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
    [Crossref]
  42. A. Drezet, C. Genet, J. Y. Laluet, and T. W. Ebbesen, “Optical chirality without optical activity: how surface plasmons give a twist to light,” Opt. Express 16(17), 12559–12550 (2008).
    [Crossref]

2020 (2)

Y. Hu, X. Wang, X. Luo, X. Ou, L. Li, Y. Chen, S. Wang, and H. Duan, “All-dielectric metasurfaces for polarization manipulation: principles and emerging applications,” Nanophotonics 9(12), 3755–3780 (2020).
[Crossref]

Y. Rao, L. Pan, C. Ouyang, Q. Xu, L. Liu, Y. Li, J. Gu, Z. Tian, J. Han, and W. Zhang, “Asymmetric transmission of linearly polarized waves based on Mie resonance in all-dielectric terahertz metamaterials,” Opt. Express 28(20), 29855–29864 (2020).
[Crossref]

2019 (3)

2018 (1)

2017 (4)

N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “The origin and limit of asymmetric transmission in chiral resonators,” ACS Photonics 4(4), 884–890 (2017).
[Crossref]

L. Zinkiewicz, M. Nawrot, J. Haberko, and P. Wasylczyk, “Polarization-independent asymmetric light transmission in all-dielectric photonic structures,” Opt. Mater. 73, 484–488 (2017).
[Crossref]

F. Zhang, M. Pu, X. Li, P. Gao, X. Ma, J. Luo, H. Yu, and X. Luo, “All-Dielectric metasurfaces for simultaneous giant circular asymmetric transmission and wavefront shaping based on asymmetric photonic spin-orbit interactions,” Adv. Funct. Mater. 27(47), 1704295 (2017).
[Crossref]

H. Jiang, W. Zhao, and Y. Jiang, “High-efficiency tunable circular asymmetric transmission using dielectric metasurface integrated with graphene sheet,” Opt. Express 25(17), 19732–19739 (2017).
[Crossref]

2016 (1)

J. Liu, Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “High-efficiency mutual dual-Band asymmetric transmission of circularly polarized waves with few-layer anisotropic metasurfaces,” Adv. Opt. Mater. 4(12), 2028–2034 (2016).
[Crossref]

2014 (2)

D. Liu, L. Yao, X. Zhai, M. Li, and J. Dong, “Diode-like asymmetric transmission of circularly polarized waves,” Appl. Phys. A 116(1), 9–13 (2014).
[Crossref]

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

2013 (7)

S. Zhang, F. Liu, T. Zentgraf, and J. Li, “Interference-induced asymmetric transmission through a monolayer of anisotropic chiral metamolecules,” Phys. Rev. A 88(2), 023823 (2013).
[Crossref]

L. Wu, Z. Yang, Y. Cheng, Z. Lu, P. Zhang, M. Zhao, R. Gong, X. Yuan, Y. Zheng, and J. Duan, “Electromagnetic manifestation of chirality in layer-by-layer chiral metamaterials,” Opt. Express 21(5), 5239–5246 (2013).
[Crossref]

Z. Li, M. Gokkavas, and E. Ozbay, “Manipulation of Asymmetric Transmission in planar chiral nanostructures by anisotropic loss,” Adv. Opt. Mater. 1(7), 482–488 (2013).
[Crossref]

M. Stolarek, D. Yavorskiy, R. Kotynski, C. J. Zapata Rodriguez, J. Lusakowski, and T. Szoplik, “Asymmetric transmission of terahertz radiation through a double grating,” Opt. Lett. 38(6), 839–841 (2013).
[Crossref]

E. Battal, T. A. Yogurt, and A. K. Okyay, “Ultrahigh contrast one-way optical transmission through a subwavelength slit,” Plasmonics 8(2), 509–513 (2013).
[Crossref]

J. H. Shi, X. C. Liu, S. W. Yu, T. T. Lv, Z. Zhu, H. F. Ma, and T. J. Cui, “Dual-band asymmetric transmission of linear polarization in bilayered chiral metamaterial,” Appl. Phys. Lett. 102(19), 191905 (2013).
[Crossref]

L. Wu, Z. Y. Yang, Y. Z. Cheng, M. Zhao, R. Z. Gong, Y. Zheng, J. Duan, and X. H. Yuan, “Giant asymmetric transmission of circular polarization in layer-by-layer chiral metamaterials,” Appl. Phys. Lett. 103(2), 021903 (2013).
[Crossref]

