Abstract

We study theoretically the properties of a thin film of a semiconductor embedded in the interface of two kinds of single-negative materials. At some frequencies the structure with suitable size is equivalent to an effective (near) zero-index medium. The coupling of exciton resonance in the semiconductor and the interface mode in a zero-index medium leads to Rabi splitting. Compared with Rabi splitting observed in cavities, the splitting modes in zero-index media are robust against the scaling change of the length and direction of incident wave.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2006 (2)

2005 (3)

2004 (2)

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, Phys. Rev. E 69, 066607 (2004).
[CrossRef]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

2003 (3)

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

A. Lakhtakia and C. M. Krowne, Optik (Stuttgart) 114, 305 (2003).
[CrossRef]

A. Lakhtakia and J. A. Sherwin, Int. J. Infrared Millim. Waves 24, 19 (2003).
[CrossRef]

2002 (2)

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

D. R. Fredkin and A. Ron, Appl. Phys. Lett. 81, 1753 (2002).
[CrossRef]

2001 (2)

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

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

2000 (1)

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, Phys. Rev. Lett. 84, 2136 (2000).
[CrossRef] [PubMed]

1999 (2)

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, Rev. Mod. Phys. 71, 1591 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

1998 (1)

S. Haroche, Phys. Today 51(7), 36 (1998).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

1992 (1)

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992).
[CrossRef] [PubMed]

1946 (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Alu, A.

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

Arakawa, Y.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992).
[CrossRef] [PubMed]

Brune, M.

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

Chen, H.

H. T. Jiang, H. Chen, and S. Y. Zhu, Phys. Rev. E 73, 046601 (2006).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, Phys. Rev. E 69, 066607 (2004).
[CrossRef]

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, Phys. Rev. Lett. 84, 2136 (2000).
[CrossRef] [PubMed]

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Dolling, G.

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Engheta, N.

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

Enkrich, C.

Enoch, S.

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

Fleischhauer, M.

J. Kästel and M. Fleischhauer, Phys. Rev. A 71, 011804(R) (2005).
[CrossRef]

Fredkin, D. R.

D. R. Fredkin and A. Ron, Appl. Phys. Lett. 81, 1753 (2002).
[CrossRef]

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, Rev. Mod. Phys. 71, 1591 (1999).
[CrossRef]

Guérin, N.

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

Haroche, S.

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

S. Haroche, Phys. Today 51(7), 36 (1998).
[CrossRef]

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Ishikawa, A.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992).
[CrossRef] [PubMed]

Jahnke, F.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, Rev. Mod. Phys. 71, 1591 (1999).
[CrossRef]

Jiang, H. T.

H. T. Jiang, H. Chen, and S. Y. Zhu, Phys. Rev. E 73, 046601 (2006).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, Phys. Rev. E 69, 066607 (2004).
[CrossRef]

Kästel, J.

J. Kästel and M. Fleischhauer, Phys. Rev. A 71, 011804(R) (2005).
[CrossRef]

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, Rev. Mod. Phys. 71, 1591 (1999).
[CrossRef]

Kim, K. Y.

Kira, M.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, Rev. Mod. Phys. 71, 1591 (1999).
[CrossRef]

Koch, S. W.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, Rev. Mod. Phys. 71, 1591 (1999).
[CrossRef]

Krowne, C. M.

A. Lakhtakia and C. M. Krowne, Optik (Stuttgart) 114, 305 (2003).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia and J. A. Sherwin, Int. J. Infrared Millim. Waves 24, 19 (2003).
[CrossRef]

A. Lakhtakia and C. M. Krowne, Optik (Stuttgart) 114, 305 (2003).
[CrossRef]

Li, H. Q.

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, Phys. Rev. E 69, 066607 (2004).
[CrossRef]

Linden, S.

Nishioka, M.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Purcell, E. M.

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Raimond, J. M.

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Ron, A.

D. R. Fredkin and A. Ron, Appl. Phys. Lett. 81, 1753 (2002).
[CrossRef]

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Sabouroux, P.

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

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Schultz, S.

