Abstract

We present a theoretical and experimental investigation into the energy transport in a conjugate matched bilayer consisting of ε-negative (ENG) and μ-negative (MNG) slabs. It is proved that the conjugated matched ENG/MNG bilayer is a subwavelength open-cavity resonator, in which the resonance frequency is determined by the complete tunneling condition, and the Q factor increases exponentially with the slab thickness. It is revealed that the wave is not evanescent inside the bilayer, but it is a hybrid of a traveling wave and a reactive standing wave. It is also manifested during the transient wave propagation that the reactive field energy stored inside the bilayer is provided by the incident wave.

© 2011 Optical Society of America

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    [CrossRef]

2010

2009

C. Ciracì and E. Centeno, Phys. Rev. Lett. 103, 063901(2009).
[CrossRef] [PubMed]

S. M. Xiao, U. D. Chettiar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, Opt. Lett. 34, 3478 (2009).
[CrossRef] [PubMed]

D. A. Powell, A. Alù, B. Edwards, A. Vakil, Y. S. Kivshar, and N. Engheta, Phys. Rev. B 79, 245135 (2009).
[CrossRef]

2008

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

2007

R. P. Liu, B. Zhao, X. Q. Lin, Q. Cheng, and T. J. Cui, Phys. Rev. B 75, 125118 (2007).
[CrossRef]

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

2006

A. Alù, N. Engheta, and R. W. Ziolkowski, Phys. Rev. E 74, 016604 (2006).
[CrossRef]

T. L. Floyd, Electric Circuit Fundamentals, 2nd ed. (Prentice Hall, 2006).

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

Y. Z. Wang, Y. W. Zhang, L. He, H. Q. Li, H. Chen, F. Q. Liu, and C. Caloz, J. Appl. Phys. 100, 113503 (2006).
[CrossRef]

2005

L. Zhou, W. J. Wen, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

2003

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

A. Alù and N. Engheta, IEEE Trans. Antennas Propag. 51, 2558 (2003).
[CrossRef]

2000

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).
[CrossRef]

1995

P. S. Neelakanta, Handbook of Electromagnetic Materials (CRC Press, 1995).

1968

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

Alù, A.

D. A. Powell, A. Alù, B. Edwards, A. Vakil, Y. S. Kivshar, and N. Engheta, Phys. Rev. B 79, 245135 (2009).
[CrossRef]

A. Alù, N. Engheta, and R. W. Ziolkowski, Phys. Rev. E 74, 016604 (2006).
[CrossRef]

A. Alù and N. Engheta, IEEE Trans. Antennas Propag. 51, 2558 (2003).
[CrossRef]

Bartal, G.

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

Caloz, C.

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

Y. Z. Wang, Y. W. Zhang, L. He, H. Q. Li, H. Chen, F. Q. Liu, and C. Caloz, J. Appl. Phys. 100, 113503 (2006).
[CrossRef]

Centeno, E.

C. Ciracì and E. Centeno, Phys. Rev. Lett. 103, 063901(2009).
[CrossRef] [PubMed]

Chan, C. T.

L. Zhou, W. J. Wen, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

Chen, H.

Y. Z. Wang, Y. W. Zhang, L. He, H. Q. Li, H. Chen, F. Q. Liu, and C. Caloz, J. Appl. Phys. 100, 113503 (2006).
[CrossRef]

Cheng, Q.

R. P. Liu, B. Zhao, X. Q. Lin, Q. Cheng, and T. J. Cui, Phys. Rev. B 75, 125118 (2007).
[CrossRef]

Chettiar, U. D.

Ciracì, C.

C. Ciracì and E. Centeno, Phys. Rev. Lett. 103, 063901(2009).
[CrossRef] [PubMed]

Cui, T. J.

R. P. Liu, B. Zhao, X. Q. Lin, Q. Cheng, and T. J. Cui, Phys. Rev. B 75, 125118 (2007).
[CrossRef]

Drachev, V. P.

Du, B.

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Economou, E. N.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Edwards, B.

D. A. Powell, A. Alù, B. Edwards, A. Vakil, Y. S. Kivshar, and N. Engheta, Phys. Rev. B 79, 245135 (2009).
[CrossRef]

Engheta, N.

D. A. Powell, A. Alù, B. Edwards, A. Vakil, Y. S. Kivshar, and N. Engheta, Phys. Rev. B 79, 245135 (2009).
[CrossRef]

A. Alù, N. Engheta, and R. W. Ziolkowski, Phys. Rev. E 74, 016604 (2006).
[CrossRef]

A. Alù and N. Engheta, IEEE Trans. Antennas Propag. 51, 2558 (2003).
[CrossRef]

Floyd, T. L.

T. L. Floyd, Electric Circuit Fundamentals, 2nd ed. (Prentice Hall, 2006).

Foteinopoulou, S.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Genov, D. A.

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Ham, B. S.

He, L.

Y. Z. Wang, Y. W. Zhang, L. He, H. Q. Li, H. Chen, F. Q. Liu, and C. Caloz, J. Appl. Phys. 100, 113503 (2006).
[CrossRef]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

Itoh, T.

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

Kang, L.

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Kildishev, A. V.

Kivshar, Y. S.

D. A. Powell, A. Alù, B. Edwards, A. Vakil, Y. S. Kivshar, and N. Engheta, Phys. Rev. B 79, 245135 (2009).
[CrossRef]

Lee, H.

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Lee, Y. P.

Li, H. Q.

Y. Z. Wang, Y. W. Zhang, L. He, H. Q. Li, H. Chen, F. Q. Liu, and C. Caloz, J. Appl. Phys. 100, 113503 (2006).
[CrossRef]

Lin, X. Q.

