Abstract

The possibility of laser ignition using zero index metamaterials (ZIM) is investigated theoretically. Using this method, multiple laser beams can be focused automatically regardless of the number and location of electromagnetic sources in the ZIM, and it is not necessary to aim all beams at the focus. Our calculation shows that although the size of the focus is dependent on the wavelength, the beams can be focused to a tiny spot. Methods for achieving practical performance are proposed.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2010 (4)

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

A. Ciattoni, C. Rizza, and E. Palange, Phys. Rev. A 81, 043839 (2010).
[CrossRef]

A. Ciattoni, C. Rizza, and E. Palange, Opt. Express 18, 11911(2010).
[CrossRef] [PubMed]

A. Ciattoni, C. Rizza, and E. Palange, Opt. Lett. 35, 2130(2010).
[CrossRef] [PubMed]

2009 (3)

2008 (8)

W. Jiang, T. Cui, Q. Cheng, J. Chin, X. Yang, R. Liu, and D. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

A. Yaghjian and S. Maci, New J. Phys. 10, 115022 (2008).
[CrossRef]

R. Liu, Q. Cheng, T. Hand, J. Mock, T. Cui, S. Cummer, and D. Smith, Phys. Rev. Lett. 100, 23903 (2008).
[CrossRef]

B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 33903 (2008).
[CrossRef]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

G. Yu, W. Jiang, X. Zhou, and T. Cui, Eur. Phys. J. Appl. Phys. 44, 181 (2008).
[CrossRef]

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, Photon. Nanostr. Fundam. Appl. 6, 87 (2008).
[CrossRef]

W. Wang, L. Lin, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, Opt. Express 16, 11431 (2008).
[CrossRef] [PubMed]

2007 (2)

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

M. Silveirinha and N. Engheta, Phys. Rev. B 76, 245109(2007).
[CrossRef]

2006 (4)

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

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

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

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

2004 (1)

R. Ziolkowski, Phys. Rev. E 70, 46608 (2004).
[CrossRef]

2003 (1)

J. Li, L. Zhou, C. Chan, and P. Sheng, Phys. Rev. Lett. 90, 83901 (2003).
[CrossRef]

2002 (1)

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

Alù, A.

B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 33903 (2008).
[CrossRef]

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

Chan, C.

J. Li, L. Zhou, C. Chan, and P. Sheng, Phys. Rev. Lett. 90, 83901 (2003).
[CrossRef]

Chen, H.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Cheng, Q.

R. Liu, Q. Cheng, T. Hand, J. Mock, T. Cui, S. Cummer, and D. Smith, Phys. Rev. Lett. 100, 23903 (2008).
[CrossRef]

W. Jiang, T. Cui, Q. Cheng, J. Chin, X. Yang, R. Liu, and D. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Chin, J.

W. Jiang, T. Cui, Q. Cheng, J. Chin, X. Yang, R. Liu, and D. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Ciattoni, A.

Cui, J.

Cui, T.

W. Jiang, T. Cui, Q. Cheng, J. Chin, X. Yang, R. Liu, and D. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

R. Liu, Q. Cheng, T. Hand, J. Mock, T. Cui, S. Cummer, and D. Smith, Phys. Rev. Lett. 100, 23903 (2008).
[CrossRef]

G. Yu, W. Jiang, X. Zhou, and T. Cui, Eur. Phys. J. Appl. Phys. 44, 181 (2008).
[CrossRef]

Cummer, S.

R. Liu, Q. Cheng, T. Hand, J. Mock, T. Cui, S. Cummer, and D. Smith, Phys. Rev. Lett. 100, 23903 (2008).
[CrossRef]

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, Photon. Nanostr. Fundam. Appl. 6, 87 (2008).
[CrossRef]

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

Du, C.

Edwards, B.

B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 33903 (2008).
[CrossRef]

Engheta, N.

B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 33903 (2008).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. B 76, 245109(2007).
[CrossRef]

A. Alù, M. 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] [PubMed]

Enoch, S.

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

Guerin, N.

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

Hand, T.

R. Liu, Q. Cheng, T. Hand, J. Mock, T. Cui, S. Cummer, and D. Smith, Phys. Rev. Lett. 100, 23903 (2008).
[CrossRef]

Hao, J.

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

Hu, C.

Huang, M.

Jiang, W.

W. Jiang, T. Cui, Q. Cheng, J. Chin, X. Yang, R. Liu, and D. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

G. Yu, W. Jiang, X. Zhou, and T. Cui, Eur. Phys. J. Appl. Phys. 44, 181 (2008).
[CrossRef]

Justice, B.

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

Kong, J.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Leonhardt, U.

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

Li, J.

J. Li, L. Zhou, C. Chan, and P. Sheng, Phys. Rev. Lett. 90, 83901 (2003).
[CrossRef]

Lin, L.

Liu, D.

Liu, L.

Liu, R.

R. Liu, Q. Cheng, T. Hand, J. Mock, T. Cui, S. Cummer, and D. Smith, Phys. Rev. Lett. 100, 23903 (2008).
[CrossRef]

W. Jiang, T. Cui, Q. Cheng, J. Chin, X. Yang, R. Liu, and D. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Luo, X.

Luo, Y.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Ma, J.

Maci, S.

A. Yaghjian and S. Maci, New J. Phys. 10, 115022 (2008).
[CrossRef]

Mock, J.

R. Liu, Q. Cheng, T. Hand, J. Mock, T. Cui, S. Cummer, and D. Smith, Phys. Rev. Lett. 100, 23903 (2008).
[CrossRef]

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

Palange, E.

Pendry, J.

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, Photon. Nanostr. Fundam. Appl. 6, 87 (2008).
[CrossRef]

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

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

Peng, J.

Qiu, M.

