Abstract

By employing a thermally active magnetic material, we theoretically design a kind of electromagnetic metamaterial with intrinsic magnetic response, termed magnetic metamaterial (MM). The retrieved effective electric permittivity εeff and magnetic permeability μeff exhibit a nearly continuous transition from double negative to double zero, and then to double positive by controlling the temperature, indicating a flexible tunability of the effective refractive index. The beam splitting, collimation, focusing, and total reflection are achieved at different typical temperatures. Most importantly, with the MM implemented under a gradient temperature, a gradient negative-zero-positive index metamaterial (NZPIM) can possibly be realized, thus providing a new platform to study wave features in NZPIM.

© 2014 Optical Society of America

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2014 (1)

N. F. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[CrossRef]

2013 (3)

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, Phys. Rev. Lett. 110, 037403 (2013).
[CrossRef]

K. Bi, G. Y. Dong, X. J. Fu, and J. Zhou, Appl. Phys. Lett. 103, 131915 (2013).
[CrossRef]

Y. S. Ding, C. T. Chan, and R. P. Wang, Sci. Rep. 3, 2954 (2013).

2012 (2)

J. J. Yu, H. J. Chen, Y. B. Wu, and S. Y. Liu, EPL 100, 47007 (2012).

Y. Poo, R. X. Wu, S. Y. Liu, Y. Yang, Z. F. Lin, and S. T. Chui, Appl. Phys. Lett. 101, 081912 (2012).
[CrossRef]

2011 (4)

M. Shen, L. X. Ruan, X. L. Wang, J. L. Shi, and Q. Wang, Phys. Rev. A 83, 045804 (2011).
[CrossRef]

V. Yannopapas and A. Vanakaras, Phys. Rev. B 84, 045128 (2011).
[CrossRef]

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 84, 045425 (2011).
[CrossRef]

2010 (1)

N. I. Zheludev, Science 328, 582 (2010).
[CrossRef]

2009 (1)

J. J. Jin, S. Y. Liu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 80, 115101 (2009).
[CrossRef]

2008 (4)

N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, Opt. Lett. 33, 2350 (2008).
[CrossRef]

X. Y. Hu, P. Jian, C. Y. Ding, H. Yang, and Q. H. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

S. Y. Liu, J. J. Du, Z. F. Lin, R. X. Wu, and S. T. Chui, Phys. Rev. B 78, 155101 (2008).
[CrossRef]

S. Y. Liu, W. K. Chen, J. J. Du, Z. F. Lin, S. T. Chui, and C. T. Chan, Phys. Rev. Lett. 101, 157407 (2008).
[CrossRef]

2007 (1)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).
[CrossRef]

2006 (5)

V. V. Kotlyar and A. G. Nalimov, Opt. Express 14, 6316 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

D. Schurig, J. Mock, B. Justice, S. Cummer, J. B. Pendry, A. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

2005 (1)

N. Fang, H. Lee, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef]

2000 (2)

P. Halevi and F. Ramos-Mendieta, Phys. Rev. Lett. 85, 1875 (2000).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

1999 (2)

K. Busch and S. John, Phys. Rev. Lett. 83, 967 (1999).
[CrossRef]

M. Golosovsky, Y. Saado, and D. Davidov, Appl. Phys. Lett. 75, 4168 (1999).
[CrossRef]

1982 (1)

H. A. Algra and P. Hansen, Appl. Phys. A 29, 83 (1982).
[CrossRef]

Algra, H. A.

H. A. Algra and P. Hansen, Appl. Phys. A 29, 83 (1982).
[CrossRef]

Alù, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Bi, K.

K. Bi, G. Y. Dong, X. J. Fu, and J. Zhou, Appl. Phys. Lett. 103, 131915 (2013).
[CrossRef]

Busch, K.

K. Busch and S. John, Phys. Rev. Lett. 83, 967 (1999).
[CrossRef]

Capasso, F.

N. F. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[CrossRef]

Chan, C. T.

Y. S. Ding, C. T. Chan, and R. P. Wang, Sci. Rep. 3, 2954 (2013).

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

S. Y. Liu, W. K. Chen, J. J. Du, Z. F. Lin, S. T. Chui, and C. T. Chan, Phys. Rev. Lett. 101, 157407 (2008).
[CrossRef]

Chen, H. J.

