Abstract

Theoretical analysis of interaction of stochastic electromagnetic beamlike fields with positive- and negative-phase materials suggests that suitable combinations of such materials can serve as media where spectral, coherence, and polarization properties of beams can self-reconstruct.

© 2010 Optical Society of America

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References

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  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. A. D. Boardman, N. King, and L. Velasco, Electromagnetics 25, 1 (2005).
    [CrossRef]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  4. B.-J. Seo, T. Ueda, T. Itoh, and H. Fetterman, Appl. Phys. Lett. 88, 161122 (2006).
    [CrossRef]
  5. J. Zhang, H. Chen, L. Ran, Y. Luo, B. Wu, and J. A. Kong, Appl. Phys. Lett. 92, 084108 (2008).
    [CrossRef]
  6. G.V.Eleftheriades and K.G.Balmain, eds., Negative Refraction Metamaterials: Fundamental Principles and Applications (John Wiley and Sons, 2005).
    [CrossRef]
  7. J. Zhou, H. Luo, S. Wen, and Y. Zeng, Opt. Commun. 282, 2670 (2009).
    [CrossRef]
  8. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
    [CrossRef]
  9. J. Pu, O. Korotkova, and E. Wolf, Opt. Lett. 31, 2097 (2006).
    [CrossRef] [PubMed]
  10. J. Pu and O. Korotkova, “Spectral and polarization properties of stochastic electromagnetic beams propagating in gain and absorbing media,” Opt. Commun. (to be published).
  11. H. Roychowdhury, G. P. Agrawal, and E. Wolf, J. Opt. Soc. Am. A 23, 940 (2006).
    [CrossRef]
  12. Q. Lin and Y. Cai, Opt. Lett. 27, 216 (2002).
    [CrossRef]
  13. O. Korotkova and E. Wolf, J. Mod. Opt. 52, 2673 (2005).
    [CrossRef]
  14. H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).
  15. S. A. Collins, J. Opt. Soc. Am. A 60, 1168 (1970).
    [CrossRef]
  16. E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  17. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]

2009 (1)

J. Zhou, H. Luo, S. Wen, and Y. Zeng, Opt. Commun. 282, 2670 (2009).
[CrossRef]

2008 (1)

J. Zhang, H. Chen, L. Ran, Y. Luo, B. Wu, and J. A. Kong, Appl. Phys. Lett. 92, 084108 (2008).
[CrossRef]

2006 (3)

2005 (2)

A. D. Boardman, N. King, and L. Velasco, Electromagnetics 25, 1 (2005).
[CrossRef]

O. Korotkova and E. Wolf, J. Mod. Opt. 52, 2673 (2005).
[CrossRef]

2002 (1)

2001 (2)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

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

2000 (1)

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

1970 (1)

S. A. Collins, J. Opt. Soc. Am. A 60, 1168 (1970).
[CrossRef]

1968 (1)

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

1965 (1)

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

Agrawal, G. P.

Boardman, A. D.

A. D. Boardman, N. King, and L. Velasco, Electromagnetics 25, 1 (2005).
[CrossRef]

Borghi, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Cai, Y.

Chen, H.

J. Zhang, H. Chen, L. Ran, Y. Luo, B. Wu, and J. A. Kong, Appl. Phys. Lett. 92, 084108 (2008).
[CrossRef]

Collins, S. A.

S. A. Collins, J. Opt. Soc. Am. A 60, 1168 (1970).
[CrossRef]

Fetterman, H.

B.-J. Seo, T. Ueda, T. Itoh, and H. Fetterman, Appl. Phys. Lett. 88, 161122 (2006).
[CrossRef]

Gori, F.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Itoh, T.

B.-J. Seo, T. Ueda, T. Itoh, and H. Fetterman, Appl. Phys. Lett. 88, 161122 (2006).
[CrossRef]

King, N.

A. D. Boardman, N. King, and L. Velasco, Electromagnetics 25, 1 (2005).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

Kong, J. A.

