## Multi-band circular polarizer using planar spiral metamaterial structure |

Optics Express, Vol. 20, Issue 14, pp. 16050-16058 (2012)

http://dx.doi.org/10.1364/OE.20.016050

Acrobat PDF (1468 KB)

### Abstract

A multi-band circular polarizer is proposed by using multi layered planar spiral metamaterial structure in analogy with classic spiral antenna. At three distinct resonant frequencies, the incident linearly polarized wave with electric field paralleling to one specific direction is transformed into left/right-handed circularly polarized waves through electric field coupling. Measured and simulated results show that right-handed circularly polarized wave is produced at 13.33 GHz and 16.75 GHz while left-handed circularly polarized wave is obtained at 15.56 GHz. The surface current distributions are studied to investigate the transformation behavior for both circular polarizations. The relationship between the resonant positions and the structure parameters is discussed as well.

© 2012 OSA

## 1. Introduction

1. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. **76**(25), 4773–4776 (1996). [CrossRef] [PubMed]

2. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science **305**(5685), 788–792 (2004). [CrossRef] [PubMed]

3. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. **85**(18), 3966–3969 (2000). [CrossRef] [PubMed]

4. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science **314**(5801), 977–980 (2006). [CrossRef] [PubMed]

5. 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]

8. D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express **16**(16), 11802–11807 (2008). [CrossRef] [PubMed]

9. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science **325**(5947), 1513–1515 (2009). [CrossRef] [PubMed]

14. J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki, and C. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B **79**(12), 121104 (2009). [CrossRef]

*et al.*[9

9. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science **325**(5947), 1513–1515 (2009). [CrossRef] [PubMed]

10. S. X. Li, Z. Y. Yang, J. Wang, and M. Zhao, “Broadband terahertz circular polarizers with single- and double-helical array metamaterials,” J. Opt. Soc. Am. A **28**(1), 19–23 (2011). [CrossRef] [PubMed]

11. C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. **107**(17), 177401 (2011). [CrossRef] [PubMed]

12. 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]

15. 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]

6. M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization convertor,” IEEE Trans. Antenn. Propag. **58**(7), 2457–2459 (2010). [CrossRef]

## 2. Design principle

### 2.1 Dual-band circular polarizer

*h*, relative permittivity of

*ε*= 2.55 and loss tangent of 0.0007. The metallic arcs of each layer are concentric in

_{r}*XOY*plane with the same radius of

*R*and width of

*w*. The other parameters include the structure periodic

*P*, the central angle of each arc

*θ*, and the angle of the gap between the two metallic arcs

*Φ*. The optimized geometrical parameters are

_{1}*P*= 11.5 mm,

*R*= 4.75 mm,

*w*= 0.85 mm,

*h*= 3 mm,

*θ*= 80°,

*Φ*= 40°.

_{1}*y*direction, the electric field of the transmitted wave can be stated as [16]:where

*E*

_{0}is amplitude of the incident electric field,

*T*and

_{xy}*T*are transmissions of the linearly polarized wave, and the first subscript indicates the transmitted polarization (

_{yy}*x*- or

*y*-polarized), while the second indicates the incident polarization. The transmitted wave would be LCP (RCP) if the amplitudes of

*T*and

_{xy}*T*equal to each other, and the phase difference Φ(|

_{yy}*T*|) - Φ(|

_{xy}*T*|) equal to −90° (90°).

_{yy}*y*-polarized electric filed is used as the excitation source in the simulation. Thus the information of the frequencies we interest in can be totally covered. In the process of simulation, the boundaries along

*x*and

*y*directions are set to be periodic boundary condition, while perfectly matched layers are set along

*z*direction.

*T*and

_{xy}*T*while the phases of

_{yy}*T*and

_{xy}*T*are shown in Fig. 2(b). It can be calculated that the ratio between the amplitude of

_{yy}*T*and

_{xy}*T*(|

_{yy}*T*|/|

_{xy}*T*|) equals to 0.93 at 14.25 GHz (denoted as

_{yy}*f*) and 1.02 at 16.35 GHz (denoted as

_{1}*f*), and the phase difference Φ(|

_{2}*T*|) - Φ(|

_{xy}*T*|) equals to −91.2° and 90.4° at the above two resonant frequencies, respectively. It indicates that a LCP wave is induced at 14.25 GHz, whereas a RCP wave is induced at 16.35 GHz.