J. J. Yu, H. J. Chen, Y. B. Wu, and S. Y. Liu, EPL 100, 47007 (2012).

Chen, W. K.

S. Y. Liu, W. K. Chen, J. J. Du, Z. F. Lin, S. T. Chui, and C. T. Chan, Phys. Rev. Lett. 101, 157407 (2008).
[CrossRef]

Chui, S. T.

Y. Poo, R. X. Wu, S. Y. Liu, Y. Yang, Z. F. Lin, and S. T. Chui, Appl. Phys. Lett. 101, 081912 (2012).
[CrossRef]

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 84, 045425 (2011).
[CrossRef]

J. J. Jin, S. Y. Liu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 80, 115101 (2009).
[CrossRef]

S. Y. Liu, W. K. Chen, J. J. Du, Z. F. Lin, S. T. Chui, and C. T. Chan, Phys. Rev. Lett. 101, 157407 (2008).
[CrossRef]

S. Y. Liu, J. J. Du, Z. F. Lin, R. X. Wu, and S. T. Chui, Phys. Rev. B 78, 155101 (2008).
[CrossRef]

Cummer, S.

D. Schurig, J. Mock, B. Justice, S. Cummer, J. B. Pendry, A. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Davidov, D.

M. Golosovsky, Y. Saado, and D. Davidov, Appl. Phys. Lett. 75, 4168 (1999).
[CrossRef]

Ding, C. Y.

X. Y. Hu, P. Jian, C. Y. Ding, H. Yang, and Q. H. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Ding, Y. S.

Y. S. Ding, C. T. Chan, and R. P. Wang, Sci. Rep. 3, 2954 (2013).

Dong, G. Y.

K. Bi, G. Y. Dong, X. J. Fu, and J. Zhou, Appl. Phys. Lett. 103, 131915 (2013).
[CrossRef]

Du, J. J.

S. Y. Liu, W. K. Chen, J. J. Du, Z. F. Lin, S. T. Chui, and C. T. Chan, Phys. Rev. Lett. 101, 157407 (2008).
[CrossRef]

S. Y. Liu, J. J. Du, Z. F. Lin, R. X. Wu, and S. T. Chui, Phys. Rev. B 78, 155101 (2008).
[CrossRef]

Engheta, N.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Fainstein, A.

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, Phys. Rev. Lett. 110, 037403 (2013).
[CrossRef]

Fang, N.

N. Fang, H. Lee, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Fu, X. J.

K. Bi, G. Y. Dong, X. J. Fu, and J. Zhou, Appl. Phys. Lett. 103, 131915 (2013).
[CrossRef]

Gabitov, I. R.

Golosovsky, M.

M. Golosovsky, Y. Saado, and D. Davidov, Appl. Phys. Lett. 75, 4168 (1999).
[CrossRef]

Gong, Q. H.

X. Y. Hu, P. Jian, C. Y. Ding, H. Yang, and Q. H. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Halevi, P.

P. Halevi and F. Ramos-Mendieta, Phys. Rev. Lett. 85, 1875 (2000).
[CrossRef]

Hang, Z. H.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

Hansen, P.

H. A. Algra and P. Hansen, Appl. Phys. A 29, 83 (1982).
[CrossRef]

Hu, X. Y.

X. Y. Hu, P. Jian, C. Y. Ding, H. Yang, and Q. H. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Huang, X. Q.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

Jian, P.

X. Y. Hu, P. Jian, C. Y. Ding, H. Yang, and Q. H. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Jin, J. J.

J. J. Jin, S. Y. Liu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 80, 115101 (2009).
[CrossRef]

John, S.

K. Busch and S. John, Phys. Rev. Lett. 83, 967 (1999).
[CrossRef]

Jusserand, B.

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, Phys. Rev. Lett. 110, 037403 (2013).
[CrossRef]

Justice, B.

D. Schurig, J. Mock, B. Justice, S. Cummer, J. B. Pendry, A. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Kotlyar, V. V.

Lai, Y.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

Lanzillotti-Kimura, N. D.

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, Phys. Rev. Lett. 110, 037403 (2013).
[CrossRef]

Lee, H.

