Abstract

We propose a scheme for realizing electromagnetically induced grating via the giant Kerr nonlinearity in a coherently driven four-level system with spontaneously generated coherence. In the presence of spontaneously generated coherence, Kerr nonlinearity can be enhanced with vanishing linear absorption. Thus, with a standing-wave coupling field, one can achieve a pure absorption grating, which leads the probe field to gather the zero-order direction when the detuning of the coupling field is on resonance. Moreover, we can obtain a pure phase grating, which diffracts a weak probe light into the first-order direction and the second-order direction when the detuning of the coupling field is off resonance.

© 2013 Optical Society of America

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  1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
    [CrossRef]
  2. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  3. M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
    [CrossRef]
  4. J. H. Wu, G. C. La Rocca, and M. Artoni, “Controlled light-pulse propagation in driven color center in diamond,” Phys. Rev. B 77, 113106 (2008).
    [CrossRef]
  5. J. W. Gao, J. H. Wu, N. Ba, C. L. Cui, and X. X. Tian, “Efficient all-optical routing using dynamically induced transparency windows and photonic band gaps,” Phys. Rev. A 81, 013804 (2010).
    [CrossRef]
  6. C. L. Cui, J. H. Wu, J. W. Gao, Y. Zhang, and N. Ba, “Double photonic bandgaps dynamically induced in a tripod system of cold atoms,” Opt. Express 18, 4538–4546 (2010).
    [CrossRef]
  7. H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
    [CrossRef]
  8. B. K. Dutta and P. K. Mahapatra, “Electromagetically induced grating in a three-level ladder-type system driven by a strong standing wave pump and weak probe field,” J. Phys. B 39, 1145–1157 (2006).
  9. Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
    [CrossRef]
  10. L. E. E. de Araujo, “Electromagnetically induced phase grating,” Opt. Lett. 35, 977–979 (2010).
    [CrossRef]
  11. R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
    [CrossRef]
  12. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
    [CrossRef]
  13. 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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
  14. S. M. Ma, H. Xu, and B. S. Ham, “Electromagnetically induced transparency and slow light in GaAs/AlGaAs multiple quantum wells in a transient regime,” Opt. Express 17, 14902–14908 (2009).
    [CrossRef]
  15. C. Li. Cui, J. K. Jia, Y. Zhang, Y. Xue, H. L. Xu, and J. H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B 44, 215504 (2011).
    [CrossRef]
  16. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
    [CrossRef]
  17. H. Y. Lo, P. C. Su, and Y. F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
    [CrossRef]
  18. S. W. Du, “Atomic-resonance-enhanced nonlinear optical frequency conversion with entangled photon pairs,” Phys. Rev. A 83, 033807 (2011).
    [CrossRef]
  19. M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
    [CrossRef]
  20. M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65, 022314 (2002).
    [CrossRef]
  21. A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Polariton picture of light propagation and storing in a tripod system,” Opt. Commun. 260, 73–80 (2006).
    [CrossRef]
  22. S. Menon and G. S. Argarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Lambda system,” Phys. Rev. A 57, 4014–4018 (1998).
    [CrossRef]
  23. E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
    [CrossRef]
  24. J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Lambda system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
    [CrossRef]
  25. S. Y. Zhu, R. C. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
    [CrossRef]
  26. S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
    [CrossRef]
  27. K. T. Kapale, M. O. Scully, S. Y. Zhu, and M. S. Zubairy, “Quenching of spontaneous emission through interference of incoherent pump processes,” Phys. Rev. A 67, 023804 (2003).
    [CrossRef]
  28. V. V. Kozlov, Y. Rostovtsev, and M. O. Scully, “Whispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
    [CrossRef]
  29. W. H. Xu, J. H. Wu, and J. Y. Gao, “Large index of refraction without absorption via decay-induced coherence in a three-level V system,” Eur. Phys. J. D 30, 137–141 (2004).
    [CrossRef]
  30. Y. P. Niu and S. Q. Gong, “Enhancing Kerr nonlinearity via spontaneously generated coherence,” Phys. Rev. A 73, 053811 (2006).
    [CrossRef]
  31. X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
    [CrossRef]
  32. J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
    [CrossRef]
  33. J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
    [CrossRef]

2011 (3)

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[CrossRef]

C. Li. Cui, J. K. Jia, Y. Zhang, Y. Xue, H. L. Xu, and J. H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B 44, 215504 (2011).
[CrossRef]

