Abstract

A novel type of electromagnetically induced gratings based on the Raman nonlinearity in the field of standing pump waves are proposed. Unlike electromagnetically induced absorption gratings, these gratings are based on the spatial modulation of Raman susceptibility. We present a theoretical study of the optical response of such a spatial periodically modulated three-level atomic medium. It is shown that transmission and reflection of a probe Raman wave can be simultaneously amplified in the grating. Transmission and reflection spectra can be controlled by varying the pump field intensity. The basic mechanism responsible for all-optical control of transmission and reflection in the samples of Raman driven atoms are discussed.

© 2014 Optical Society of America

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References

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  1. C. Denz, S. Flach, and Y. S. Kivshar, eds., Nonlinearities in Periodic Structures and Metamaterials (Springer-Verlag, 2009), Vol. 150.
  2. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).
  3. M. Artoni, G. La Rocca, and F. Bassani, Phys. Rev. E 72, 046604 (2005).
    [CrossRef]
  4. I. Gabitov, A. O. Korotkevich, A. I. Maimistov, and J. B. McMahon, “Coherent optical pulse dynamics in nanocomposite plasmonic Bragg gratings,” arXiv:nlin/0702035 [nlin.PS] (2007).
  5. N. N. Rozanov, S. V. Fedorov, R. S. Savel’ev, A. A. Sukhorukov, and Y. S. Kivshar, J. Exp. Theor. Phys. 114, 782 (2012).
    [CrossRef]
  6. Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 60, 712 (1999).
    [CrossRef]
  7. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
    [CrossRef]
  8. A. André and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
    [CrossRef]
  9. X. M. Su and B. S. Ham, Phys. Rev. A 71, 013821 (2005).
    [CrossRef]
  10. M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
    [CrossRef]
  11. S.-q. Kuang, R.-g. Wan, P. Du, Y. Jiang, and J.-y. Gao, Opt. Express 16, 15455 (2008).
    [CrossRef]
  12. J.-H. Wu, G. C. La Rocca, and M. Artoni, Phys. Rev. B 77, 113106 (2008).
    [CrossRef]
  13. J.-H. Wu, A. Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, and G. La Rocca, J. Mod. Opt. 56, 768 (2009).
    [CrossRef]
  14. M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
    [CrossRef]
  15. K. R. Hansen and K. Molmer, Phys. Rev. A 75, 053802 (2007).
    [CrossRef]
  16. A. W. Brown and M. Xiao, Opt. Lett. 30, 699 (2005).
    [CrossRef]
  17. A. Dogariu, A. Kuzmich, and L. J. Wang, Phys. Rev. A 63, 053806 (2001).
    [CrossRef]
  18. M. G. Payne and L. Deng, Phys. Rev. A 64, 031802 (2001).
    [CrossRef]
  19. K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 74, 041803 (2006).
    [CrossRef]
  20. K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 76, 033819 (2007).
    [CrossRef]
  21. L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
    [CrossRef]
  22. G. S. Agarwal and S. Dasgupta, Phys. Rev. A 70, 023802 (2004).
    [CrossRef]
  23. C. Hang and G. Huang, Opt. Express 18, 2952 (2010).
    [CrossRef]
  24. V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 80, 061802 (2009).
    [CrossRef]
  25. V. G. Arkhipkin and S. A. Myslivets, J. Exp. Theor. Phys. 111, 898 (2010).
    [CrossRef]
  26. V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 88, 033847 (2013).
    [CrossRef]
  27. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  28. S. Rautian, Opt. Spectrosc. 104, 112 (2008).
    [CrossRef]
  29. V. G. Arkhipkin and S. A. Myslivets, Quantum Electron. 39, 157 (2009).
    [CrossRef]

2013 (1)

V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 88, 033847 (2013).
[CrossRef]

2012 (1)

N. N. Rozanov, S. V. Fedorov, R. S. Savel’ev, A. A. Sukhorukov, and Y. S. Kivshar, J. Exp. Theor. Phys. 114, 782 (2012).
[CrossRef]