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

Rahm, M.

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, Photon. Nanostr. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Ran, L.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Rizza, C.

Roberts, D.

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, Photon. Nanostr. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Sabouroux, P.

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

Salandrino, A.

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

Schurig, D.

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, Photon. Nanostr. Fundam. Appl. 6, 87 (2008).
[CrossRef]

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

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

Sheng, P.

J. Li, L. Zhou, C. Chan, and P. Sheng, Phys. Rev. Lett. 90, 83901 (2003).
[CrossRef]

Silveirinha, M.

B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 33903 (2008).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. B 76, 245109(2007).
[CrossRef]

A. Alù, M. 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] [PubMed]

Smith, D.

R. Liu, Q. Cheng, T. Hand, J. Mock, T. Cui, S. Cummer, and D. Smith, Phys. Rev. Lett. 100, 23903 (2008).
[CrossRef]

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, Photon. Nanostr. Fundam. Appl. 6, 87 (2008).
[CrossRef]

W. Jiang, T. Cui, Q. Cheng, J. Chin, X. Yang, R. Liu, and D. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

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

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

Starr, A.

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

Tayeb, G.

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

Vincent, P.

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

Wang, C.

Wang, W.

Xiao, Z.

Yaghjian, A.

A. Yaghjian and S. Maci, New J. Phys. 10, 115022 (2008).
[CrossRef]

Yan, W.

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

Yang, C.

Yang, J.

Yang, X.

W. Jiang, T. Cui, Q. Cheng, J. Chin, X. Yang, R. Liu, and D. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

Young, M.

B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 33903 (2008).
[CrossRef]

Yu, G.

G. Yu, W. Jiang, X. Zhou, and T. Cui, Eur. Phys. J. Appl. Phys. 44, 181 (2008).
[CrossRef]

Zhai, T.

Zhang, J.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Zhao, Z.

Zhou, J.

Zhou, L.

J. Li, L. Zhou, C. Chan, and P. Sheng, Phys. Rev. Lett. 90, 83901 (2003).
[CrossRef]

Zhou, X.

G. Yu, W. Jiang, X. Zhou, and T. Cui, Eur. Phys. J. Appl. Phys. 44, 181 (2008).
[CrossRef]

Zhou, Y.

Ziolkowski, R.

R. Ziolkowski, Phys. Rev. E 70, 46608 (2004).
[CrossRef]

Appl. Phys. Lett. (2)

W. Jiang, T. Cui, Q. Cheng, J. Chin, X. Yang, R. Liu, and D. Smith, Appl. Phys. Lett. 92, 264101 (2008).
[CrossRef]

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

Eur. Phys. J. Appl. Phys. (1)

G. Yu, W. Jiang, X. Zhou, and T. Cui, Eur. Phys. J. Appl. Phys. 44, 181 (2008).
[CrossRef]

New J. Phys. (1)

A. Yaghjian and S. Maci, New J. Phys. 10, 115022 (2008).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Photon. Nanostr. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. Roberts, S. Cummer, D. Smith, and J. Pendry, Photon. Nanostr. Fundam. Appl. 6, 87 (2008).
[CrossRef]

Phys. Rev. A (1)

A. Ciattoni, C. Rizza, and E. Palange, Phys. Rev. A 81, 043839 (2010).
[CrossRef]

Phys. Rev. B (3)

M. Silveirinha and N. Engheta, Phys. Rev. B 76, 245109(2007).
[CrossRef]

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

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, Phys. Rev. B 77, 125127 (2008).
[CrossRef]

Phys. Rev. E (1)

R. Ziolkowski, Phys. Rev. E 70, 46608 (2004).
[CrossRef]

Phys. Rev. Lett. (5)

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

J. Li, L. Zhou, C. Chan, and P. Sheng, Phys. Rev. Lett. 90, 83901 (2003).
[CrossRef]

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

R. Liu, Q. Cheng, T. Hand, J. Mock, T. Cui, S. Cummer, and D. Smith, Phys. Rev. Lett. 100, 23903 (2008).
[CrossRef]

B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, Phys. Rev. Lett. 100, 33903 (2008).
[CrossRef]

Science (3)

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

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

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

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Figures (7)

Fig. 1
Fig. 1

Schematic of the focuser and the simulation parameters.

Fig. 2
Fig. 2

Field and energy distributions for the electromagnetic wave. The white cross denotes a point-source. Field distribution with the point-source located in (a) free space, (b) in the ZIM focuser. (c) Energy distribution corresponding to (b).

Fig. 3
Fig. 3

Power flow (real part of the Poynting vector) distributions for various ZIM structures. The white lines denote the power flow, the red arrows denote the direction of the power flow, and the white crosses denote point-sources. (a) ZIM with square outer boundary and circular inner boundary. (b) ZIM with circular outer boundary and square inner boundary. (c) ZIM with circular outer boundary and circular inner boundary.

Fig. 4
Fig. 4

Focusing effect of that focuser and an arbitrary outer boundary. The white cross denotes a point- source. Field distribution with the point-source located in (a) free space and (b) the electromagnetic focuser. (c) Energy distribution corresponding to (b).

Fig. 5
Fig. 5

Focusing effect of a focuser for three point-sources. The white crosses denote the point-sources. Field distribution with the point-sources located in (a) free space, (b) the ZIM focuser, and (c) energy distribution corresponding to (b).

Fig. 6
Fig. 6

Intensity and focal spot size versus source wavelength.

Fig. 7
Fig. 7

(a) Possible practical method for achieving multiple wave focusing. The large circles are the cavities. (b) Dependence of the source number on the intensity of the focus. White bar in (a) denotes the x axis in (b).

Equations (1)

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ε r = μ r = 1 ω p 2 ω ( ω + i Γ ) ,

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