## Asymmetric transmission of linearly polarized waves and polarization angle dependent wave rotation using a chiral metamaterial |

Optics Express, Vol. 19, Issue 15, pp. 14290-14299 (2011)

http://dx.doi.org/10.1364/OE.19.014290

Acrobat PDF (1829 KB)

### Abstract

An electrically thin chiral metamaterial structure composed of four U-shaped split ring resonator pairs is utilized in order to realize polarization rotation that is dependent on the polarization of the incident wave at 6.2 GHz. The structure is optimized such that a plane wave that is linearly polarized at an arbitrary angle is an eigenwave of the system at this frequency. The analytical relation between the incident polarization and the polarization rotation is derived using transmission matrices. Furthermore, the proposed structure exhibits an asymmetric transmission of linearly polarized waves at 6.2 GHz. Plane waves traveling in opposite but perpendicular directions to the material plane are rotated by different angles. On the other hand, four incident polarization angles have been found for the same structure, at which the transmission is symmetric. The experiment results are in good agreement with the numerical results.

© 2011 OSA

## 1. Introduction

*et al.*proposed a design to realize negative permeability [1

1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. **47**(11), 2075–2084 (1999). [CrossRef]

2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. **84**(18), 4184–4187 (2000). [CrossRef] [PubMed]

3. V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. **30**(24), 3356–3358 (2005). [CrossRef] [PubMed]

5. N. Katsarakis, T. Koschny, M. Kafesaki, E. Economou, E. Ozbay, and C. Soukoulis, “Left- and right-handed transmission peaks near the magnetic resonance frequency in composite metamaterials,” Phys. Rev. B **70**(20), 201101 (2004). [CrossRef]

6. N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. **82**(2), 161–163 (2003). [CrossRef]

8. K. Aydin, I. Bulu, and E. Ozbay, “Focusing of electromagnetic waves by a left-handed metamaterial flat lens,” Opt. Express **13**(22), 8753–8759 (2005). [CrossRef] [PubMed]

9. K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture,” Phys. Rev. Lett. **102**(1), 013904 (2009). [CrossRef] [PubMed]

10. I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, and H. A. Atwater, “Highly strained compliant optical metamaterials with large frequency tunability,” Nano Lett. **10**(10), 4222–4227 (2010). [CrossRef] [PubMed]

11. K. Aydin and E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl. Phys. **101**(2), 024911 (2007). [CrossRef]

12. J. B. Pendry, “A chiral route to negative refraction,” Science **306**(5700), 1353–1355 (2004). [CrossRef] [PubMed]

13. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. **32**(7), 856–858 (2007). [CrossRef] [PubMed]

14. Z. Li, K. B. Alici, E. Colak, and E. Ozbay, “Complementary chiral metamaterials with giant optical activity and negative refractive index,” Appl. Phys. Lett. **98**(16), 161907 (2011). [CrossRef]

15. S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. **102**(2), 023901 (2009). [CrossRef] [PubMed]

19. Z. Li, R. Zhao, T. Koschny, M. Kafesaki, K. B. Alici, E. Colak, H. Caglayan, E. Ozbay, and C. M. Soukoulis, ““Chiral metamaterials with negative refractive index based on four “U” split ring resonators,” Appl. Phys. Lett. **97**(8), 081901 (2010). [CrossRef]

20. Y. Ye and S. He, “90° polarization rotator using a bilayered chiral metamaterial with giant optical activity,” Appl. Phys. Lett. **96**(20), 203501 (2010). [CrossRef]

23. E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. **90**(22), 223113 (2007). [CrossRef]

24. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Asymmetric chiral metamaterial circular polarizer based on four U-shaped split ring resonators,” Opt. Lett. **36**(9), 1653–1655 (2011). [CrossRef] [PubMed]

26. J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. **99**(6), 063908 (2007). [CrossRef] [PubMed]

20. Y. Ye and S. He, “90° polarization rotator using a bilayered chiral metamaterial with giant optical activity,” Appl. Phys. Lett. **96**(20), 203501 (2010). [CrossRef]