_{yy}*C*as the transformation coefficient for RCP wave and

_{RCP}*C*for LCP wave, and the conversion from the linear transmission coefficients to the circular transformation coefficients can be obtained as follows [15

_{LCP}15. 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]

*C*and

_{RCP}*C*are depicted in Fig. 3 . It can be seen that the transformed field is LCP at 14.25GHz, while is RCP at 16.35GHz. Besides, the transformation coefficient of LCP wave is 29 dB higher than that of RCP wave at 14.25 GHz, whereas is 36 dB lower than that of RCP wave at 16.35 GHz. As a result, relatively pure circularly polarized waves with different rotation are realized at these two frequencies.

_{LCP}*x*direction of is induced. The electric field induced by metal layer 1 and metal layer 2 can be resolved into

*x*and

*y*components. It is clear that the

*x*component of electric field is along +

*x*direction and the

*y*component is along -

*y*direction at 14.25 GHz, which illustrates that a LCP wave is transformed. However, at 16.35 GHz, the

*x*component of electric field is along -

*x*direction and the

*y*component is along -

*y*direction, which indicates that a RCP wave is realized.

### 2.2 Triple-band circular polarizer

*w*= 0.85 mm, and the central angle is

*θ*= 80°.The period and thickness of the polarizer are

*P*= 11.5 mm and 2 ×

*h*= 3.048 mm, which equal to about 0.5

*λ*and 0.135

*λ*(

*λ*represents the wavelength) at the lowest operating frequency, respectively.

*Φ*represents the angle between the upper end of metal layer 1 and

_{1}*x*axis, and angle

*Φ*denotes the angle of the gap between two neighboring arcs. When

_{2}*Φ*is varied, the metal structure of each unit cell is rotated along

_{1}*z*axis. In this design,

*Φ*is 22.5°, while angle

_{1}*Φ*is designed to be 40°. The whole optimization process will be shown in the discussion section.

_{2}*f*= 13.33 GHz, the instantaneous surface current distributions are illustrated in Fig. 7(a) . It shows that the currents rotate clockwise at these three metal arcs. Then we take the current vectors from the surface current distributions to explain the rotation of the transmitted circularly polarized wave, as seen in Fig. 7(d). The numbers 1, 2, and 3 represent the current vectors in the middle of the corresponding metal layer. Obviously, the vectors from metallic layer 1 to layer 3 form a counter-clockwise rotation, which is coincident with the rotation of electric field for RCP wave. Therefore, it is well understood that the linearly polarized incident wave is transformed to RCP wave.

*y*-polarized electric field. When the polarization of the electric field is changed from

*y*to

*x*-direction, different conversion coefficients for LCP and RCP waves can be obtained, as shown in Fig. 8 . The three resonances are at 12.96 GHz, 15.26 GHz, and 17.17 GHz, respectively. This difference is due to the lack of C4 symmetric for this triple-band polarizer, that is to say, the sample cannot be superimposed on itself when it is rotated by 90° around its center in

*XOY*plane.

## 3. Discussion

*θ*is degree, and the value of

*θ*is optimized to be 80° in this triple-band circular polarizer. According to the above formula, the structure parameters can influence the value of

*L*. Since the operating wavelength is directly proportional to

_{eff}*L*, the resonant frequencies would shift towards lower (higher) frequency when

_{eff}*R*or

*h*increases (decreases). In order to validate the assumption, the analysis of the parameters is carried out by varying one parameter while keeping the other parameters fixed. Figures 9(a) and 9(b) present the transformation for LCP and RCP waves with different values of

*R*. We can see that the positions of transformation frequencies for LCP and RCP waves all shift towards lower frequency when

*R*increases. Since the effective wavelength is directly proportional to

*L*, the increase of effective length

_{eff}*L*of the arcs would result in red shift of the resonant frequency when

_{eff}*R*varies from 4.5 mm to 5.0 mm.