N. Fang, H. Lee, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

N. Fang, H. Lee, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Lin, Z. F.

Y. Poo, R. X. Wu, S. Y. Liu, Y. Yang, Z. F. Lin, and S. T. Chui, Appl. Phys. Lett. 101, 081912 (2012).
[CrossRef]

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 84, 045425 (2011).
[CrossRef]

J. J. Jin, S. Y. Liu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 80, 115101 (2009).
[CrossRef]

S. Y. Liu, W. K. Chen, J. J. Du, Z. F. Lin, S. T. Chui, and C. T. Chan, Phys. Rev. Lett. 101, 157407 (2008).
[CrossRef]

S. Y. Liu, J. J. Du, Z. F. Lin, R. X. Wu, and S. T. Chui, Phys. Rev. B 78, 155101 (2008).
[CrossRef]

Litchinitser, N. M.

Liu, S. Y.

Y. Poo, R. X. Wu, S. Y. Liu, Y. Yang, Z. F. Lin, and S. T. Chui, Appl. Phys. Lett. 101, 081912 (2012).
[CrossRef]

J. J. Yu, H. J. Chen, Y. B. Wu, and S. Y. Liu, EPL 100, 47007 (2012).

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 84, 045425 (2011).
[CrossRef]

J. J. Jin, S. Y. Liu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 80, 115101 (2009).
[CrossRef]

S. Y. Liu, W. K. Chen, J. J. Du, Z. F. Lin, S. T. Chui, and C. T. Chan, Phys. Rev. Lett. 101, 157407 (2008).
[CrossRef]

S. Y. Liu, J. J. Du, Z. F. Lin, R. X. Wu, and S. T. Chui, Phys. Rev. B 78, 155101 (2008).
[CrossRef]

Lu, W. L.

S. Y. Liu, W. L. Lu, Z. F. Lin, and S. T. Chui, Phys. Rev. B 84, 045425 (2011).
[CrossRef]

Maimistov, A. I.

Mock, J.

D. Schurig, J. Mock, B. Justice, S. Cummer, J. B. Pendry, A. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Nalimov, A. G.

Ozbay, E.

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

Pendry, J. B.

D. Schurig, J. Mock, B. Justice, S. Cummer, J. B. Pendry, A. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Perrin, B.

A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, Phys. Rev. Lett. 110, 037403 (2013).
[CrossRef]

Poo, Y.

Y. Poo, R. X. Wu, S. Y. Liu, Y. Yang, Z. F. Lin, and S. T. Chui, Appl. Phys. Lett. 101, 081912 (2012).
[CrossRef]

Pozar, D. M.

D. M. Pozar, Microwave Engineering (Wiley, New York, 2004).

Ramos-Mendieta, F.

P. Halevi and F. Ramos-Mendieta, Phys. Rev. Lett. 85, 1875 (2000).
[CrossRef]

Ruan, L. X.

M. Shen, L. X. Ruan, X. L. Wang, J. L. Shi, and Q. Wang, Phys. Rev. A 83, 045804 (2011).
[CrossRef]

Saado, Y.

M. Golosovsky, Y. Saado, and D. Davidov, Appl. Phys. Lett. 75, 4168 (1999).
[CrossRef]

Sagdeev, R. Z.

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef]

Schurig, D.

D. Schurig, J. Mock, B. Justice, S. Cummer, J. B. Pendry, A. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

Shalaev, V. M.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef]

Shen, M.

M. Shen, L. X. Ruan, X. L. Wang, J. L. Shi, and Q. Wang, Phys. Rev. A 83, 045804 (2011).
[CrossRef]

Shi, J. L.

M. Shen, L. X. Ruan, X. L. Wang, J. L. Shi, and Q. Wang, Phys. Rev. A 83, 045804 (2011).
[CrossRef]

Silveirinha, M.

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Smith, D. R.

D. Schurig, J. Mock, B. Justice, S. Cummer, J. B. Pendry, A. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef]

Starr, A.

D. Schurig, J. Mock, B. Justice, S. Cummer, J. B. Pendry, A. Starr, and D. R. Smith, Science 314, 977 (2006).
[CrossRef]

Sun, C.

N. Fang, H. Lee, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Vanakaras, A.

V. Yannopapas and A. Vanakaras, Phys. Rev. B 84, 045128 (2011).
[CrossRef]

Wang, Q.

M. Shen, L. X. Ruan, X. L. Wang, J. L. Shi, and Q. Wang, Phys. Rev. A 83, 045804 (2011).
[CrossRef]

Wang, R. P.

Y. S. Ding, C. T. Chan, and R. P. Wang, Sci. Rep. 3, 2954 (2013).

Wang, X. L.