2010 (2)

V. G. Arkhipkin and S. A. Myslivets, J. Exp. Theor. Phys. 111, 898 (2010).
[CrossRef]

C. Hang and G. Huang, Opt. Express 18, 2952 (2010).
[CrossRef]

2009 (3)

V. G. Arkhipkin and S. A. Myslivets, Quantum Electron. 39, 157 (2009).
[CrossRef]

J.-H. Wu, A. Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, and G. La Rocca, J. Mod. Opt. 56, 768 (2009).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 80, 061802 (2009).
[CrossRef]

2008 (3)

J.-H. Wu, G. C. La Rocca, and M. Artoni, Phys. Rev. B 77, 113106 (2008).
[CrossRef]

S. Rautian, Opt. Spectrosc. 104, 112 (2008).
[CrossRef]

S.-q. Kuang, R.-g. Wan, P. Du, Y. Jiang, and J.-y. Gao, Opt. Express 16, 15455 (2008).
[CrossRef]

2007 (3)

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 76, 033819 (2007).
[CrossRef]

L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

K. R. Hansen and K. Molmer, Phys. Rev. A 75, 053802 (2007).
[CrossRef]

2006 (2)

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 74, 041803 (2006).
[CrossRef]

M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef]

2005 (4)

M. Artoni, G. La Rocca, and F. Bassani, Phys. Rev. E 72, 046604 (2005).
[CrossRef]

X. M. Su and B. S. Ham, Phys. Rev. A 71, 013821 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

A. W. Brown and M. Xiao, Opt. Lett. 30, 699 (2005).
[CrossRef]

2004 (1)

G. S. Agarwal and S. Dasgupta, Phys. Rev. A 70, 023802 (2004).
[CrossRef]

2003 (1)

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef]

2002 (1)

A. André and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef]

2001 (2)

A. Dogariu, A. Kuzmich, and L. J. Wang, Phys. Rev. A 63, 053806 (2001).
[CrossRef]

M. G. Payne and L. Deng, Phys. Rev. A 64, 031802 (2001).
[CrossRef]

1999 (1)

Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 60, 712 (1999).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and S. Dasgupta, Phys. Rev. A 70, 023802 (2004).
[CrossRef]

André, A.

A. André and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef]

Arkhipkin, V. G.

V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 88, 033847 (2013).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, J. Exp. Theor. Phys. 111, 898 (2010).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, Quantum Electron. 39, 157 (2009).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 80, 061802 (2009).
[CrossRef]

Artoni, M.

J.-H. Wu, A. Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, and G. La Rocca, J. Mod. Opt. 56, 768 (2009).
[CrossRef]

J.-H. Wu, G. C. La Rocca, and M. Artoni, Phys. Rev. B 77, 113106 (2008).
[CrossRef]

M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef]

M. Artoni, G. La Rocca, and F. Bassani, Phys. Rev. E 72, 046604 (2005).
[CrossRef]

Bajcsy, M.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef]

Bassani, F.

M. Artoni, G. La Rocca, and F. Bassani, Phys. Rev. E 72, 046604 (2005).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Brown, A. W.

Dasgupta, S.

G. S. Agarwal and S. Dasgupta, Phys. Rev. A 70, 023802 (2004).
[CrossRef]

Deng, L.

L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 76, 033819 (2007).
[CrossRef]

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 74, 041803 (2006).
[CrossRef]

M. G. Payne and L. Deng, Phys. Rev. A 64, 031802 (2001).
[CrossRef]

Dogariu, A.

A. Dogariu, A. Kuzmich, and L. J. Wang, Phys. Rev. A 63, 053806 (2001).
[CrossRef]

Du, P.

Fedorov, S. V.

N. N. Rozanov, S. V. Fedorov, R. S. Savel’ev, A. A. Sukhorukov, and Y. S. Kivshar, J. Exp. Theor. Phys. 114, 782 (2012).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Gabitov, I.

