Abstract

We show that nanosphere dispersed liquid crystal (NDLC) metamaterial can be characterized in near IR spectral region as an indefinite medium whose real parts of effective ordinary and extraordinary permittivities are opposite in signs. Based on this fact we designed an electro-optic effect: an external electric-field-driven switch between normal refraction, negative refraction, and reflection of TM incident electromagnetic wave from the boundary vacuum/NDLC. A detailed analysis of its functionality is given based on effective medium theory combined with a study of negative refraction in anisotropic metamaterials and finite elements simulations.

© 2014 Optical Society of America

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  1. N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations (Wiley, 2006).
  2. W. Cai and V. Shalaev, Optical Metamaterials Fundamentals and Applications (Springer, 2010).
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  16. G. Pawlik, M. Jarema, W. Walasik, A. C. Mitus, and I. C. Khoo, J. Opt. Soc. Am. B 27, 567 (2010).
    [CrossRef]
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    [CrossRef]
  18. G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8828, 88280E (2013).
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    [CrossRef]
  20. D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
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2014 (1)

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

2013 (3)

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8828, 88280E (2013).
[CrossRef]

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8901, 890111 (2013).
[CrossRef]

2012 (1)

2011 (2)

E. Spinozzi and A. Ciattoni, Opt. Mater. Express 1, 732 (2011).
[CrossRef]

S.-H. Liu and L.-X. Guo, Prog. Electromagn. Res. 115, 243 (2011).

2010 (4)

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Y. A. Barnakov, and M. A. Noginov, Appl. Phys. Lett. 97, 131107 (2010).
[CrossRef]

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhara, Appl. Phys. Lett. 96, 0231114 (2010).
[CrossRef]

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, Opt. Lett. 35, 16 (2010).
[CrossRef]

G. Pawlik, M. Jarema, W. Walasik, A. C. Mitus, and I. C. Khoo, J. Opt. Soc. Am. B 27, 567 (2010).
[CrossRef]

2009 (2)

2008 (1)

J. Zhao, Y. Chen, and Y. Fen, Appl. Phys. Lett. 92, 071114 (2008).
[CrossRef]

2007 (2)

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, Opt. Express 15, 15886 (2007).
[CrossRef]

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. V. Kildishev, and V. M. Shalaev, Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

2006 (3)

2005 (1)

T. M. Grzegorczyk, M. Nikku, X. Chen, B.-I. Wu, and J. A. Kong, IEEE Trans. Microw. Theory Tech. 53, 1443 (2005).
[CrossRef]

2004 (1)

2003 (1)

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Alekseyev, L. V.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Y. A. Barnakov, and M. A. Noginov, Appl. Phys. Lett. 97, 131107 (2010).
[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, Opt. Express 14, 8247 (2006).
[CrossRef]

Barnakov, Y. A.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Y. A. Barnakov, and M. A. Noginov, Appl. Phys. Lett. 97, 131107 (2010).
[CrossRef]

Bartal, G.

Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials Fundamentals and Applications (Springer, 2010).

Cao, Z.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Casse, B. D. F.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhara, Appl. Phys. Lett. 96, 0231114 (2010).
[CrossRef]

Chen, X.

T. M. Grzegorczyk, M. Nikku, X. Chen, B.-I. Wu, and J. A. Kong, IEEE Trans. Microw. Theory Tech. 53, 1443 (2005).
[CrossRef]

Chen, Y.

J. Zhao, Y. Chen, and Y. Fen, Appl. Phys. Lett. 92, 071114 (2008).
[CrossRef]

Ciattoni, A.

Diaz, A.

Engheta, N.

N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations (Wiley, 2006).

Fang, A.

A. Fang, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 79, 245127 (2009).
[CrossRef]

Fen, Y.

J. Zhao, Y. Chen, and Y. Fen, Appl. Phys. Lett. 92, 071114 (2008).
[CrossRef]

Grzegorczyk, T. M.

T. M. Grzegorczyk, M. Nikku, X. Chen, B.-I. Wu, and J. A. Kong, IEEE Trans. Microw. Theory Tech. 53, 1443 (2005).
[CrossRef]

Gultepe, E.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhara, Appl. Phys. Lett. 96, 0231114 (2010).
[CrossRef]

Guo, L.-X.

S.-H. Liu and L.-X. Guo, Prog. Electromagn. Res. 115, 243 (2011).

Hu, L.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Hu, X.

Huang, Y. J.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhara, Appl. Phys. Lett. 96, 0231114 (2010).
[CrossRef]

Jacob, Z.

Jarema, M.

Jia, D.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Jiang, X.

Khoo, I. C.

