Abstract

The Dirac point (DP) with a double-cone structure for optical fields can be realized in optically homogenous media. The condition for the realization of DP in optical systems is the varying of refractive index from negative to zero and then to positive. Our analysis verify that, similar to electrons in graphene, the light field near DP possesses of the pseudodiffusive property obeying the 1L scaling law, where L is the propagation distance inside the media.

© 2009 Optical Society of America

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  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
    [CrossRef] [PubMed]
  2. A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, Phys. Rev. Lett. 100, 117401 (2008).
    [CrossRef] [PubMed]
  3. J. Cserti and G. Dávid, Phys. Rev. B 74, 172305 (2006).
    [CrossRef]
  4. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, 1995).
  5. F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
    [CrossRef] [PubMed]
  6. O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
    [CrossRef] [PubMed]
  7. R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, Phys. Rev. A 75, 063813 (2007).
    [CrossRef]
  8. X. Zhang, Phys. Rev. Lett. 100, 113903 (2008).
    [CrossRef] [PubMed]
  9. M. I. Katsnelson, Eur. Phys. J. B 51, 157 (2006).
    [CrossRef]
  10. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  11. F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, J. Appl. Phys. 103, 084312 (2008).
    [CrossRef]
  12. R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004).
    [CrossRef]
  13. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).
    [CrossRef] [PubMed]
  14. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
    [CrossRef]
  15. L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Lett. A , 350, 410 (2006).
    [CrossRef]

2008

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, Phys. Rev. Lett. 100, 117401 (2008).
[CrossRef] [PubMed]

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef] [PubMed]

X. Zhang, Phys. Rev. Lett. 100, 113903 (2008).
[CrossRef] [PubMed]

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

2007

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef] [PubMed]

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, Phys. Rev. A 75, 063813 (2007).
[CrossRef]

2006

J. Cserti and G. Dávid, Phys. Rev. B 74, 172305 (2006).
[CrossRef]

M. I. Katsnelson, Eur. Phys. J. B 51, 157 (2006).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Lett. A , 350, 410 (2006).
[CrossRef]

2004

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

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

2001

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

1999

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

1996

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

Bartal, G.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef] [PubMed]

Bazaliy, Y. B.

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, Phys. Rev. A 75, 063813 (2007).
[CrossRef]

Beenakker, C. W. J.

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, Phys. Rev. A 75, 063813 (2007).
[CrossRef]

Carbone, F.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, Phys. Rev. Lett. 100, 117401 (2008).
[CrossRef] [PubMed]

Chaubet, M.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Chen, H.

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Lett. A , 350, 410 (2006).
[CrossRef]

Christodoulides, D. N.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef] [PubMed]

Cserti, J.

J. Cserti and G. Dávid, Phys. Rev. B 74, 172305 (2006).
[CrossRef]

Dávid, G.

J. Cserti and G. Dávid, Phys. Rev. B 74, 172305 (2006).
[CrossRef]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

Freedman, B.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef] [PubMed]

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

Haldane, F. D. M.

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[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]

Houzet, G.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

Katsnelson, M. I.

M. I. Katsnelson, Eur. Phys. J. B 51, 157 (2006).
[CrossRef]

Kuzmenko, A. B.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, Phys. Rev. Lett. 100, 117401 (2008).
[CrossRef] [PubMed]

Lheurette, E.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Lippens, D.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Manela, O.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef] [PubMed]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

Novoselov, K. S.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

Peleg, O.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[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]

Peskin, M. E.

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, 1995).

Raghu, S.

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef] [PubMed]

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]

Schroeder, D. V.

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, 1995).

Schultz, S.

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

Segev, M.

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef] [PubMed]

Sepkhanov, R. A.

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, Phys. Rev. A 75, 063813 (2007).
[CrossRef]

Shelby, R. A.

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

Smith, D. R.

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

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]

van der Marel, D.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, Phys. Rev. Lett. 100, 117401 (2008).
[CrossRef] [PubMed]

van Heumen, E.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, Phys. Rev. Lett. 100, 117401 (2008).
[CrossRef] [PubMed]

Wang, L. G.

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Lett. A , 350, 410 (2006).
[CrossRef]

Youngs, I.

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

Zhang, F.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Zhang, X.

X. Zhang, Phys. Rev. Lett. 100, 113903 (2008).
[CrossRef] [PubMed]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

Zhao, X.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Zhu, S. Y.

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Lett. A , 350, 410 (2006).
[CrossRef]

Ziolkowski, R. W.

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

Eur. Phys. J. B

M. I. Katsnelson, Eur. Phys. J. B 51, 157 (2006).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

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

J. Appl. Phys.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, J. Appl. Phys. 103, 084312 (2008).
[CrossRef]

Phys. Lett. A

L. G. Wang, H. Chen, and S. Y. Zhu, Phys. Lett. A , 350, 410 (2006).
[CrossRef]

Phys. Rev. A

R. A. Sepkhanov, Y. B. Bazaliy, and C. W. J. Beenakker, Phys. Rev. A 75, 063813 (2007).
[CrossRef]

Phys. Rev. B

J. Cserti and G. Dávid, Phys. Rev. B 74, 172305 (2006).
[CrossRef]

Phys. Rev. E

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

Phys. Rev. Lett.

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

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, Phys. Rev. Lett. 100, 117401 (2008).
[CrossRef] [PubMed]

X. Zhang, Phys. Rev. Lett. 100, 113903 (2008).
[CrossRef] [PubMed]

F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008).
[CrossRef] [PubMed]

O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007).
[CrossRef] [PubMed]

Science

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
[CrossRef] [PubMed]

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

Other

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, 1995).

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Figures (4)

Fig. 1
Fig. 1

(a) SI system and (b) transmitted spectral distribution at position L. Dashed lines denote the light cone, and dark gray and white areas denote the large transmission (passbands) and the prohibition of light (gaps), respectively. The medium has ε 1 ( ω ) = μ 1 ( ω ) = 1 ω D 2 ( ω 2 + i γ ω ) with ω D = 2 π × 10 GHz and γ = 10 5 GHz .

Fig. 2
Fig. 2

Evolutions of total electric fields for a Gaussian beam through the interface at frequencies with W = 5 λ 0 ( λ 0 corresponds to ω D ). Other parameters are the same as in Fig. 1 except for γ = 10 4 GHz .

Fig. 3
Fig. 3

Dependence of ξ on L inside an SI structure under different ω. The inset shows the change of S 0 with ω. Other parameters are the same as in Fig. 2.

Fig. 4
Fig. 4

Change of ξ as a function of x inside different slabs, with ω = ω D and W = 10 λ 0 . Other parameters are the same as in Fig. 2

Equations (4)

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

( 0 i ( x i y ) i ( x + i y ) 0 ) Ψ = k ( ω ) Ψ ,
k ( ω ) = ( ω ω D ) v D .
[ 0 i v D ( x i y ) i v D ( x + i y ) 0 ] Ψ = ( ω ω D ) Ψ .
T All = t ( L , k y ) 2 d k y = 1 L ,

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