I. Gabitov, A. O. Korotkevich, A. I. Maimistov, and J. B. McMahon, “Coherent optical pulse dynamics in nanocomposite plasmonic Bragg gratings,” arXiv:nlin/0702035 [nlin.PS] (2007).

Gao, J.-y.

Ham, B. S.

X. M. Su and B. S. Ham, Phys. Rev. A 71, 013821 (2005).
[CrossRef]

Hang, C.

Hansen, K. R.

K. R. Hansen and K. Molmer, Phys. Rev. A 75, 053802 (2007).
[CrossRef]

Huang, G.

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Jiang, K. J.

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 76, 033819 (2007).
[CrossRef]

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 74, 041803 (2006).
[CrossRef]

Jiang, Y.

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Kivshar, Y. S.

N. N. Rozanov, S. V. Fedorov, R. S. Savel’ev, A. A. Sukhorukov, and Y. S. Kivshar, J. Exp. Theor. Phys. 114, 782 (2012).
[CrossRef]

Korotkevich, A. O.

I. Gabitov, A. O. Korotkevich, A. I. Maimistov, and J. B. McMahon, “Coherent optical pulse dynamics in nanocomposite plasmonic Bragg gratings,” arXiv:nlin/0702035 [nlin.PS] (2007).

Kuang, S.-q.

Kuzmich, A.

A. Dogariu, A. Kuzmich, and L. J. Wang, Phys. Rev. A 63, 053806 (2001).
[CrossRef]

La Rocca, G.

J.-H. Wu, A. Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, and G. La Rocca, J. Mod. Opt. 56, 768 (2009).
[CrossRef]

M. Artoni, G. La Rocca, and F. Bassani, Phys. Rev. E 72, 046604 (2005).
[CrossRef]

La Rocca, G. C.

J.-H. Wu, G. C. La Rocca, and M. Artoni, Phys. Rev. B 77, 113106 (2008).
[CrossRef]

M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef]

Lukin, M. D.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef]

A. André and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef]

Maimistov, A. I.

I. Gabitov, A. O. Korotkevich, A. I. Maimistov, and J. B. McMahon, “Coherent optical pulse dynamics in nanocomposite plasmonic Bragg gratings,” arXiv:nlin/0702035 [nlin.PS] (2007).

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Matsko, A. B.

Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 60, 712 (1999).
[CrossRef]

McMahon, J. B.

I. Gabitov, A. O. Korotkevich, A. I. Maimistov, and J. B. McMahon, “Coherent optical pulse dynamics in nanocomposite plasmonic Bragg gratings,” arXiv:nlin/0702035 [nlin.PS] (2007).

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Molmer, K.

K. R. Hansen and K. Molmer, Phys. Rev. A 75, 053802 (2007).
[CrossRef]

Myslivets, S. A.

V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 88, 033847 (2013).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, J. Exp. Theor. Phys. 111, 898 (2010).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, Quantum Electron. 39, 157 (2009).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 80, 061802 (2009).
[CrossRef]

Payne, M. G.

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 76, 033819 (2007).
[CrossRef]

L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 74, 041803 (2006).
[CrossRef]

M. G. Payne and L. Deng, Phys. Rev. A 64, 031802 (2001).
[CrossRef]

Raczynski, A.

J.-H. Wu, A. Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, and G. La Rocca, J. Mod. Opt. 56, 768 (2009).
[CrossRef]

Rautian, S.

S. Rautian, Opt. Spectrosc. 104, 112 (2008).
[CrossRef]

Rostovtsev, Y. V.

Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 60, 712 (1999).
[CrossRef]

Rozanov, N. N.

N. N. Rozanov, S. V. Fedorov, R. S. Savel’ev, A. A. Sukhorukov, and Y. S. Kivshar, J. Exp. Theor. Phys. 114, 782 (2012).
[CrossRef]

Savel’ev, R. S.

N. N. Rozanov, S. V. Fedorov, R. S. Savel’ev, A. A. Sukhorukov, and Y. S. Kivshar, J. Exp. Theor. Phys. 114, 782 (2012).
[CrossRef]

Scully, M. O.

Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 60, 712 (1999).
[CrossRef]

Su, X. M.

X. M. Su and B. S. Ham, Phys. Rev. A 71, 013821 (2005).
[CrossRef]

Sukhorukov, A. A.

N. N. Rozanov, S. V. Fedorov, R. S. Savel’ev, A. A. Sukhorukov, and Y. S. Kivshar, J. Exp. Theor. Phys. 114, 782 (2012).
[CrossRef]

Wan, R.-g.

Wang, L. J.

A. Dogariu, A. Kuzmich, and L. J. Wang, Phys. Rev. A 63, 053806 (2001).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Wu, J.-H.

J.-H. Wu, A. Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, and G. La Rocca, J. Mod. Opt. 56, 768 (2009).
[CrossRef]

J.-H. Wu, G. C. La Rocca, and M. Artoni, Phys. Rev. B 77, 113106 (2008).
[CrossRef]

Xiao, M.

Zaremba, J.

J.-H. Wu, A. Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, and G. La Rocca, J. Mod. Opt. 56, 768 (2009).
[CrossRef]

Zibrov, A. S.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef]

Zielinska-Kaniasty, S.

J.-H. Wu, A. Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, and G. La Rocca, J. Mod. Opt. 56, 768 (2009).
[CrossRef]

J. Exp. Theor. Phys. (2)

N. N. Rozanov, S. V. Fedorov, R. S. Savel’ev, A. A. Sukhorukov, and Y. S. Kivshar, J. Exp. Theor. Phys. 114, 782 (2012).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, J. Exp. Theor. Phys. 111, 898 (2010).
[CrossRef]

J. Mod. Opt. (1)

J.-H. Wu, A. Raczyński, J. Zaremba, S. Zielińska-Kaniasty, M. Artoni, and G. La Rocca, J. Mod. Opt. 56, 768 (2009).
[CrossRef]

Nature (1)

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, Nature 426, 638 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Spectrosc. (1)

S. Rautian, Opt. Spectrosc. 104, 112 (2008).
[CrossRef]

Phys. Rev. A (10)

V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 88, 033847 (2013).
[CrossRef]

G. S. Agarwal and S. Dasgupta, Phys. Rev. A 70, 023802 (2004).
[CrossRef]

V. G. Arkhipkin and S. A. Myslivets, Phys. Rev. A 80, 061802 (2009).
[CrossRef]

K. R. Hansen and K. Molmer, Phys. Rev. A 75, 053802 (2007).
[CrossRef]

A. Dogariu, A. Kuzmich, and L. J. Wang, Phys. Rev. A 63, 053806 (2001).
[CrossRef]

M. G. Payne and L. Deng, Phys. Rev. A 64, 031802 (2001).
[CrossRef]

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 74, 041803 (2006).
[CrossRef]

K. J. Jiang, L. Deng, and M. G. Payne, Phys. Rev. A 76, 033819 (2007).
[CrossRef]

Y. V. Rostovtsev, A. B. Matsko, and M. O. Scully, Phys. Rev. A 60, 712 (1999).
[CrossRef]

X. M. Su and B. S. Ham, Phys. Rev. A 71, 013821 (2005).
[CrossRef]

Phys. Rev. B (1)

J.-H. Wu, G. C. La Rocca, and M. Artoni, Phys. Rev. B 77, 113106 (2008).
[CrossRef]

Phys. Rev. E (1)

M. Artoni, G. La Rocca, and F. Bassani, Phys. Rev. E 72, 046604 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

M. Artoni and G. C. La Rocca, Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef]

L. Deng and M. G. Payne, Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef]

A. André and M. D. Lukin, Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef]

Quantum Electron. (1)

V. G. Arkhipkin and S. A. Myslivets, Quantum Electron. 39, 157 (2009).
[CrossRef]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Other (4)

I. Gabitov, A. O. Korotkevich, A. I. Maimistov, and J. B. McMahon, “Coherent optical pulse dynamics in nanocomposite plasmonic Bragg gratings,” arXiv:nlin/0702035 [nlin.PS] (2007).