J. Zhang, H. Chen, L. Ran, Y. Luo, B. Wu, and J. A. Kong, Appl. Phys. Lett. 92, 084108 (2008).
[CrossRef]

Korotkova, O.

J. Pu, O. Korotkova, and E. Wolf, Opt. Lett. 31, 2097 (2006).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, J. Mod. Opt. 52, 2673 (2005).
[CrossRef]

J. Pu and O. Korotkova, “Spectral and polarization properties of stochastic electromagnetic beams propagating in gain and absorbing media,” Opt. Commun. (to be published).

Lin, Q.

Luo, H.

J. Zhou, H. Luo, S. Wen, and Y. Zeng, Opt. Commun. 282, 2670 (2009).
[CrossRef]

Luo, Y.

J. Zhang, H. Chen, L. Ran, Y. Luo, B. Wu, and J. A. Kong, Appl. Phys. Lett. 92, 084108 (2008).
[CrossRef]

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Pendry, J. B.

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

Piquero, G.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Pu, J.

J. Pu, O. Korotkova, and E. Wolf, Opt. Lett. 31, 2097 (2006).
[CrossRef] [PubMed]

J. Pu and O. Korotkova, “Spectral and polarization properties of stochastic electromagnetic beams propagating in gain and absorbing media,” Opt. Commun. (to be published).

Ran, L.

J. Zhang, H. Chen, L. Ran, Y. Luo, B. Wu, and J. A. Kong, Appl. Phys. Lett. 92, 084108 (2008).
[CrossRef]

Roychowdhury, H.

Santarsiero, M.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Schultz, S.

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

Seo, B.-J.

B.-J. Seo, T. Ueda, T. Itoh, and H. Fetterman, Appl. Phys. Lett. 88, 161122 (2006).
[CrossRef]

Shelby, R. A.

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

Simon, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Smith, D. R.

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

Ueda, T.

B.-J. Seo, T. Ueda, T. Itoh, and H. Fetterman, Appl. Phys. Lett. 88, 161122 (2006).
[CrossRef]

Velasco, L.

A. D. Boardman, N. King, and L. Velasco, Electromagnetics 25, 1 (2005).
[CrossRef]

Veselago, V. G.

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

Wen, S.

J. Zhou, H. Luo, S. Wen, and Y. Zeng, Opt. Commun. 282, 2670 (2009).
[CrossRef]

Wolf, E.

J. Pu, O. Korotkova, and E. Wolf, Opt. Lett. 31, 2097 (2006).
[CrossRef] [PubMed]

H. Roychowdhury, G. P. Agrawal, and E. Wolf, J. Opt. Soc. Am. A 23, 940 (2006).
[CrossRef]

O. Korotkova and E. Wolf, J. Mod. Opt. 52, 2673 (2005).
[CrossRef]

E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge U. Press, 2007).

Wu, B.

J. Zhang, H. Chen, L. Ran, Y. Luo, B. Wu, and J. A. Kong, Appl. Phys. Lett. 92, 084108 (2008).
[CrossRef]

Zeng, Y.

J. Zhou, H. Luo, S. Wen, and Y. Zeng, Opt. Commun. 282, 2670 (2009).
[CrossRef]

Zhang, J.

J. Zhang, H. Chen, L. Ran, Y. Luo, B. Wu, and J. A. Kong, Appl. Phys. Lett. 92, 084108 (2008).
[CrossRef]

Zhou, J.

J. Zhou, H. Luo, S. Wen, and Y. Zeng, Opt. Commun. 282, 2670 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

B.-J. Seo, T. Ueda, T. Itoh, and H. Fetterman, Appl. Phys. Lett. 88, 161122 (2006).
[CrossRef]

J. Zhang, H. Chen, L. Ran, Y. Luo, B. Wu, and J. A. Kong, Appl. Phys. Lett. 92, 084108 (2008).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965).