M. Shen, L. X. Ruan, X. L. Wang, J. L. Shi, and Q. Wang, Phys. Rev. A 83, 045804 (2011).
[CrossRef]

Wu, R. X.

Y. Poo, R. X. Wu, S. Y. Liu, Y. Yang, Z. F. Lin, and S. T. Chui, Appl. Phys. Lett. 101, 081912 (2012).
[CrossRef]

S. Y. Liu, J. J. Du, Z. F. Lin, R. X. Wu, and S. T. Chui, Phys. Rev. B 78, 155101 (2008).
[CrossRef]

Wu, Y. B.

J. J. Yu, H. J. Chen, Y. B. Wu, and S. Y. Liu, EPL 100, 47007 (2012).

Yang, H.

X. Y. Hu, P. Jian, C. Y. Ding, H. Yang, and Q. H. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Yang, Y.

Y. Poo, R. X. Wu, S. Y. Liu, Y. Yang, Z. F. Lin, and S. T. Chui, Appl. Phys. Lett. 101, 081912 (2012).
[CrossRef]

Yannopapas, V.

V. Yannopapas and A. Vanakaras, Phys. Rev. B 84, 045128 (2011).
[CrossRef]

Yu, J. J.

J. J. Yu, H. J. Chen, Y. B. Wu, and S. Y. Liu, EPL 100, 47007 (2012).

Yu, N. F.

N. F. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef]

Zheludev, N. I.

N. I. Zheludev, Science 328, 582 (2010).
[CrossRef]

Zheng, H. H.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

Zhou, J.

K. Bi, G. Y. Dong, X. J. Fu, and J. Zhou, Appl. Phys. Lett. 103, 131915 (2013).
[CrossRef]

Appl. Phys. A (1)

H. A. Algra and P. Hansen, Appl. Phys. A 29, 83 (1982).
[CrossRef]

Appl. Phys. Lett. (3)

K. Bi, G. Y. Dong, X. J. Fu, and J. Zhou, Appl. Phys. Lett. 103, 131915 (2013).
[CrossRef]

M. Golosovsky, Y. Saado, and D. Davidov, Appl. Phys. Lett. 75, 4168 (1999).
[CrossRef]

Y. Poo, R. X. Wu, S. Y. Liu, Y. Yang, Z. F. Lin, and S. T. Chui, Appl. Phys. Lett. 101, 081912 (2012).
[CrossRef]

EPL (1)

J. J. Yu, H. J. Chen, Y. B. Wu, and S. Y. Liu, EPL 100, 47007 (2012).

Nat. Mater. (2)

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, Nat. Mater. 10, 582 (2011).
[CrossRef]

N. F. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[CrossRef]

Nat. Photonics (1)

X. Y. Hu, P. Jian, C. Y. Ding, H. Yang, and Q. H. Gong, Nat. Photonics 2, 185 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

M. Shen, L. X. Ruan, X. L. Wang, J. L. Shi, and Q. Wang, Phys. Rev. A 83, 045804 (2011).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Photonic band diagrams (a), (c), and (e) and the real parts of the retrieved effective parameters εeff and μeff (b), (d), and (f) under three different temperatures: (a), (b) T=306K; (c), (d) T=335K; and (e), (f) T=362K. The hexagonal MM has the lattice constant a=10mm and rod radius rs=3.4mm, magnetized under an effective magnetic field H0=485Oe. The green solid line marks the working frequency fw=2.53GHz. In calculating photonic band diagrams, loss is neglected.

Fig. 2.
Fig. 2.

Real parts of the effective electric permittivity εeff and the magnetic permeability μeff versus the temperature T from 273.15 to 373.15 K at the working frequency fw=2.53GHz. The saturation magnetization 4πMs is also plotted as the function of T as marked by the blue dotted line.

Fig. 3.
Fig. 3.

Electric field intensity |E|2 (a)–(e) and electric field Re{E} (f)–(o) patterns for a Gaussian beam illuminating a prism with the apex angle θ=90° under the temperatures T=306K (a), (f), (k); T=335K (b), (g), (l); T=362K (c), (h), (m); T=367K (d), (i), (n); and T=281K (e), (j), (o). Panels (a)–(j)/(k)–(o) are results without/with loss.

Equations (1)

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μ^=(μriμκ0iμκμr0001),

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