## Incident-angle-insensitive and polarization independent polarization rotator

Optics Express, Vol. 18, Issue 11, pp. 11990-12001 (2010)

http://dx.doi.org/10.1364/OE.18.011990

Acrobat PDF (1619 KB)

### Abstract

This paper proposes a method to design an incident-angle-insensitive polarization-independent polarization rotator. This polarization rotator is composed of layers of impedance-matched anisotropic metamaterial (IMAM) with each layer’s optical axes gradually rotating an angle. Numerical simulation based on the generalized 4 × 4 transfer matrix method is applied, and the results reveal that the IMAM rotator is not only polarization-independent but also insensitive to the angle of incidence. A 90° polarization rotation with tiny ellipticity variation is still available at a wide range of incident angles from 0 to 40°, which is further confirmed with a microwave bi-split-ring resonator (bi-SRR) rotator. This may be valuable for the design of optoelectronic and microwave devices.

© 2010 OSA

## 1. Introduction

2. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science **321**(5891), 930 (2008). [CrossRef] [PubMed]

8. J.-M. Lourtioz, “Photonic crystals and metamaterials,” C. R. Phys. **9**(1), 4–15 (2008). [CrossRef]

9. M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Polarization selection with stacked hole array metamaterial,” J. Appl. Phys. **103**(5), 053102 (2008). [CrossRef]

12. V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdré, M. V. Kotlyar, L. O’Faolain, and T. F. Krauss, “Self-collimating photonic crystal polarization beam splitter,” Opt. Lett. **32**(5), 530–532 (2007). [CrossRef] [PubMed]

5. W. Zhang, J. Liu, W. P. Huang, and W. Zhao, “Self-collimating photonic-crystal wave plates,” Opt. Lett. **34**(17), 2676–2678 (2009). [CrossRef] [PubMed]

13. 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]

17. M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. **95**(22), 227401 (2005). [CrossRef] [PubMed]

18. S. K. Awasthi and S. P. Ojha, “Wide-angle, broadband plate polarizer with 1D photonic crystal,” Prog. Electromag. Res. **PIER 88**, 321–335 (2008). [CrossRef]

10. J. Zhao, Y. Chen, and Y. Feng, “Polarization beam splitting through an anisotropic metamaterial slab realized by a layered metal-dielectric structure,” Appl. Phys. Lett. **92**(7), 071114 (2008). [CrossRef]

11. H. Luo, Z. Ren, W. Shu, and F. Li, “Construct a polarizing beam splitter by an anisotropic metamaterial slab,” Appl. Phys. B **87**(2), 283–287 (2007). [CrossRef]

19. Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B **79**(4), 045131 (2009). [CrossRef]

## 2. General formalism of IMAM polarization rotator

20. J. L. Tsalamengas, “Interaction of electromagnetic waves with general bianisotropicslabs,” IEEE Trans. Microwave Theory Tech. **40**(10), 1870–1878 (1992). [CrossRef]

*φ*is the polarization angle of the incident wave.

*Z*is the wave impedance, and

_{th}slab can be written as

*δ*is the angle between the x axis and the crystal axis 1 of the first layer;

*ϕ*is the angle of the crystal axes between adjacent layers. We once again project

*n*is odd, the Jones matrix can be simplified as follows:

*T*is not considered, the Jones matrix is a coordinate transformation matrix by rotating an angle of

*be tuned dynamically and is independent of*

*φ*and

*linear*polarization rotation in planar metallic chiral structures due to dichroism; while in dielectric chiral structures, one can achieve linear polarization rotation but this property strongly depends on incident direction, as has been pointed out [22

22. B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A **76**(2), 023811 (2007). [CrossRef]

## 3. Incident-angle-insensitivity and polarization independency

*h*of each layer is chosen as

*θ*(denoted by

*δ*and incident polarization angle

*φ*should be considered. Figures 3(a) to 3(d) show the polarization changes of the transmitted light. The ellipticity

*Δ*and the polarization rotation angle

*δ*is actually equivalent to the change of incidence in polar direction. Now we look about how the performance of the polarization rotator depends on

*δ*when

*φ*= 45°. Figure 3(a) is the projection of the three-dimensional (3D) curvature of ellipticity Δ as a function of

*δ*and

*δ*and

*δ*ranges from 0° to 360°,

*φ*on the polarization rotation at the oblique incidence of

*40*°. The insets plot the variations of

*Δ*and

*δ*and

*φ*at a

*40*° incident angle. The projections of these curvatures onto

*φ*changes from −90° to 90°, the maximum variation range of Δ is

*φ*and

## 4. Comparison and discussion

*h*of each layer is chosen as

*b*= 1 is impedance-matched among the three cases. Since

*at normal incidence*; when two identical plates are stacked together in the aforementioned way, i.e.