*w*of arc is varied from 0.75 mm to 0.95 mm. The resonant positions shift towards higher frequency while

*w*increases. As the current would flow along the possible shortest path, so the increase of

*w*reduces the effective radius

*R*of the arc, resulting in the decrease of effective wavelength according to the Eq. (4) above. Transformation behavior for different thickness

*h*of dielectric lamina from 1.27 mm to 1.778 mm with a step of 0.254 mm is depicted in Fig. 11 . Similar to the shift trend of changing radius

*R*, the resonant positions shift towards lower frequency when

*h*increases. The thickness

*h*analogously acts as the helix pitch of the metallic helix antenna, so the resonant frequencies red shift when

*h*increases according to the antenna theory.

*R*is stronger than that on

*w*and

*h*, thus

*R*can be taken as the main parameter to determine the resonant positions while

*w*and

*h*are suitable for slight tuning.

*Φ*on the transformation performance. The value of

_{1}*Φ*determines the relative angle of each arc to

_{1}*x*axis. So changing

*Φ*would result in the variation of the

_{1}*x*and

*y*component of induced electric field, that is to say, the variation of

*Φ*can influence the phase differences between the transmission coefficients of |

_{1}*T*| and |

_{xy}*T*|, and its ratio |

_{yy}*T*|/|

_{xy}*T*|. As shown in Fig. 12(a) and 12(b), the resonant frequencies are shifted and transformation values are varied as well when

_{yy}*Φ*changes from 10° to 30°, proving the important role of

_{1}*Φ*in the design of the circular polarizer stated above.

_{1}## 4. Conclusion

## Acknowledgment

## References and links

1. | J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. |

2. | D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science |

3. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

4. | D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science |

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

6. | M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization convertor,” IEEE Trans. Antenn. Propag. |

7. | M. G. Silveirinha, “Design of linear-to-circular polarization transformers made of long densely packed metallic helices,” IEEE Trans. Antenn. Propag. |

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

9. | J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science |

10. | S. X. Li, Z. Y. Yang, J. Wang, and M. Zhao, “Broadband terahertz circular polarizers with single- and double-helical array metamaterials,” J. Opt. Soc. Am. A |

11. | C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett. |

12. | 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. |

13. | 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 chiral metamaterial with U-shaped resonator assembly,” Phys. Rev. B |

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

15. | 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. |

16. | J. D. Jackson, |

**OCIS Codes**

(260.5430) Physical optics : Polarization

(260.5740) Physical optics : Resonance

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: April 16, 2012

Manuscript Accepted: June 19, 2012

Published: June 29, 2012

**Citation**

Xiaoliang Ma, Cheng Huang, Mingbo Pu, Chenggang Hu, Qin Feng, and Xiangang Luo, "Multi-band circular polarizer using planar spiral metamaterial structure," Opt. Express **20**, 16050-16058 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-16050

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### References

- J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett.76(25), 4773–4776 (1996). [CrossRef] [PubMed]
- D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004). [CrossRef] [PubMed]
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000). [CrossRef] [PubMed]
- D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
- 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]
- M. Euler, V. Fusco, R. Cahill, and R. Dickie, “325 GHz single layer sub-millimeter wave FSS based split slot ring linear to circular polarization convertor,” IEEE Trans. Antenn. Propag.58(7), 2457–2459 (2010). [CrossRef]
- M. G. Silveirinha, “Design of linear-to-circular polarization transformers made of long densely packed metallic helices,” IEEE Trans. Antenn. Propag.56(2), 390–401 (2008). [CrossRef]
- D. H. Kwon, P. L. Werner, and D. H. Werner, “Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation,” Opt. Express16(16), 11802–11807 (2008). [CrossRef] [PubMed]
- J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325(5947), 1513–1515 (2009). [CrossRef] [PubMed]
- S. X. Li, Z. Y. Yang, J. Wang, and M. Zhao, “Broadband terahertz circular polarizers with single- and double-helical array metamaterials,” J. Opt. Soc. Am. A28(1), 19–23 (2011). [CrossRef] [PubMed]
- C. Wu, H. Li, X. Yu, F. Li, H. Chen, and C. T. Chan, “Metallic helix array as a broadband wave plate,” Phys. Rev. Lett.107(17), 177401 (2011). [CrossRef] [PubMed]
- 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. 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 chiral metamaterial with U-shaped resonator assembly,” Phys. Rev. B81(7), 075119 (2010). [CrossRef]
- J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki, and C. Soukoulis, “Negative refractive index due to chirality,” Phys. Rev. B79(12), 121104 (2009). [CrossRef]
- 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]
- J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999), pp. 205–207.

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