Abstract

The microwave zero index metamaterials (ZIMs) can be realized by loading lumped elements into two-dimensional transmission lines (TLs) with Dirac cones whose linear dispersion can appear around the center of the Brillouin zone. Based on Snell’s law, the refracted angle of waves nearly equals zero when a point source radiates from the ZIM TL into the double positive (DPS) one in the ZIM-DPS TL structure. Experimental results demonstrate that at Dirac point the curved wavefronts in the ZIM region are transformed into planar ones in DPS region.

© 2012 Optical Society of America

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2012 (3)

2011 (1)

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

2010 (3)

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

Y. Jin, P. Zhang, and S. He, Phys. Rev. B. 81, 085117 (2010).
[CrossRef]

2009 (1)

2008 (1)

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

2007 (2)

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

H. T. Jiang, H. Chen, and S. Y. Zhu, Opt. Lett. 32, 1980 (2007).
[CrossRef]

2006 (1)

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

2004 (2)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 5685 (2004).

R. W. Ziolkowski, Phys. Rev. E. 70, 046608 (2004).
[CrossRef]

2003 (2)

A. Grbic and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 51, 2604 (2003).
[CrossRef]

A. K. Iyer, P. C. Kremer, and G. V. Eleftheriades, Opt. Express 11, 696 (2003).
[CrossRef]

2002 (1)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

2000 (1)

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

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Alù, A.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

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

Caloz, C.

C. Caloz and T. Itoh, Electromagnetic Metamaterials, Transmission Line Theory and Microwave Applications (Wiley, 2006).

Chan, C. T.

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

Chen, H.

Chen, L.

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

Edwards, B.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 51, 2604 (2003).
[CrossRef]

A. K. Iyer, P. C. Kremer, and G. V. Eleftheriades, Opt. Express 11, 696 (2003).
[CrossRef]

Engheta, N.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

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]

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Fang, K.

K. Fang, L. W. Zhang, F. F. Li, W. S. Wang, and Y. W. Zhang, iWAT, 5752350 (2011).

Feng, S.

S. Feng, Phys. Rev. Lett. 108, 193904 (2012).
[CrossRef]

Grbic, A.

A. Grbic and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 51, 2604 (2003).
[CrossRef]

Guérin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Halterman, K.

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

Hang, Z. H.

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

Hao, J.

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

He, S.

Y. Jin, P. Zhang, and S. He, Phys. Rev. B. 81, 085117 (2010).
[CrossRef]

Huang, X.

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

Itoh, T.

C. Caloz and T. Itoh, Electromagnetic Metamaterials, Transmission Line Theory and Microwave Applications (Wiley, 2006).

Iyer, A. K.

Jiang, H. T.

Jin, Y.

Y. Jin, P. Zhang, and S. He, Phys. Rev. B. 81, 085117 (2010).
[CrossRef]

Kremer, P. C.

Lai, Y.

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

Li, F. F.

K. Fang, L. W. Zhang, F. F. Li, W. S. Wang, and Y. W. Zhang, iWAT, 5752350 (2011).

Nguyen, V. C.

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 5685 (2004).

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

Qiu, M.

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Sakoda, K.

Salandrino, A.

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

Silveirinha, M.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

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. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 5685 (2004).

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

Wang, L. G.

Wang, W. S.

K. Fang, L. W. Zhang, F. F. Li, W. S. Wang, and Y. W. Zhang, iWAT, 5752350 (2011).

Wang, Z. G.

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 5685 (2004).

Yan, W.

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

Zhang, J. X.

Zhang, L. W.

K. Fang, L. W. Zhang, F. F. Li, W. S. Wang, and Y. W. Zhang, iWAT, 5752350 (2011).

Zhang, P.

Y. Jin, P. Zhang, and S. He, Phys. Rev. B. 81, 085117 (2010).
[CrossRef]

Zhang, Y. W.

K. Fang, L. W. Zhang, F. F. Li, W. S. Wang, and Y. W. Zhang, iWAT, 5752350 (2011).

Zheng, H.

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

Zhu, S. Y.

Ziolkowski, R. W.

R. W. Ziolkowski, Phys. Rev. E. 70, 046608 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

J. Hao, W. Yan, and M. Qiu, Appl. Phys. Lett. 96, 101109 (2010).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Grbic and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 51, 2604 (2003).
[CrossRef]

Nat. Mater. (1)

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

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. B. (2)

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

Y. Jin, P. Zhang, and S. He, Phys. Rev. B. 81, 085117 (2010).
[CrossRef]

Phys. Rev. E. (1)

R. W. Ziolkowski, Phys. Rev. E. 70, 046608 (2004).
[CrossRef]

Phys. Rev. Lett. (6)

S. Feng, Phys. Rev. Lett. 108, 193904 (2012).
[CrossRef]

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

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef]

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

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 033903 (2008).
[CrossRef]

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

Science (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 5685 (2004).

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (2)

C. Caloz and T. Itoh, Electromagnetic Metamaterials, Transmission Line Theory and Microwave Applications (Wiley, 2006).

K. Fang, L. W. Zhang, F. F. Li, W. S. Wang, and Y. W. Zhang, iWAT, 5752350 (2011).

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Figures (4)

Fig. 1.
Fig. 1.

Dispersion relation with Dirac point in 2D balanced CRLH microwave metamaterials. Left: Dispersion relation. Right: Zoom of the linear dispersion around the Dirac point.

Fig. 2.
Fig. 2.

(a) 2D microwave collimation sample. (b) Transient voltage distribution at Dirac point frequency from experimental measurements.

Fig. 3.
Fig. 3.

Time-domain experimental results of waveforms in the ZIM-DPS microwave collimation sample.

Fig. 4.
Fig. 4.

Phase differences of the signal in different columns along x axis in DPS region.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

kx2+ky2=[β1/Z0ωCd]·[2βZ0/ωLd],
k2d2=ZY=(1/ωωLrCd)2/CL.
ω=ω0+c1k+O(k2),
μ=(Lr1/ω2Cd)/g
ε=g(Cr1/ω2Ld),

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