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

Shchekin, O. B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Shelby, R. A.

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

Sherwin, J. A.

A. Lakhtakia and J. A. Sherwin, Int. J. Infrared Millim. Waves 24, 19 (2003).
[CrossRef]

Smith, D. R.

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

Soukoulis, C. M.

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Tayeb, G.

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

Vincent, P.

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

Wegener, M.

Weisbuch, C.

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992).
[CrossRef] [PubMed]

Yang, Y. P.

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, Phys. Rev. Lett. 84, 2136 (2000).
[CrossRef] [PubMed]

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

Zhang, Y. W.

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, Phys. Rev. E 69, 066607 (2004).
[CrossRef]

Zheng, H.

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, Phys. Rev. Lett. 84, 2136 (2000).
[CrossRef] [PubMed]

Zhou, J. F.

Zhu, S. Y.

H. T. Jiang, H. Chen, and S. Y. Zhu, Phys. Rev. E 73, 046601 (2006).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, Phys. Rev. E 69, 066607 (2004).
[CrossRef]

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, Phys. Rev. Lett. 84, 2136 (2000).
[CrossRef] [PubMed]

Zi, J.

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, Phys. Rev. E 69, 066607 (2004).
[CrossRef]

Zubairy, M. S.

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, Phys. Rev. Lett. 84, 2136 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

D. R. Fredkin and A. Ron, Appl. Phys. Lett. 81, 1753 (2002).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

A. Lakhtakia and J. A. Sherwin, Int. J. Infrared Millim. Waves 24, 19 (2003).
[CrossRef]

Nature (1)

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, Nature 432, 200 (2004).
[CrossRef] [PubMed]

Opt. Lett. (3)

Optik (Stuttgart) (1)

A. Lakhtakia and C. M. Krowne, Optik (Stuttgart) 114, 305 (2003).
[CrossRef]

Phys. Rev. (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).
[CrossRef]

Phys. Rev. A (1)

J. Kästel and M. Fleischhauer, Phys. Rev. A 71, 011804(R) (2005).
[CrossRef]

Phys. Rev. E (2)

H. T. Jiang, H. Chen, and S. Y. Zhu, Phys. Rev. E 73, 046601 (2006).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, Phys. Rev. E 69, 066607 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

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

S. Y. Zhu, Y. P. Yang, H. Chen, H. Zheng, and M. S. Zubairy, Phys. Rev. Lett. 84, 2136 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, Phys. Rev. Lett. 69, 3314 (1992).
[CrossRef] [PubMed]

Phys. Today (1)

S. Haroche, Phys. Today 51(7), 36 (1998).
[CrossRef]

Rev. Mod. Phys. (2)

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[CrossRef]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, Rev. Mod. Phys. 71, 1591 (1999).
[CrossRef]

Science (1)

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

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Figures (4)

Fig. 1
Fig. 1

Schematic of a structure consisting of a ε-negative layer, a μ-negative layer, and a thin film of a semiconductor in the peak of an interface field.

Fig. 2
Fig. 2

(a) Transmittance of a structure with (solid line) and without (dashed line) excitons. (b) Transmittance of another structure whose lengths is scaled by 4 3 .

Fig. 3
Fig. 3

Transmittance with different incident angles for a TE wave.

Fig. 4
Fig. 4

Transmittance of structures when the thickness of the semiconductor is 5 nm .

Equations (6)

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

ε A = ε a α 2 ω 2 , μ A = μ a
ε B = ε b , μ B = μ b β 2 ω 2 + i ω Γ
χ res ( ω ) = G ( ω ω res ) + i γ ,
ε ¯ ( ω ) = ε A ( ω ) d A + ε B d B d A + d B = 0 ,
μ ¯ ( ω ) = μ A d A + μ B ( ω ) d B d A + d B = 0 .
[ 2 z 2 + ω 2 c 2 ε ( z ) μ ( z ) ] E ( z , ω ) + ω 2 c 2 χ res ( ω ) E ( z , ω ) δ ( z z 0 ) = 0 ,

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