27. T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. **93**(2), 021110 (2008). [CrossRef]

28. W. Sun, Q. He, J. Hao, and L. Zhou, “A transparent metamaterial to manipulate electromagnetic wave polarizations,” Opt. Lett. **36**(6), 927–929 (2011). [CrossRef] [PubMed]

28. W. Sun, Q. He, J. Hao, and L. Zhou, “A transparent metamaterial to manipulate electromagnetic wave polarizations,” Opt. Lett. **36**(6), 927–929 (2011). [CrossRef] [PubMed]

20. Y. Ye and S. He, “90° polarization rotator using a bilayered chiral metamaterial with giant optical activity,” Appl. Phys. Lett. **96**(20), 203501 (2010). [CrossRef]

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

32. 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]

33. D. M. H. Leung, B. M. A. Rahman, and K. T. V. Grattan, “Numerical analysis of asymmetric silicon nanowire waveguide as compact polarization rotator,” IEEE Photon. J. **3**(3), 381–389 (2011). [CrossRef]

34. Z. Li, H. Caglayan, E. Colak, J. Zhou, C. M. Soukoulis, and E. Ozbay, “Coupling effect between two adjacent chiral structure layers,” Opt. Express **18**(6), 5375–5383 (2010). [CrossRef] [PubMed]

## 2. Proposed Geometry

19. Z. Li, R. Zhao, T. Koschny, M. Kafesaki, K. B. Alici, E. Colak, H. Caglayan, E. Ozbay, and C. M. Soukoulis, ““Chiral metamaterials with negative refractive index based on four “U” split ring resonators,” Appl. Phys. Lett. **97**(8), 081901 (2010). [CrossRef]

21. X. Xiong, W. H. Sun, Y. J. Bao, M. Wang, R. W. Peng, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B **81**(7), 075119 (2010). [CrossRef]

35. R. Zhao, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Comparison of chiral metamaterial designs for repulsive Casimir force,” Phys. Rev. B **81**(23), 235126 (2010). [CrossRef]

_{4}) symmetry. Thus, circularly polarized waves are not eigenwaves of the proposed design. This fact can be used as an advantage for the purpose of creating polarization angle dependent rotation. As a consequence of the broken C

_{4}symmetry, orthogonal electric field components (

*x*and

*y*components in this context) of an incident wave encounter different transmission coefficients, both in terms of magnitude and phase. This discrepancy between the transmission coefficients can be optimized to yield a linearly polarized transmitted wave whose polarization angle is a function of the polarization angle of the linearly polarized incident wave. In this study, we demonstrate the results of this optimization numerically and experimentally. Afterwards, a closed form relationship is derived that relates the polarization rotation introduced by the CMM to the polarization angle of the incident wave.

19. Z. Li, R. Zhao, T. Koschny, M. Kafesaki, K. B. Alici, E. Colak, H. Caglayan, E. Ozbay, and C. M. Soukoulis, ““Chiral metamaterials with negative refractive index based on four “U” split ring resonators,” Appl. Phys. Lett. **97**(8), 081901 (2010). [CrossRef]

21. X. Xiong, W. H. Sun, Y. J. Bao, M. Wang, R. W. Peng, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B **81**(7), 075119 (2010). [CrossRef]

35. R. Zhao, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Comparison of chiral metamaterial designs for repulsive Casimir force,” Phys. Rev. B **81**(23), 235126 (2010). [CrossRef]

*x*-direction [24

24. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Asymmetric chiral metamaterial circular polarizer based on four U-shaped split ring resonators,” Opt. Lett. **36**(9), 1653–1655 (2011). [CrossRef] [PubMed]

*a*=

_{x}*a*= 13.6 mm,

_{y}*s*= 6 mm,

_{1}*s*= 4.8 mm,

_{2}*w*= 0.7 mm,

_{1}*w*= 0.55 mm,

_{2}*d*= 1.4 mm, and

*t*= 1.5 mm. A FR-4 board with a relative permittivity of 4 and a dielectric loss tangent of 0.025 is utilized as the substrate. For the metallic parts, copper that is 30 µm thick is used. As it will be presented subsequently, the operating frequency of the CMM is 6.2 GHz. At this frequency, the structure is electrically thin with

*t / λ*≈0.031. In addition, the periodicity in the transverse plane is electrically small at 6.2 GHz, since

*a*=

_{x}*a*corresponds to 0.281

_{y}*λ*.