2012 (5)

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref]

Z. H. Zhu, K. Liu, W. Xu, Z. Luo, C. C. Guo, B. Yang, T. Ma, X. D. Yuan, and W. M. Ye, “One-way transmission of linearly polarized light in plasmonic subwavelength metallic grating cascaded with dielectric grating,” Opt. Lett. 37(19), 4008–4010 (2012).
[Crossref]

C. Huang, Y. Feng, J. Zhao, Z. Wang, and T. Jiang, “Asymmetric electromagnetic wave transmission of linear polarization via polarization conversion through chiral metamaterial structures,” Phys. Rev. B 85(19), 195131 (2012).
[Crossref]

A. V. Novitsky, V. M. Galynsky, and S. V. Zhukovsky, “Asymmetric transmission in planar chiral split-ring metamaterials: Microscopic Lorentz-theory approach,” Phys. Rev. B 86(7), 075138 (2012).
[Crossref]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref]

2011 (5)

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Asymmetric transmission: a generic property of two-dimensional periodic patterns,” J. Opt. 13(2), 024006 (2011).
[Crossref]

M. Kang, J. Chen, H. X. Cui, Y. N. Li, and H. T. Wang, “Asymmetric transmission for linearly polarized electromagnetic radiation,” Opt. Express 19(9), 8347–8356 (2011).
[Crossref]

S. Cakmakyapan, H. Caglayan, A. E. Serebryannikov, and E. Ozbay, “Experimental validation of strong directional selectivity in nonsymmetric metallic gratings with a subwavelength slit,” Appl. Phys. Lett. 98(5), 051103 (2011).
[Crossref]

W. M. Ye, X. D. Yuan, and C. Zeng, “Unidirectional transmission realized by two nonparallel gratings made of isotropic media,” Opt. Lett. 36(15), 2842 (2011).
[Crossref]

J. Han, H. Li, Y. Fan, Z. Wei, C. Wu, Y. Cao, X. Yu, F. Li, and Z. Wang, “An ultrathin twist-structure polarization transformer based on fish-scale metallic wires,” Appl. Phys. Lett. 98(15), 151908 (2011).
[Crossref]

2010 (4)

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “One-way transmission through the subwavelength slit in nonsymmetric metallic gratings,” Opt. Lett. 35(15), 2597–2599 (2010).
[Crossref]

W. M. Ye, X. D. Yuan, C. C. Guo, and C. Zen, “Unidirectional transmission in non-symmetric gratings made of isotropic material,” Opt. Express 18(8), 7590–7595 (2010).
[Crossref]

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref]

C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced Jones calculus for the classification of periodic metamaterials,” Phys. Rev. A 82(5), 053811 (2010).
[Crossref]

2009 (4)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref]

R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, and N. I. Zheludev, “Terahertz metamaterial with asymmetric transmission,” Phys. Rev. B 80(15), 153104 (2009).
[Crossref]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Planar metamaterial with transmission and reflection that depend on the direction of incidence,” Appl. Phys. Lett. 94(13), 131901 (2009).
[Crossref]

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B 80(15), 155117 (2009).
[Crossref]

2008 (2)

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93(19), 191911 (2008).
[Crossref]

A. Drezet, C. Genet, J. Y. Laluet, and T. W. Ebbesen, “Optical chirality without optical activity: how surface plasmons give a twist to light,” Opt. Express 16(17), 12559–12550 (2008).
[Crossref]

2006 (1)

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref]

1994 (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

Akosman, A. E.

M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Diodelike asymmetric transmission of linearly polarized waves using magnetoelectric coupling and electromagnetic wave tunneling,” Phys. Rev. Lett. 108(21), 213905 (2012).
[Crossref]

Alpeggiani, F.

N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, “The origin and limit of asymmetric transmission in chiral resonators,” ACS Photonics 4(4), 884–890 (2017).
[Crossref]

Azad, A. K.

R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, and N. I. Zheludev, “Terahertz metamaterial with asymmetric transmission,” Phys. Rev. B 80(15), 153104 (2009).
[Crossref]

Battal, E.