*at normal incidence*. However, the impedance-matched conditions are not satisfied at oblique incidence, and this will bring in negative influences on the performance of the rotators. Nevertheless, as is shown above, the structure composed of IMAM slabs (

*b*= 1) is more insensitive to incident angle.

*φ*= 45°. It is clear that for the impendence-matched polarization rotator, the incident angle region with

*b*= 2 as an example, the polarization rotation becomes −105° and the ellipticity is around-0.6 at a 40° incidence.

*k*, indicating the existence of high-order Fabry-Perot interference. While for the IMAM slab,

_{x}5. W. Zhang, J. Liu, W. P. Huang, and W. Zhao, “Self-collimating photonic-crystal wave plates,” Opt. Lett. **34**(17), 2676–2678 (2009). [CrossRef] [PubMed]

## 5. Construct a microwave IMAM rotator with bi-SRR structure

23. C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B **77**(19), 195328 (2008). [CrossRef]

24. J. D. Baena, L. Jelinek, R. Marques, and J. Zehentner, “Electrically small isotropic three-dimensional magnetic resonators for metamaterial design,” Appl. Phys. Lett. **88**(13), 134108 (2006). [CrossRef]

*t*= 0.5 mm. The other dimensions of a unit cell are as follows: lattice constant

*a*=

_{z}*a*= 5 mm; the length of metal slices (perfect electric conductor) in Z and Y directions

_{y}*z = y = 4*mm, the separation distance of the metal slices

*p*= 0.12 mm, the gap

*g*= 0.2 mm, the separation distance between adjacent unit cells

*s*= 1.0 mm, and the width

*w*and thickness of metal are 0.2 mm and 0.08mm respectively. The design principle of the IMAM half-wave retarder is that only TM component can excite magnetic resonances while TE wave propagates “quietly” through the structure. Thus nearly full transmission and low effective refractive index can be obtained for TE wave, while high effective index is available for TM component at the impedance-matched frequency near the resonance. By tuning the dimensions or the substrate material, one can change the impedance-matched frequency and the phase difference between the two orthogonal components of the transmitted waves.

*O*(

*T*) represents the first order approximation. The ellipticity and polarization rotation angle with respect to incident wave polarization under different incident angles can then be worked out. For clarity but without loss of generality, we only give out the results for incident polar angle

## 6. Conclusion

## Acknowledgement

## References and links

1. | D. Y. Yu, and H. Y. Tan, |

2. | J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science |

3. | S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. |

4. | A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B |

5. | W. Zhang, J. Liu, W. P. Huang, and W. Zhao, “Self-collimating photonic-crystal wave plates,” Opt. Lett. |

6. | J. Zhao, Y. Feng, B. Zhu, and T. Jiang, “Sub-wavelength image manipulating through compensated anisotropic metamaterial prisms,” Opt. Express |

7. | J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature |

8. | J.-M. Lourtioz, “Photonic crystals and metamaterials,” C. R. Phys. |

9. | M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Polarization selection with stacked hole array metamaterial,” J. Appl. Phys. |

10. | J. Zhao, Y. Chen, and Y. Feng, “Polarization beam splitting through an anisotropic metamaterial slab realized by a layered metal-dielectric structure,” Appl. Phys. Lett. |

11. | H. Luo, Z. Ren, W. Shu, and F. Li, “Construct a polarizing beam splitter by an anisotropic metamaterial slab,” Appl. Phys. B |

12. | V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdré, M. V. Kotlyar, L. O’Faolain, and T. F. Krauss, “Self-collimating photonic crystal polarization beam splitter,” Opt. Lett. |

13. | 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. |

14. | K. Bayat, S. K. Chaudhuri, and S. Safavi-Naeini, “Ultra-compact photonic crystal based polarization rotator,” Opt. Lett. |

15. | J. Y. Chin, J. N. Gollub, J. J. Mock, R. Liu, C. Harrison, D. R. Smith, and T. J. Cui, “An efficient broadband metamaterial wave retarder,” Opt. Express |

16. | 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. |

17. | M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. |

18. | S. K. Awasthi and S. P. Ojha, “Wide-angle, broadband plate polarizer with 1D photonic crystal,” Prog. Electromag. Res. |

19. | Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B |

20. | J. L. Tsalamengas, “Interaction of electromagnetic waves with general bianisotropicslabs,” IEEE Trans. Microwave Theory Tech. |

21. | R. M. A. Azzam, and N. M. Bashara, |

22. | B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A |

23. | C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B |

24. | J. D. Baena, L. Jelinek, R. Marques, and J. Zehentner, “Electrically small isotropic three-dimensional magnetic resonators for metamaterial design,” Appl. Phys. Lett. |

**OCIS Codes**

(230.0230) Optical devices : Optical devices

(230.5440) Optical devices : Polarization-selective devices

(160.3918) Materials : Metamaterials

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: March 30, 2010

Revised Manuscript: May 8, 2010

Manuscript Accepted: May 10, 2010

Published: May 21, 2010

**Citation**

Mingkai Liu, Yanbing Zhang, Xuehua Wang, and Chongjun Jin, "Incident-angle-insensitive and polarization independent polarization rotator," Opt. Express **18**, 11990-12001 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-11-11990

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### References

- D. Y. Yu, and H. Y. Tan, Engineering Optics(in chinese) (China Machine Press, Beijing, 2006).
- J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008). [CrossRef] [PubMed]
- S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Prog. Phys. 68(2), 449–521 (2005). [CrossRef]
- A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]
- W. Zhang, J. Liu, W. P. Huang, and W. Zhao, “Self-collimating photonic-crystal wave plates,” Opt. Lett. 34(17), 2676–2678 (2009). [CrossRef] [PubMed]
- J. Zhao, Y. Feng, B. Zhu, and T. Jiang, “Sub-wavelength image manipulating through compensated anisotropic metamaterial prisms,” Opt. Express 16(22), 18057–18066 (2008). [CrossRef] [PubMed]
- J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]
- J.-M. Lourtioz, “Photonic crystals and metamaterials,” C. R. Phys. 9(1), 4–15 (2008). [CrossRef]
- M. Beruete, M. Navarro-Cía, M. Sorolla, and I. Campillo, “Polarization selection with stacked hole array metamaterial,” J. Appl. Phys. 103(5), 053102 (2008). [CrossRef]
- J. Zhao, Y. Chen, and Y. Feng, “Polarization beam splitting through an anisotropic metamaterial slab realized by a layered metal-dielectric structure,” Appl. Phys. Lett. 92(7), 071114 (2008). [CrossRef]
- H. Luo, Z. Ren, W. Shu, and F. Li, “Construct a polarizing beam splitter by an anisotropic metamaterial slab,” Appl. Phys. B 87(2), 283–287 (2007). [CrossRef]
- V. Zabelin, L. A. Dunbar, N. Le Thomas, R. Houdré, M. V. Kotlyar, L. O’Faolain, and T. F. Krauss, “Self-collimating photonic crystal polarization beam splitter,” Opt. Lett. 32(5), 530–532 (2007). [CrossRef] [PubMed]
- 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]
- K. Bayat, S. K. Chaudhuri, and S. Safavi-Naeini, “Ultra-compact photonic crystal based polarization rotator,” Opt. Lett. 17, 7145–7158 (2009).
- J. Y. Chin, J. N. Gollub, J. J. Mock, R. Liu, C. Harrison, D. R. Smith, and T. J. Cui, “An efficient broadband metamaterial wave retarder,” Opt. Express 17(9), 7640–7647 (2009). [CrossRef] [PubMed]
- 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]
- M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. 95(22), 227401 (2005). [CrossRef] [PubMed]
- S. K. Awasthi and S. P. Ojha, “Wide-angle, broadband plate polarizer with 1D photonic crystal,” Prog. Electromag. Res. PIER 88, 321–335 (2008). [CrossRef]
- Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79(4), 045131 (2009). [CrossRef]
- J. L. Tsalamengas, “Interaction of electromagnetic waves with general bianisotropicslabs,” IEEE Trans. Microwave Theory Tech. 40(10), 1870–1878 (1992). [CrossRef]
- R. M. A. Azzam, and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland Pub. Co., New York, 1977).
- B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A 76(2), 023811 (2007). [CrossRef]
- C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, “Retrieving effective parameters for metamaterials at oblique incidence,” Phys. Rev. B 77(19), 195328 (2008). [CrossRef]
- J. D. Baena, L. Jelinek, R. Marques, and J. Zehentner, “Electrically small isotropic three-dimensional magnetic resonators for metamaterial design,” Appl. Phys. Lett. 88(13), 134108 (2006). [CrossRef]

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