## 3. Numerical Results

*x*and

*y*directions are adjusted to be periodic in order to obtain periodicity in the transverse plane. The boundary condition along the

*z*direction is selected to be absorbing. In order to characterize the response of the CMM, the structure is illuminated by plane waves propagating in the

*–z*direction. Assuming the linearity of the CMM, linear transmission coefficients

*T*and

_{xx}*T*are obtained from the simulations when the incident wave is

_{yx}*x*-polarized. Similarly, for a

*y*-polarized incident wave, linear transmission coefficients

*T*and

_{xy}*T*are obtained. The magnitudes of the four linear transmission coefficients are shown in Fig. 2(a) and 2(b). The mutual phase differences between

_{yy}*T*and

_{xx}*T*, and

_{yx}*T*and

_{yy}*T*are shown in Fig. 2(c).

_{xy}*T*and

_{xy}*T*are non-zero. In addition, the simulation results reveal that

_{yx}*T*and

_{xx}*T*are equal in terms of magnitude and phase (phase not shown here). In other words, the transmitted

_{yy}*x*-polarization due to an

*x*-polarized incidence is equal in terms of magnitude and phase to the transmitted

*y*-polarization due to a

*y*-polarized incidence. Conversely, it is noticed that the transmitted

*y*-polarization due to an

*x*-polarized incidence is strongly different than the transmission of the

*x*-polarization due to a

*y*-polarized incidence. Using these observations, it can be deduced that this CMM configuration creates polarization angle dependent chirality.

*y*-direction and propagating in the

*–z*direction is equivalent to illumination by a plane wave polarized in the

*x*-direction and propagating in the

*+ z*direction. The two waves encounter the same transmission coefficients with respect to their polarization direction, e.g.,

*T*becomes

_{xx}*T*and

_{yy}*T*becomes

_{yx}*T*. Thus, the transmission of the CMM is asymmetric.

_{xy}*T*and

_{xx}*T*, and

_{yx}*T*and

_{yy}*T*. At 6.2 GHz, which is the operating frequency of the device, the mutual phase differences are approximately equal to 0°, in turn demonstrating that at this frequency optical activity is observed. Although the mutual phase differences are 0°, the phases of all the elements must be equal in order to avoid the transmission of elliptically polarized wave. We investigated the numerical results and observed that at 6.2 GHz, the phases of all linear transmission coefficients are equalized. As a result, combining the two orthogonal cases, linearly polarized waves are eigenwaves of the CMM at 6.2 GHz and are transmitted with a polarization rotation.

_{xy}24. M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Asymmetric chiral metamaterial circular polarizer based on four U-shaped split ring resonators,” Opt. Lett. **36**(9), 1653–1655 (2011). [CrossRef] [PubMed]

*x*-polarized and

*y*-polarized incident fields are approximately equal to zero at 6.2 GHz, which corresponds to pure optical activity at this frequency. The corresponding azimuth polarization rotation angles for

*x*-polarized and

*y*-polarized incident fields are shown in Fig. 3(b).

*x*direction is rotated by 46° at 6.2 GHz, whereas a

*y*-polarized incident wave is rotated by 15° at the same frequency. Due to different rotations for

*x*and

*y*polarizations, each incident polarization angle encounters a different rotation. The relationship between the incident polarization angle and the resulting polarization rotation can be derived by performing simple geometrical calculations based on the rotation values provided above. However, for simplicity, we will employ the transfer matrix formulation subsequently for determining this relation.