C. Denz, S. Flach, and Y. S. Kivshar, eds., Nonlinearities in Periodic Structures and Metamaterials (Springer-Verlag, 2009), Vol. 150.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

R. W. Boyd, Nonlinear Optics (Academic, 1992).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Energy-level diagram for a Raman scheme driven by a standing wave pump ω 1 and a traveling wave probe ω 2 . (b) Imaginary and real parts of ± s ( ω 2 ) versus scaled Raman detuning Δ 20 / γ 20 for the pump Rabi frequency Ω 1 / γ 10 . 1 Im ( s ) , 2 Im ( s ) , 3 Re ( s ) , 4 Re ( s ) . (c)–(e) Spatial intensity distribution of the forward t (1,3) and backward r (2,4) probe components inside a sample of length L 0.6 mm for various pump Rabi frequencies and Raman detunings. (c)  Ω 1 = 0.5 γ 10 , 1 , 2 Δ 20 = 0 , and 3 , 4 Δ 20 = γ 20 , (d)  Ω 1 = γ 10 , 1 , 2 Δ 20 = 0 , and 3 , 4 Δ 20 = 0.95 γ 20 , and (e)  Ω 1 = 1.7 γ 10 , 1 , 2 Δ 20 = 0 and 3 , 4 Δ 20 = 2 γ 20 . Δ 1 = 30 γ 10 , other parameters are listed in the text.

Fig. 2.
Fig. 2.

(a)–(c) Spatial distribution of the amplitude A 1 , 2 , and (d)–(f) phase φ 1 , 2 of spatial harmonics for the forward probe wave inside a sample for frequency detunings corresponding to the Raman resonance Δ 20 = 0 and transmission peaks Δ 20 = ± 2 γ 20 when Ω 1 = 1.7 γ 10 . Other parameters are the same as in Fig. 1.

Fig. 3.
Fig. 3.

(a)–(c) Reflection and transmission spectra as a function of scaled Raman detuning Δ 20 / γ 20 for the different pump Rabi frequencies Ω 1 . (d)–(f) Normalized intensities of spatial harmonics A 1 2 and A 2 2 at the output of the sample for the forward wave.

Fig. 4.
Fig. 4.

(a) Transmission and (b) reflection versus the Raman detuning and pump Rabi frequency.

Equations (13)

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

ε 2 ( z ) = 1 + 4 π N χ 2 + 4 π N χ R | E 1 | 2 cos 2 ( k 1 z ) = ε 20 + Δ ε ( 1 + cos ( 2 k 1 z ) ) ,
χ R = 1 4 3 d 21 2 d 10 2 Δ 1 2 ( Δ 20 + i γ 20 ) .
d 2 E 2 d z 2 + k 20 2 ε 2 ( z ) E 2 = 0.
d 2 E 2 d z 2 + k 2 2 [ 1 + β ( 1 + cos 2 k 1 z ) ] E 2 = 0 ,
E 2 ( z ) = A ( z ) e i k 2 z + B ( z ) e i k 2 z ,
d A d z = i α A + i σ B e i 2 Δ k z , d B d z = i α B i σ A e i 2 Δ k z ,
E 2 + ( z ) = e i k 1 z ( a 1 e i s z + a 2 e i s z ) ,
E 2 ( z ) = e i k 1 z ( b 1 e i s z + b 2 e i s z ) ,
κ ( ω 2 ) = k 1 ± s = k 1 ± ( Δ k α ) 2 σ 2 .
a 1 , 2 = A 0 [ s ( Δ k α ) ] e i s L / 2 D ,
b 1 , 2 = ± i A 0 σ e ± i s L / 2 D ,
t ( z ) = | [ s cos s ( L z ) + i ( Δ k α ) sin s ( L z ) ] / D | 2 ,
r ( z ) = | [ σ sin s ( L z ) ] / D | 2 .

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