R. P. Liu, B. Zhao, X. Q. Lin, Q. Cheng, and T. J. Cui, Phys. Rev. B 75, 125118 (2007).
[CrossRef]

Liu, F. Q.

Y. Z. Wang, Y. W. Zhang, L. He, H. Q. Li, H. Chen, F. Q. Liu, and C. Caloz, J. Appl. Phys. 100, 113503 (2006).
[CrossRef]

Liu, R. P.

R. P. Liu, B. Zhao, X. Q. Lin, Q. Cheng, and T. J. Cui, Phys. Rev. B 75, 125118 (2007).
[CrossRef]

Liu, Z. W.

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Lu, Y. H.

Neelakanta, P. S.

P. S. Neelakanta, Handbook of Electromagnetic Materials (CRC Press, 1995).

Powell, D. A.

D. A. Powell, A. Alù, B. Edwards, A. Vakil, Y. S. Kivshar, and N. Engheta, Phys. Rev. B 79, 245135 (2009).
[CrossRef]

Shalaev, V. M.

Sheng, P.

L. Zhou, W. J. Wen, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

Soukoulis, C. M.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Sullivan, D. M.

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).
[CrossRef]

Sun, C.

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

Ulin-Avila, E.

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Vakil, A.

D. A. Powell, A. Alù, B. Edwards, A. Vakil, Y. S. Kivshar, and N. Engheta, Phys. Rev. B 79, 245135 (2009).
[CrossRef]

Veselago, V. S.

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

Wang, Y. Z.

Y. Z. Wang, Y. W. Zhang, L. He, H. Q. Li, H. Chen, F. Q. Liu, and C. Caloz, J. Appl. Phys. 100, 113503 (2006).
[CrossRef]

Wen, W. J.

L. Zhou, W. J. Wen, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

Xiao, S. M.

Xiong, Y.

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Xu, H.

Zhang, X.

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Zhang, Y. W.

Y. Z. Wang, Y. W. Zhang, L. He, H. Q. Li, H. Chen, F. Q. Liu, and C. Caloz, J. Appl. Phys. 100, 113503 (2006).
[CrossRef]

Zhao, B.

R. P. Liu, B. Zhao, X. Q. Lin, Q. Cheng, and T. J. Cui, Phys. Rev. B 75, 125118 (2007).
[CrossRef]

Zhao, H.

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Zhao, Q.

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Zhou, L.

L. Zhou, W. J. Wen, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

Ziolkowski, R. W.

A. Alù, N. Engheta, and R. W. Ziolkowski, Phys. Rev. E 74, 016604 (2006).
[CrossRef]

IEEE Trans. Antennas Propag.

A. Alù and N. Engheta, IEEE Trans. Antennas Propag. 51, 2558 (2003).
[CrossRef]

J. Appl. Phys.

Y. Z. Wang, Y. W. Zhang, L. He, H. Q. Li, H. Chen, F. Q. Liu, and C. Caloz, J. Appl. Phys. 100, 113503 (2006).
[CrossRef]

Nature

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, Nature 450, 397 (2007).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

R. P. Liu, B. Zhao, X. Q. Lin, Q. Cheng, and T. J. Cui, Phys. Rev. B 75, 125118 (2007).
[CrossRef]

D. A. Powell, A. Alù, B. Edwards, A. Vakil, Y. S. Kivshar, and N. Engheta, Phys. Rev. B 79, 245135 (2009).
[CrossRef]

Phys. Rev. E

A. Alù, N. Engheta, and R. W. Ziolkowski, Phys. Rev. E 74, 016604 (2006).
[CrossRef]

Phys. Rev. Lett.

L. Zhou, W. J. Wen, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 94, 243905 (2005).
[CrossRef]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

C. Ciracì and E. Centeno, Phys. Rev. Lett. 103, 063901(2009).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, H. Zhao, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Phys. Rev. Lett. 101, 027402 (2008).
[CrossRef] [PubMed]

Science

Z. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Sov. Phys. Usp.

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

Other

T. L. Floyd, Electric Circuit Fundamentals, 2nd ed. (Prentice Hall, 2006).

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

P. S. Neelakanta, Handbook of Electromagnetic Materials (CRC Press, 1995).

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Normalized amplitudes (left scale) and phases of electric and magnetic fields and their phase difference (right scale) in a conjugate matched ENG/MNG bilayer.

Fig. 2
Fig. 2

FDTD simulated time histories of the electric fields at the entrance to ENG, at the ENG/MNG interface and at the exit of MNG slab, respectively.

Fig. 3
Fig. 3

Simulated and measured S-parameters of the ENG TL, MNG TL containing ten TL units and the pair ENG 6 MNG 6 , respectively. Insets, the circuit model and the fabricated pair structure.

Fig. 4
Fig. 4

Simulated and measured charging-up characteristic time (logarithmic scale) of ENG n / MNG n versus the unit number n with different dielectric loss. Inset, analytical and FDTD-simulated τ / T versus thickness d.

Equations (5)

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

| μ 1 | | ε 1 | d 1 = | μ 2 | | ε 2 | d 2 and | μ 1 | / | ε 1 | = | μ 2 | / | ε 2 | ,
E x 1 = E 0 cos h ( k z ) j η η 0 E 0 sin h ( k z ) = | E x 1 | e j θ E 1 ,
H y 1 = E 0 η 0 cos h ( k z ) + j E 0 η sin h ( k z ) = | H y 1 | e j θ H 1 .
E x 2 = E 0 cos h [ k ( z 2 d ) ] + j η η 0 E 0 sin h [ k ( z 2 d ) ] = | E x 2 | e j θ E 2 ,
H y 2 = E 0 η 0 cos h [ k ( z - 2 d ) ] j E 0 η sin h [ k ( z 2 d ) ] = | H y 2 | e j θ H 2 ,

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