E. Battal, T. A. Yogurt, and A. K. Okyay, “Ultrahigh contrast one-way optical transmission through a subwavelength slit,” Plasmonics 8(2), 509–513 (2013).
[Crossref]

Bloemer, M. J.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

Bowden, C. M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

Briggs, D. P.

Y. Yang, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “All-dielectric metasurface analogue of electromagnetically induced transparency,” Nat. Commun. 5(1), 5753 (2014).
[Crossref]

Caglayan, H.

S. Cakmakyapan, H. Caglayan, A. E. Serebryannikov, and E. Ozbay, “Experimental validation of strong directional selectivity in nonsymmetric metallic gratings with a subwavelength slit,” Appl. Phys. Lett. 98(5), 051103 (2011).
[Crossref]

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “One-way transmission through the subwavelength slit in nonsymmetric metallic gratings,” Opt. Lett. 35(15), 2597–2599 (2010).
[Crossref]

Cakmakyapan, S.

S. Cakmakyapan, H. Caglayan, A. E. Serebryannikov, and E. Ozbay, “Experimental validation of strong directional selectivity in nonsymmetric metallic gratings with a subwavelength slit,” Appl. Phys. Lett. 98(5), 051103 (2011).
[Crossref]

S. Cakmakyapan, A. E. Serebryannikov, H. Caglayan, and E. Ozbay, “One-way transmission through the subwavelength slit in nonsymmetric metallic gratings,” Opt. Lett. 35(15), 2597–2599 (2010).
[Crossref]

Cao, Y.

J. Han, H. Li, Y. Fan, Z. Wei, C. Wu, Y. Cao, X. Yu, F. Li, and Z. Wang, “An ultrathin twist-structure polarization transformer based on fish-scale metallic wires,” Appl. Phys. Lett. 98(15), 151908 (2011).
[Crossref]

Chen, J.

Chen, S.

D. Ma, Z. Li, Y. Zhang, W. Liu, H. Cheng, S. Chen, and J. Tian, “Giant spin-selective asymmetric transmission in multipolar-modulated metasurfaces,” Opt. Lett. 44(15), 3805–3808 (2019).
[Crossref]

J. Liu, Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “High-efficiency mutual dual-Band asymmetric transmission of circularly polarized waves with few-layer anisotropic metasurfaces,” Adv. Opt. Mater. 4(12), 2028–2034 (2016).
[Crossref]

Chen, Y.

Y. Hu, X. Wang, X. Luo, X. Ou, L. Li, Y. Chen, S. Wang, and H. Duan, “All-dielectric metasurfaces for polarization manipulation: principles and emerging applications,” Nanophotonics 9(12), 3755–3780 (2020).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref]

Cheng, H.

D. Ma, Z. Li, Y. Zhang, W. Liu, H. Cheng, S. Chen, and J. Tian, “Giant spin-selective asymmetric transmission in multipolar-modulated metasurfaces,” Opt. Lett. 44(15), 3805–3808 (2019).
[Crossref]

J. Liu, Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “High-efficiency mutual dual-Band asymmetric transmission of circularly polarized waves with few-layer anisotropic metasurfaces,” Adv. Opt. Mater. 4(12), 2028–2034 (2016).
[Crossref]

Cheng, Y.

Cheng, Y. Z.

L. Wu, Z. Y. Yang, Y. Z. Cheng, M. Zhao, R. Z. Gong, Y. Zheng, J. Duan, and X. H. Yuan, “Giant asymmetric transmission of circular polarization in layer-by-layer chiral metamaterials,” Appl. Phys. Lett. 103(2), 021903 (2013).
[Crossref]

Cheville, R. A.

R. Singh, E. Plum, C. Menzel, C. Rockstuhl, A. K. Azad, R. A. Cheville, F. Lederer, W. Zhang, and N. I. Zheludev, “Terahertz metamaterial with asymmetric transmission,” Phys. Rev. B 80(15), 153104 (2009).
[Crossref]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref]

Cui, H. X.

Cui, T. J.

J. H. Shi, X. C. Liu, S. W. Yu, T. T. Lv, Z. Zhu, H. F. Ma, and T. J. Cui, “Dual-band asymmetric transmission of linear polarization in bilayered chiral metamaterial,” Appl. Phys. Lett. 102(19), 191905 (2013).
[Crossref]

Dong, J.