## 4. Experiment Results

*x*and

*y*components of the transmitted fields due to

*x*and

*y*polarized incident waves are measured for characterization. Phase information is also obtained from the network analyzer in order to calculate the rotation and ellipticity for the transmitted waves. The experimental magnitudes of

*T*,

_{xx}*T*,

_{xy}*T*and

_{yx}*T*are shown in Fig. 4 , as well as the phase differences between

_{yy}*T*and

_{xx}*T*, and

_{yx}*T*and

_{yy}*T*. In Fig. 2(c), the phase differences are approximately equal to 0° at 6.2GHz. For the experiment results, at 6.2 GHz we obtain −6° for the phase difference between

_{xy}*T*and

_{xx}*T*and −7° for the

_{yx}*T*and

_{yy}*T*case. Throughout the scanned frequency range, the experiment results agree closely with the simulations.

_{xy}*x*-polarized incidence is 4.2°. Similarly, for a

*y*-polarized incident wave, the ellipticity of the transmitted wave is 2.9°. These results are very close to the numerical results, where both ellipticities are approximately equal to 0°. Subsequently, we examine the experimental results for polarization rotation. Experiment results indicate that the amount of rotation is 49° for an

*x*-polarized incident wave at 6.2 GHz. This value differs by 3° from the simulation results, which indicates a good agreement. However, we obtain a 26° rotation for a

*y*-polarized wave at the same frequency. Numerical results provided 15° rotation for a

*y*-polarized field, which differs by 11° from the experiment result. These discrepancies can be attributed to the inaccuracies in the fabrication stage, multi-reflections in the experiment setup, diffraction effects from the sharp edges of the CMM structure, probable misalignments and non-zero cross-polarization response of the antennas. In addition, the resonance frequencies slightly shift to higher frequencies in the experiments. The possible reasons are the variance of the dielectric permittivity of the FR-4, experiment inaccuracies and simulation inaccuracies, i.e., mesh size affects the resonance frequencies. Overall, we conclude that the agreement between the numerical and experiment results is good and the operation of the CMM is verified experimentally.

## 5. Formulation

*x*and

*y*directions represent the two inputs and the two outputs of the system, a transmission matrix

*T*, with the elements

*T*,

_{xx}*T*,

_{xy}*T*and

_{yx}*T*can be defined so that the following relation holdswhere

_{yy}*E*and

_{xd}*E*are the transmitted fields along the

_{yd}*x*and

*y*directions, respectively. Similarly,

*E*and

_{x0}*E*represent the electric field components of the incident field along the

_{y0}*x*and

*y*directions. In linear equation form, Eq. (4) can be rewritten as the follows:Subsequent to the calculation of transmitted

*x*and

*y*components for an arbitrary input to the system, the polarization angle of the transmitted wave is calculated asIn order to relate the transmitted polarization angle to the incident polarization angle, without loss of generality, we assume that the magnitude of the incoming wave is unity in all cases. Under this assumption, Eq. (6) is modified aswhere

*φ*denotes the polarization angle of the incident wave. It is noteworthy that the inverse tangent is a multi-valued function that requires special attention. The quadrant where

*ϕ*lies depends on the signs of the numerator and denominator of Eq. (7). Finally, the corresponding polarization rotation is defined asThen, to calculate the polarization rotation introduced by the CMM at 6.2 GHz, we constructed the transmission matrices using the simulation results for waves propagating in the

*–z*and

*+ z*directions. Thereby, the asymmetric transmission of the design would be demonstrated simultaneously with the incident polarization angle dependent polarization rotation. For an incident wave propagating in the

*–z*direction, the elements of the transmission matrix are given as

*T*= 0.3568,

_{xx}*T*= 0.1104,

_{xy}*T*= 0.3599 and

_{yx}*T*= 0.3568. In general, these elements are complex quantities carrying phase information. However, in this case we omit the phases of the elements, since the simulation and experiment results prove that all the elements are in-phase. Thus, using only the magnitude information is sufficient. Similarly, for a +

_{yy}*z*propagating wave, the transmission matrix elements are given as

*T*= 0.3568,

_{xx}*T*= −0.3599,

_{xy}*T*= −0.1104 and

_{yx}*T*= 0.3568. The two transmission matrices demonstrate the asymmetric transmission of the structure, since

_{yy}*T*and

_{xy}*T*values are not equal for the +

_{yx}*z*and –

*z*cases. Figure 6(a) shows the calculated polarization angle of the transmitted wave, using Eq. (7), due to incident waves linearly polarized from 0° to 360° and propagating in the –

*z*and +

*z*directions. The corresponding polarization rotation calculated using Eq. (8) is presented in Fig. 6(b).

