Abstract

We design a one-dimensional compound photonic crystal constituted of a periodic arrangement of electromagnetic-induced transparency atomic vapor. It is shown that, when a stochastic electromagnetic beam propagates through the compound photonic crystal, the spectral degrees of polarization and cross polarization of the beam can be modulated by changing the parameters of the supercells of the compound photonic crystal.

© 2011 Optical Society of America

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  1. S. E. Harris, Phys. Today 50, 36 (1997).
    [CrossRef]
  2. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
    [CrossRef] [PubMed]
  3. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
    [CrossRef] [PubMed]
  4. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
    [CrossRef]
  5. F. Zhuang, X. Du, and D. Zhao, J. Opt. Soc. Am. B 27, 2279 (2010).
    [CrossRef]
  6. O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
    [CrossRef]
  7. H. Roychowdhury, G. P. Agrawal, and E. Wolf, J. Opt. Soc. Am. A 23, 940 (2006).
    [CrossRef]
  8. O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
    [CrossRef]
  9. X. Du and D. Zhao, Opt. Express 17, 4257 (2009).
    [CrossRef] [PubMed]
  10. T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
    [CrossRef]
  11. S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
    [CrossRef]
  12. S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
    [CrossRef]
  13. J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
    [CrossRef]
  14. F. Ding, Y. Chen, and J. Shi, J. Opt. Soc. Am. A 27, 422 (2010).
    [CrossRef]
  15. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  16. S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

2010 (2)

2009 (3)

X. Du and D. Zhao, Opt. Express 17, 4257 (2009).
[CrossRef] [PubMed]

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
[CrossRef]

2008 (1)

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

2007 (1)

T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
[CrossRef]

2006 (1)

2005 (1)

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

2004 (1)

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

2003 (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

1999 (1)

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

1997 (1)

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

1996 (1)

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef] [PubMed]

1995 (1)

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef] [PubMed]

Agrawal, G. P.

Chen, Y.

Ding, F.

Du, X.

Dunn, M. H.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef] [PubMed]

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Fulton, D. J.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef] [PubMed]

Harris, S. E.

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Hollberg, L.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

James, D. F. V.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Korotkova, O.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
[CrossRef]

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

Lukin, M. D.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Moseley, R. R.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef] [PubMed]

Pu, J.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
[CrossRef]

Rostovtsev, Y.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Roychowdhury, H.

Sahin, S.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

Salem, M.

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

Sautenkov, V. A.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Scully, M. O.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Shepherd, S.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef] [PubMed]

Shi, J.

Shirai, T.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
[CrossRef]

Sinclair, B. D.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef] [PubMed]

Volkov, S. N.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

Wang, S.

S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

Welch, G. R.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Wolf, E.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
[CrossRef]

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

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Zhang, G.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

Zhao, D.

Zhuang, F.

Zibrov, A. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

J. Opt. A (2)

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A 10, 055001 (2008).
[CrossRef]

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A 11, 085703 (2009).
[CrossRef]

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

J. Opt. Soc. Am. B (1)

Opt. Commun. (4)

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

O. Korotkova, M. Salem, and E. Wolf, Opt. Commun. 233, 225 (2004).
[CrossRef]

J. Pu and O. Korotkova, Opt. Commun. 282, 1691 (2009).
[CrossRef]

T. Shirai and E. Wolf, Opt. Commun. 272, 289 (2007).
[CrossRef]

Opt. Express (1)

Phys. Lett. A (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Phys. Rev. A (1)

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. A 53, 408 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, Phys. Rev. Lett. 74, 670 (1995).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, Phys. Today 50, 36 (1997).
[CrossRef]

Other (1)

S. Wang and D. Zhao, Matrix Optics (CHEP-Springer, 2000).

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Figures (4)

Fig. 1
Fig. 1

Schematic of a one-dimensional compound photonic crystal based on EIT atomic vapor.