D. Liu, L. Yao, X. Zhai, M. Li, and J. Dong, “Diode-like asymmetric transmission of circularly polarized waves,” Appl. Phys. A 116(1), 9–13 (2014).
[Crossref]

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76(4), 2023–2026 (1994).
[Crossref]

Drezet, A.

Duan, H.

Y. Hu, X. Wang, X. Luo, X. Ou, L. Li, Y. Chen, S. Wang, and H. Duan, “All-dielectric metasurfaces for polarization manipulation: principles and emerging applications,” Nanophotonics 9(12), 3755–3780 (2020).
[Crossref]

Duan, J.

L. Wu, Z. Yang, Y. Cheng, Z. Lu, P. Zhang, M. Zhao, R. Gong, X. Yuan, Y. Zheng, and J. Duan, “Electromagnetic manifestation of chirality in layer-by-layer chiral metamaterials,” Opt. Express 21(5), 5239–5246 (2013).
[Crossref]

L. Wu, Z. Y. Yang, Y. Z. Cheng, M. Zhao, R. Z. Gong, Y. Zheng, J. Duan, and X. H. Yuan, “Giant asymmetric transmission of circular polarization in layer-by-layer chiral metamaterials,” Appl. Phys. Lett. 103(2), 021903 (2013).
[Crossref]

Ebbesen, T. W.

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335(6067), 447–450 (2012).
[Crossref]

Fan, Y.

J. Han, H. Li, Y. Fan, Z. Wei, C. Wu, Y. Cao, X. Yu, F. Li, and Z. Wang, “An ultrathin twist-structure polarization transformer based on fish-scale metallic wires,” Appl. Phys. Lett. 98(15), 151908 (2011).
[Crossref]

Fedotov, V. A.

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Asymmetric transmission: a generic property of two-dimensional periodic patterns,” J. Opt. 13(2), 024006 (2011).
[Crossref]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Planar metamaterial with transmission and reflection that depend on the direction of incidence,” Appl. Phys. Lett. 94(13), 131901 (2009).
[Crossref]

E. Plum, V. A. Fedotov, and N. I. Zheludev, “Optical activity in extrinsically chiral metamaterial,” Appl. Phys. Lett. 93(19), 191911 (2008).
[Crossref]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. 97(16), 167401 (2006).
[Crossref]

Feng, Y.

C. Huang, Y. Feng, J. Zhao, Z. Wang, and T. Jiang, “Asymmetric electromagnetic wave transmission of linear polarization via polarization conversion through chiral metamaterial structures,” Phys. Rev. B 85(19), 195131 (2012).
[Crossref]

Galynsky, V. M.

A. V. Novitsky, V. M. Galynsky, and S. V. Zhukovsky, “Asymmetric transmission in planar chiral split-ring metamaterials: Microscopic Lorentz-theory approach,” Phys. Rev. B 86(7), 075138 (2012).
[Crossref]

Gao, P.

F. Zhang, M. Pu, X. Li, P. Gao, X. Ma, J. Luo, H. Yu, and X. Luo, “All-Dielectric metasurfaces for simultaneous giant circular asymmetric transmission and wavefront shaping based on asymmetric photonic spin-orbit interactions,” Adv. Funct. Mater. 27(47), 1704295 (2017).
[Crossref]

Genet, C.

Gokkavas, M.

Z. Li, M. Gokkavas, and E. Ozbay, “Manipulation of Asymmetric Transmission in planar chiral nanostructures by anisotropic loss,” Adv. Opt. Mater. 1(7), 482–488 (2013).
[Crossref]

Gong, R.

Gong, R. Z.

L. Wu, Z. Y. Yang, Y. Z. Cheng, M. Zhao, R. Z. Gong, Y. Zheng, J. Duan, and X. H. Yuan, “Giant asymmetric transmission of circular polarization in layer-by-layer chiral metamaterials,” Appl. Phys. Lett. 103(2), 021903 (2013).
[Crossref]

Gong, Y.

Gu, J.

Guo, C. C.

Haberko, J.

L. Zinkiewicz, M. Nawrot, J. Haberko, and P. Wasylczyk, “Polarization-independent asymmetric light transmission in all-dielectric photonic structures,” Opt. Mater. 73, 484–488 (2017).
[Crossref]

Han, J.