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8828, 88280E (2013).
[CrossRef]

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8901, 890111 (2013).
[CrossRef]

G. Pawlik, K. Tarnowski, W. Walasik, A. C. Mitus, and I. C. Khoo, Opt. Lett. 37, 1847 (2012).
[CrossRef]

G. Pawlik, M. Jarema, W. Walasik, A. C. Mitus, and I. C. Khoo, J. Opt. Soc. Am. B 27, 567 (2010).
[CrossRef]

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. V. Kildishev, and V. M. Shalaev, Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, Opt. Lett. 31, 2592 (2006).
[CrossRef]

Kildishev, A. V.

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. V. Kildishev, and V. M. Shalaev, Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

Kolinko, P.

Kong, J. A.

T. M. Grzegorczyk, M. Nikku, X. Chen, B.-I. Wu, and J. A. Kong, IEEE Trans. Microw. Theory Tech. 53, 1443 (2005).
[CrossRef]

Koschny, T.

A. Fang, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 79, 245127 (2009).
[CrossRef]

Kwon, D. H.

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. V. Kildishev, and V. M. Shalaev, Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

Lavrentovich, O. D.

O. P. Pishnyak and O. D. Lavrentovich, Appl. Phys. Lett. 89, 251103 (2006).
[CrossRef]

Lee, H.

Li, D.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

Li, H.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Y. A. Barnakov, and M. A. Noginov, Appl. Phys. Lett. 97, 131107 (2010).
[CrossRef]

Li, X.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

J. Yang, X. Hu, X. Li, Z. Liu, X. Jiang, and J. Zi, Opt. Lett. 35, 16 (2010).
[CrossRef]

Liang, X.

Liu, S.-H.

S.-H. Liu and L.-X. Guo, Prog. Electromagn. Res. 115, 243 (2011).

Liu, Y.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Liu, Z.

Lu, W. T.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhara, Appl. Phys. Lett. 96, 0231114 (2010).
[CrossRef]

Lu, X.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Menon, L.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhara, Appl. Phys. Lett. 96, 0231114 (2010).
[CrossRef]

Mitus, A. C.

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8901, 890111 (2013).
[CrossRef]

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8828, 88280E (2013).
[CrossRef]

G. Pawlik, K. Tarnowski, W. Walasik, A. C. Mitus, and I. C. Khoo, Opt. Lett. 37, 1847 (2012).
[CrossRef]

G. Pawlik, M. Jarema, W. Walasik, A. C. Mitus, and I. C. Khoo, J. Opt. Soc. Am. B 27, 567 (2010).
[CrossRef]

Mu, Q.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Narimanov, E.

Narimanov, E. E.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Y. A. Barnakov, and M. A. Noginov, Appl. Phys. Lett. 97, 131107 (2010).
[CrossRef]

Nikku, M.

T. M. Grzegorczyk, M. Nikku, X. Chen, B.-I. Wu, and J. A. Kong, IEEE Trans. Microw. Theory Tech. 53, 1443 (2005).
[CrossRef]

Noginov, M. A.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Y. A. Barnakov, and M. A. Noginov, Appl. Phys. Lett. 97, 131107 (2010).
[CrossRef]

Pawlik, G.

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8901, 890111 (2013).
[CrossRef]

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8828, 88280E (2013).
[CrossRef]

G. Pawlik, K. Tarnowski, W. Walasik, A. C. Mitus, and I. C. Khoo, Opt. Lett. 37, 1847 (2012).
[CrossRef]

G. Pawlik, M. Jarema, W. Walasik, A. C. Mitus, and I. C. Khoo, J. Opt. Soc. Am. B 27, 567 (2010).
[CrossRef]

Peng, Z.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Pishnyak, O. P.

O. P. Pishnyak and O. D. Lavrentovich, Appl. Phys. Lett. 89, 251103 (2006).
[CrossRef]

Schurig, D.

D. R. Smith, P. Kolinko, and D. Schurig, J. Opt. Soc. Am. B 21, 1032 (2004).
[CrossRef]

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Shalaev, V.

W. Cai and V. Shalaev, Optical Metamaterials Fundamentals and Applications (Springer, 2010).

Shalaev, V. M.

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. V. Kildishev, and V. M. Shalaev, Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

Smith, D. R.

D. R. Smith, P. Kolinko, and D. Schurig, J. Opt. Soc. Am. B 21, 1032 (2004).
[CrossRef]

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Soukoulis, C. M.

A. Fang, T. Koschny, and C. M. Soukoulis, Phys. Rev. B 79, 245127 (2009).
[CrossRef]

Spinozzi, E.

Sridhara, S.

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhara, Appl. Phys. Lett. 96, 0231114 (2010).
[CrossRef]

Sun, C.