*z*and +

*z*propagating waves are transmitted symmetrically, with the same polarization. Equating

*ϕ*given by Eq. (7) for the above-mentioned transmission matrices, we obtain the following transcendental equation to calculate these angles:

*φ*= 35.3°, 125.3°, 215.3° and 305.3°. Figure 6(b) presents

*θ*as a function of

*ϕ*, which is calculated using Eqs. (7) and 8.

*θ*for the waves propagating in the –z and + z directions, which are linearly polarized at the angles those are being equal to the solutions of Eq. (9). In turn, for polarization angles, which do not satisfy Eq. (9), the transmission is asymmetric, i.e., different for waves propagating in the

*–z*and

*+ z*directions. In both cases, linearly polarized waves are eigenwaves for both directions.

## 6. Surface Currents

*x*-polarized waves propagating in the –

*z*and +

*z*directions. The simulation results indicate that the directions of the induced surface currents are identical for both excitations. The directions of the surface currents are shown in Fig. 7 .

*x*-polarization to the

*y*-polarization decreases when the electric field vector of the incident wave is parallel to the slit of the SRR that is closer to the source. However, rotating the pair by 90°, while keeping the electric field vector direction constant, does not change the transmission of the

*x*-polarization. In the case where each SRR pair has the same dimensions, rotation does not affect the transmission coefficients. In the asymmetric case, rotation decreases coupling from

*x*-polarization to

*y*-polarization, whereas the transmission of the

*x*-polarization is not changed. When the structure is rotated, smaller SRR pairs are not at the resonance since their resonance frequencies are larger. In addition, according to the simulation results, larger SRR pairs begin to produce less

*y*-polarization compared to the previous case. Thus, illuminating the structure by an

*x*-polarized wave is not equivalent to illumination by a

*y*-polarized wave. It should also be denoted that due to the geometry of the CMM, illuminating the structure by a

*y*-polarized wave propagating in the –

*z*direction is equivalent to illuminating it by an

*x*-polarized wave propagating in the +

*z*direction. Hence, as a result of different transmission coefficients for the

*x*and

*y*polarized waves, the transmission of the structure is asymmetric.

## 7. Conclusion

*T*, depends on the propagation direction of the incoming wave. Thus, the transmission through the structure is asymmetric for linearly polarized waves. On the other hand, four angles have been found for which the transmission is symmetric. Finally, surface current distributions at 6.2 GHz are studied in order to explain the underlying mechanism behind the asymmetric transmission. The CMM can be utilized in microwave applications as a configurable polarization rotator. The ideas of the suggested design can be adapted in future research for terahertz and optical applications.

## Acknowledgments

## References and links

1. | J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. |

2. | D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. |

3. | V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. |

4. | C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. |

5. | N. Katsarakis, T. Koschny, M. Kafesaki, E. Economou, E. Ozbay, and C. Soukoulis, “Left- and right-handed transmission peaks near the magnetic resonance frequency in composite metamaterials,” Phys. Rev. B |

6. | N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. |

7. | K. Aydin, I. Bulu, and E. Ozbay, “Subwavelength resolution with a negative-index metamaterial superlens,” Appl. Phys. Lett. |

8. | K. Aydin, I. Bulu, and E. Ozbay, “Focusing of electromagnetic waves by a left-handed metamaterial flat lens,” Opt. Express |

9. | K. Aydin, A. O. Cakmak, L. Sahin, Z. Li, F. Bilotti, L. Vegni, and E. Ozbay, “Split-ring-resonator-coupled enhanced transmission through a single subwavelength aperture,” Phys. Rev. Lett. |