Fig. 2
Fig. 2

Changes in the central spectral degree of polarization ( | ρ | = 0 ) versus the number of the supercell when the stochastic electromagnetic beam propagates through the compound photonic crystal. (a)  α = 0.1 and choosing different β, (b)  β = 0.01 and choosing different α.

Fig. 3
Fig. 3

Distributions of the spectral degree of polarization at the output plane when m = 150 . We fix that α = 0.1 and choose the parameters of β as follows: (a)  β = 0.01 , (b)  β = 0.02 , and (c)  β = 0.03 .

Fig. 4
Fig. 4

Changes in the spectral degree of cross polarization of the electric field at a pair of points (a)  ρ 1 = ( 0.3 mm , 0 ) and ρ 2 = ( 0.3 mm , 0 ) and (b)  ρ 1 = ( 0.9 mm , 0 ) and ρ 2 = ( 0.9 mm , 0 ) versus the number of the supercell when the beam propagates through the compound photonic crystal. We fix that α = 0.1 and choose different β.

Equations (10)

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W ( r 1 , r 2 , ω ) [ W i j ( r 1 , r 2 , ω ) ] = [ E i * ( r 1 , ω ) E j ( r 2 , ω ) ] , ( i = x , y ; j = x , y ) ,
W i j ( in ) ( ρ 1 , ρ 2 , ω ) = A i A j B i j exp ( ρ 1 2 4 σ i 2 ρ 2 2 4 σ j 2 ) × exp ( | ρ 2 ρ 1 | 2 2 δ i j 2 ) ,
W i j ( out ) ( ρ 1 , ρ 2 , ω ) = ( k 2 π B ) 2 W i j ( in ) ( ρ 1 , ρ 2 , ω ) exp { i k 2 B [ A ( ρ 1 2 ρ 2 2 ) 2 ( ρ 1 · ρ 1 ρ 2 · ρ 2 ) + D ( ρ 1 2 ρ 2 2 ) ] } d 2 ρ 1 d 2 ρ 2 ,
[ A B C D ] = [ 1 0 0 n 1 ] · [ 1 l 1 0 1 ] · ( [ 1 0 0 n 2 / n 1 ] · [ 1 l 2 0 1 ] · [ 1 0 0 n 1 / n 2 ] · [ 1 l 1 0 1 ] ) m · [ 1 0 0 1 / n 1 ] ,
[ A B C D ] = [ 1 ( m + 1 ) α l n 1 + m ( 1 α ) l β n 1 0 1 ] ,
W i j ( out ) ( ρ 1 , ρ 2 , ω ) = A i A j B i j 1 Δ i j exp [ α i j ( ρ 1 + ρ 2 ) 2 Δ i j ] × exp { i k β n 1 2 [ β ( m + 1 ) α l + m ( 1 α ) l ] ( 1 1 Δ i j ) ( ρ 2 2 ρ 1 2 ) } × exp ( η i j | ρ 2 ρ 1 | 2 Δ i j ) ,
α i j = 1 16 ( 1 σ i 2 + 1 σ j 2 ) , β i j = 1 4 ( 1 σ i 2 1 σ j 2 ) , η i j = α i j + 1 2 δ i j 2 ,
Δ i j = [ β ( m + 1 ) α l + m ( 1 α ) l k β n 1 ] 2 × { 16 α i j η i j [ β i j + i k β n 1 β ( m + 1 ) α l + m ( 1 α ) l ] 2 } .
P ( out ) ( ρ , ω ) = 1 4 Det W ( out ) ( ρ , ρ , ω ) [ Tr W ( out ) ( ρ , ρ , ω ) ] 2 ,
P C ( out ) ( ρ 1 , ρ 2 , ω ) = 1 4 Det W ( out ) ( ρ 1 , ρ 2 , ω ) [ Tr W ( out ) ( ρ 1 , ρ 2 , ω ) ] 2 .

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