Tarnowski, K.

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8828, 88280E (2013).
[CrossRef]

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8901, 890111 (2013).
[CrossRef]

G. Pawlik, K. Tarnowski, W. Walasik, A. C. Mitus, and I. C. Khoo, Opt. Lett. 37, 1847 (2012).
[CrossRef]

Tsai, K. T.

Tumkur, T.

L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Y. A. Barnakov, and M. A. Noginov, Appl. Phys. Lett. 97, 131107 (2010).
[CrossRef]

Walasik, W.

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8901, 890111 (2013).
[CrossRef]

G. Pawlik, W. Walasik, K. Tarnowski, A. C. Mitus, and I. C. Khoo, Proc. SPIE 8828, 88280E (2013).
[CrossRef]

G. Pawlik, K. Tarnowski, W. Walasik, A. C. Mitus, and I. C. Khoo, Opt. Lett. 37, 1847 (2012).
[CrossRef]

G. Pawlik, M. Jarema, W. Walasik, A. C. Mitus, and I. C. Khoo, J. Opt. Soc. Am. B 27, 567 (2010).
[CrossRef]

Wang, X.

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. V. Kildishev, and V. M. Shalaev, Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

Wang, Y.

Wang, Y. L.

Weiner, B.

Werner, D. H.

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. V. Kildishev, and V. M. Shalaev, Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, Opt. Lett. 31, 2592 (2006).
[CrossRef]

Wu, B.-I.

T. M. Grzegorczyk, M. Nikku, X. Chen, B.-I. Wu, and J. A. Kong, IEEE Trans. Microw. Theory Tech. 53, 1443 (2005).
[CrossRef]

Xiang, X.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

Xiong, Y.

Xuan, L.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Yang, C.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Yang, J.

Yao, J.

Yao, L.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

D. Jia, C. Yang, Z. Peng, X. Li, Y. Liu, L. Yao, Z. Cao, Q. Mu, L. Hu, X. Lu, and L. Xuan, Liq. Cryst. 40, 599 (2013).
[CrossRef]

Zhang, H.

D. Jia, C. Yang, X. Li, Z. Peng, Y. Liu, Z. Cao, Q. Mu, L. Hu, D. Li, L. Yao, X. Lu, X. Xiang, H. Zhang, and L. Xuan, Liq. Cryst. 41, 207 (2014).
[CrossRef]

Zhang, X.

Zhao, J.

J. Zhao, Y. Chen, and Y. Fen, Appl. Phys. Lett. 92, 071114 (2008).
[CrossRef]

Zi, J.

Ziolkowski, R. W.

N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations (Wiley, 2006).

Appl. Phys. Lett. (5)

B. D. F. Casse, W. T. Lu, Y. J. Huang, E. Gultepe, L. Menon, and S. Sridhara, Appl. Phys. Lett. 96, 0231114 (2010).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) Geometry of the system. (b) Dependence of effective permittivity and permeability on permittivity of the LC host ε3, Eq. (2).

Fig. 2.
Fig. 2.

Dependence of tensor components (εeff)xx, (εeff)yy, and (εeff)xy on rotation angle γ.

Fig. 3.
Fig. 3.

Plots of refraction angles θr,S(θi) (solid line) and θr,k(θi) (dashed line) for a uniform configuration (γ=90°). Symbols represent FE results [18,19]. Large symbol—see Fig. 4. Inset: isofrequency contours for the TM wave incident from an isotropic material to an indefinite one with (εeff)xx<0 and (εeff)yy>0 for the angle of incidence θi=30°.

Fig. 4.
Fig. 4.

Finite element simulations of the electric and magnetic field mapping for Gaussian beam with TM polarization, θi=40°. (a) Magnitude of the electric field and Poynting vectors and (b) z component of the magnetic field.

Fig. 5.
Fig. 5.

Refraction angle θr,S in function of the orientation γ of NLC director for θi=0° (full circles), 30° (solid line), 50° (squares), and 80° (triangles). Large circles represent FE calculations for θi=30°.

Fig. 6.
Fig. 6.

Operating principle of the switch. Left, orientation of NLC host; right, magnetic field mapping for a Gaussian TM beam incident at θi=30°. Negative refraction (γ=90°, top); positive refraction (γ=110°, middle); and total reflection (γ=0°, bottom).

Equations (3)

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εLC=(ε+Δεcos2γΔεsinγcosγ0Δεsinγcosγε+Δεsin2γ000ε),
εeff=ε3(k33+4πiNa1k332πiNa1),μeff=k33+4πiNb1k332πiNb1,
kx2(εeff)yy+ky2(εeff)xx=ω2c2,

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