10. | I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, and H. A. Atwater, “Highly strained compliant optical metamaterials with large frequency tunability,” Nano Lett. |

11. | K. Aydin and E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl. Phys. |

12. | J. B. Pendry, “A chiral route to negative refraction,” Science |

13. | M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. |

14. | Z. Li, K. B. Alici, E. Colak, and E. Ozbay, “Complementary chiral metamaterials with giant optical activity and negative refractive index,” Appl. Phys. Lett. |

15. | S. Zhang, Y. S. Park, J. Li, X. Lu, W. Zhang, and X. Zhang, “Negative refractive index in chiral metamaterials,” Phys. Rev. Lett. |

16. | J. Dong, J. Zhou, T. Koschny, and C. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express |

17. | J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B |

18. | E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B |

19. | Z. Li, R. Zhao, T. Koschny, M. Kafesaki, K. B. Alici, E. Colak, H. Caglayan, E. Ozbay, and C. M. Soukoulis, ““Chiral metamaterials with negative refractive index based on four “U” split ring resonators,” Appl. Phys. Lett. |

20. | Y. Ye and S. He, “90° polarization rotator using a bilayered chiral metamaterial with giant optical activity,” Appl. Phys. Lett. |

21. | X. Xiong, W. H. Sun, Y. J. Bao, M. Wang, R. W. Peng, C. Sun, X. Lu, J. Shao, Z. F. Li, and N. B. Ming, “Construction of a chiral metamaterial with a U-shaped resonator assembly,” Phys. Rev. B |

22. | D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express |

23. | E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, “Giant optical gyrotropy due to electromagnetic coupling,” Appl. Phys. Lett. |

24. | M. Mutlu, A. E. Akosman, A. E. Serebryannikov, and E. Ozbay, “Asymmetric chiral metamaterial circular polarizer based on four U-shaped split ring resonators,” Opt. Lett. |

25. | B. Wang, T. Koschny, and C. M. Soukoulis, “Wide-angle and polarization-independent chiral metamaterial absorber,” Phys. Rev. B |

26. | J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. |

27. | T. Li, H. Liu, S.-M. Wang, X.-G. Yin, F.-M. Wang, S.-N. Zhu, and X. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. |

28. | W. Sun, Q. He, J. Hao, and L. Zhou, “A transparent metamaterial to manipulate electromagnetic wave polarizations,” Opt. Lett. |

29. | C. Menzel, C. Helgert, C. Rockstuhl, E. B. Kley, A. Tünnermann, T. Pertsch, and F. Lederer, “Asymmetric transmission of linearly polarized light at optical metamaterials,” Phys. Rev. Lett. |

30. | V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, V. V. Khardikov, and S. L. Prosvirnin, “Asymmetric transmission of light and enantiomerically sensitive plasmon resonance in planar chiral nanostructures,” Nano Lett. |

31. | 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. |

32. | 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 |

33. | D. M. H. Leung, B. M. A. Rahman, and K. T. V. Grattan, “Numerical analysis of asymmetric silicon nanowire waveguide as compact polarization rotator,” IEEE Photon. J. |

34. | Z. Li, H. Caglayan, E. Colak, J. Zhou, C. M. Soukoulis, and E. Ozbay, “Coupling effect between two adjacent chiral structure layers,” Opt. Express |

35. | R. Zhao, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Comparison of chiral metamaterial designs for repulsive Casimir force,” Phys. Rev. B |

**OCIS Codes**

(230.5440) Optical devices : Polarization-selective devices

(160.1585) Materials : Chiral media

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: June 6, 2011

Revised Manuscript: June 29, 2011

Manuscript Accepted: June 29, 2011

Published: July 11, 2011

**Citation**

Mehmet Mutlu, Ahmet E. Akosman, Andriy E. Serebryannikov, and Ekmel Ozbay, "Asymmetric transmission of linearly polarized waves and polarization angle dependent wave rotation using a chiral metamaterial," Opt. Express **19**, 14290-14299 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14290

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