Y. Rao, L. Pan, C. Ouyang, Q. Xu, L. Liu, Y. Li, J. Gu, Z. Tian, J. Han, and W. Zhang, “Asymmetric transmission of linearly polarized waves based on Mie resonance in all-dielectric terahertz metamaterials,” Opt. Express 28(20), 29855–29864 (2020).
[Crossref]

J. Han, H. Li, Y. Fan, Z. Wei, C. Wu, Y. Cao, X. Yu, F. Li, and Z. Wang, “An ultrathin twist-structure polarization transformer based on fish-scale metallic wires,” Appl. Phys. Lett. 98(15), 151908 (2011).
[Crossref]

Helgert, C.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref]

Hong, M.

Hu, Y.

Y. Hu, X. Wang, X. Luo, X. Ou, L. Li, Y. Chen, S. Wang, and H. Duan, “All-dielectric metasurfaces for polarization manipulation: principles and emerging applications,” Nanophotonics 9(12), 3755–3780 (2020).
[Crossref]

Huang, C.

C. Huang, Y. Feng, J. Zhao, Z. Wang, and T. Jiang, “Asymmetric electromagnetic wave transmission of linear polarization via polarization conversion through chiral metamaterial structures,” Phys. Rev. B 85(19), 195131 (2012).
[Crossref]

Jiang, H.

Jiang, T.

C. Huang, Y. Feng, J. Zhao, Z. Wang, and T. Jiang, “Asymmetric electromagnetic wave transmission of linear polarization via polarization conversion through chiral metamaterial structures,” Phys. Rev. B 85(19), 195131 (2012).
[Crossref]

Jiang, Y.

Joannopoulos, J. D.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref]

Kang, M.

Kley, E. B.

C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tunnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. 104(25), 253902 (2010).
[Crossref]

Kotynski, R.

Kravchenko, I. I.

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J. Han, H. Li, Y. Fan, Z. Wei, C. Wu, Y. Cao, X. Yu, F. Li, and Z. Wang, “An ultrathin twist-structure polarization transformer based on fish-scale metallic wires,” Appl. Phys. Lett. 98(15), 151908 (2011).
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J. Han, H. Li, Y. Fan, Z. Wei, C. Wu, Y. Cao, X. Yu, F. Li, and Z. Wang, “An ultrathin twist-structure polarization transformer based on fish-scale metallic wires,” Appl. Phys. Lett. 98(15), 151908 (2011).
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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. Schematic of the designed structure: (a) perspective view, (b) top view, (c) bottom view and (d) side view.
Fig. 2.
Fig. 2. The transmission coefficients of linearly polarized waves for (a) the forward (-z) and (b) the backward (+z) propagations. (c) The cross-polarized transmission coefficients and (d) the AT parameters.
Fig. 3.
Fig. 3. In the forward propagation at λ1 = 957 nm, the distributions of electric field vector (white arrow) and intensity (color map) in the (a) top silicon and (b) bottom silicon in the x-y plane under x-polarization, and (c) shows the equivalent electric field distributions with the black arrow indicating the total field. (d) - (f) show the corresponding results under y-polarization. The scales of these maps are the same.
Fig. 4.
Fig. 4. In the forward propagation at λ2 = 949 nm, the distributions of electric field vector (white arrow) and intensity (color map) in the (a) top silicon and (b) bottom silicon in the x-y plane under x-polarization, and (c) shows the equivalent electric field distributions with the black arrow indicating the total field. (d) - (f) show the corresponding results under y-polarization. The scales of these maps are the same.
Fig. 5.
Fig. 5. The AT parameter Δx varies with the geometric parameters (a) a, (b) h1 and (c) h2.
Fig. 6.
Fig. 6. (a) 3D colormap and (b) the projection of the Δx varying with the incident angle. The variation of Δx with the fitting line at (c) λ1 and (d) λ2.

Tables (1)

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Table 1. The comparison between references and our work.

Equations (3)

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( T x T y ) = ( T x x f T x y f T y x f T y y f ) ( I x I y ) = T f ( I x I y ) .
T b = ( T x x b T y x b T x y b T y y b ) .
Δ x = | T x x f | 2 + | T y x f | 2 | T x x b | 2 | T x y f | 2 = | T y x f | 2 | T x y f | 2 , Δ y = | T y y f | 2 + | T x y f | 2 | T y y b | 2 | T y x f | 2 = | T x y f | 2 | T y x f | 2 .