Electromagnetics (1)

A. D. Boardman, N. King, and L. Velasco, Electromagnetics 25, 1 (2005).
[CrossRef]

J. Mod. Opt. (1)

O. Korotkova and E. Wolf, J. Mod. Opt. 52, 2673 (2005).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

J. Zhou, H. Luo, S. Wen, and Y. Zeng, Opt. Commun. 282, 2670 (2009).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

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

Science (1)

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

Sov. Phys. Usp. (1)

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

Other (3)

G.V.Eleftheriades and K.G.Balmain, eds., Negative Refraction Metamaterials: Fundamental Principles and Applications (John Wiley and Sons, 2005).
[CrossRef]

J. Pu and O. Korotkova, “Spectral and polarization properties of stochastic electromagnetic beams propagating in gain and absorbing media,” Opt. Commun. (to be published).

E. Wolf, Introduction to Theories of Coherence and Polarization of Light (Cambridge U. Press, 2007).

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Figures (3)

Fig. 1
Fig. 1

Spectral density (intensity) of the beam (on-axis) as a function of propagation distance z from the source.

Fig. 2
Fig. 2

Degree of coherence of the beam at two points with separation distance ρ = 10 5 m as a function of propagation distance z from the source.

Fig. 3
Fig. 3

Degree of polarization of the beam (on-axis) as a function of propagation distance z from the source.

Equations (12)

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W α β ( x 1 , y 1 , x 2 , y 2 , z ; ω ) = | K | 2 ( 2 π B ) 2 exp ( 2 K i z ) × exp { i A 2 B [ K ( x 1 2 + y 1 2 ) K * ( x 2 2 + y 2 2 ) ] } exp { i B [ K ( x 1 x 1 + y 1 y 1 ) K * ( x 2 x 2 + y 2 y 2 ) ] } exp { i D 2 B [ K ( x 1 2 + y 1 2 ) K * ( x 2 2 + y 2 2 ) ] } × W α β ( 0 ) ( x 1 , y 1 , x 2 , y 2 , 0 ; ω ) d x 1 d y 1 d x 2 d y 2 .
W α β ( 0 ) ( x 1 , y 1 , x 2 , y 2 , 0 ; ω ) = I α I β B α β e [ x 1 2 + y 1 2 + x 2 2 + y 2 2 ] 4 σ 2 e [ ( x 1 x 2 ) 2 + ( y 1 y 2 ) 2 ] 2 σ α β 2 ,
W α β ( x 1 , y 1 , x 2 , y 2 , z ; ω ) = I α I β B α β | K | 2 δ α β 4 e 2 K z i B 2 ( 4 | g α β | 2 1 ) × e i D 2 B [ K ( x 1 2 + y 1 2 ) K * ( x 2 2 + y 2 2 ) ] e δ α β 2 K 2 g α β * ( x 1 2 + y 1 2 ) B 2 ( 4 | g α β | 2 1 ) × e δ α β 2 | K | 2 ( x 1 x 2 + y 1 y 2 ) B 2 ( 4 | g α β | 2 1 ) e δ α β 2 K * 2 g α β ( x 2 2 + y 2 2 ) B 2 ( 4 | g α β | 2 1 ) ,
g α β = 1 2 + δ α β 2 4 σ 2 + i A K δ α β 2 2 B .
[ A B C D ] a = [ 1 l 0 1 ] ,
[ A B C D ] b = [ 1 0 0 n 1 n 2 ] .
[ A B C D ] 1 = [ 1 l 1 0 1 ] ;
[ A B C D ] 2 = [ 1 l 1 + l 2 n p n n 0 n p n n ] ;
[ A B C D ] 3 = [ 1 l 1 + l 3 + l 2 n p n n 0 1 ] .
S ( r , ω ) = Tr W ( r , r , ω ) ,
μ ( r 1 , r 2 , ω ) = Tr W ( r 1 , r 2 , ω ) Tr W ( r 1 , r 1 , ω ) Tr W ( r 2 , r 2 , ω ) ,
P ( r , ω ) = 1 4 Det W ( r , r , ω ) [ Tr W ( r , r , ω ) ] 2 ,

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