S. W. Du, “Atomic-resonance-enhanced nonlinear optical frequency conversion with entangled photon pairs,” Phys. Rev. A 83, 033807 (2011).
[CrossRef]

2010 (5)

J. W. Gao, J. H. Wu, N. Ba, C. L. Cui, and X. X. Tian, “Efficient all-optical routing using dynamically induced transparency windows and photonic band gaps,” Phys. Rev. A 81, 013804 (2010).
[CrossRef]

C. L. Cui, J. H. Wu, J. W. Gao, Y. Zhang, and N. Ba, “Double photonic bandgaps dynamically induced in a tripod system of cold atoms,” Opt. Express 18, 4538–4546 (2010).
[CrossRef]

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

L. E. E. de Araujo, “Electromagnetically induced phase grating,” Opt. Lett. 35, 977–979 (2010).
[CrossRef]

H. Y. Lo, P. C. Su, and Y. F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

2009 (1)

2008 (1)

J. H. Wu, G. C. La Rocca, and M. Artoni, “Controlled light-pulse propagation in driven color center in diamond,” Phys. Rev. B 77, 113106 (2008).
[CrossRef]

2006 (5)

M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef]

B. K. Dutta and P. K. Mahapatra, “Electromagetically induced grating in a three-level ladder-type system driven by a strong standing wave pump and weak probe field,” J. Phys. B 39, 1145–1157 (2006).

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Polariton picture of light propagation and storing in a tripod system,” Opt. Commun. 260, 73–80 (2006).
[CrossRef]

V. V. Kozlov, Y. Rostovtsev, and M. O. Scully, “Whispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
[CrossRef]

Y. P. Niu and S. Q. Gong, “Enhancing Kerr nonlinearity via spontaneously generated coherence,” Phys. Rev. A 73, 053811 (2006).
[CrossRef]

2005 (3)

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
[CrossRef]

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

2004 (1)

W. H. Xu, J. H. Wu, and J. Y. Gao, “Large index of refraction without absorption via decay-induced coherence in a three-level V system,” Eur. Phys. J. D 30, 137–141 (2004).
[CrossRef]

2003 (1)

K. T. Kapale, M. O. Scully, S. Y. Zhu, and M. S. Zubairy, “Quenching of spontaneous emission through interference of incoherent pump processes,” Phys. Rev. A 67, 023804 (2003).
[CrossRef]

2002 (2)

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Lambda system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65, 022314 (2002).
[CrossRef]

2000 (2)

X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[CrossRef]

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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

1998 (4)

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

S. Menon and G. S. Argarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Lambda system,” Phys. Rev. A 57, 4014–4018 (1998).
[CrossRef]

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

1996 (1)

S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
[CrossRef]

1995 (1)

S. Y. Zhu, R. C. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
[CrossRef]

Argarwal, G. S.

S. Menon and G. S. Argarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Lambda system,” Phys. Rev. A 57, 4014–4018 (1998).
[CrossRef]

Artoni, M.

J. H. Wu, G. C. La Rocca, and M. Artoni, “Controlled light-pulse propagation in driven color center in diamond,” Phys. Rev. B 77, 113106 (2008).
[CrossRef]

M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef]

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Ba, N.

C. L. Cui, J. H. Wu, J. W. Gao, Y. Zhang, and N. Ba, “Double photonic bandgaps dynamically induced in a tripod system of cold atoms,” Opt. Express 18, 4538–4546 (2010).
[CrossRef]

J. W. Gao, J. H. Wu, N. Ba, C. L. Cui, and X. X. Tian, “Efficient all-optical routing using dynamically induced transparency windows and photonic band gaps,” Phys. Rev. A 81, 013804 (2010).
[CrossRef]

Bassani, F.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[CrossRef]

Chan, R. C. F.

S. Y. Zhu, R. C. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
[CrossRef]

Chen, Y. F.

H. Y. Lo, P. C. Su, and Y. F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

Cui, C. L.

J. W. Gao, J. H. Wu, N. Ba, C. L. Cui, and X. X. Tian, “Efficient all-optical routing using dynamically induced transparency windows and photonic band gaps,” Phys. Rev. A 81, 013804 (2010).
[CrossRef]

C. L. Cui, J. H. Wu, J. W. Gao, Y. Zhang, and N. Ba, “Double photonic bandgaps dynamically induced in a tripod system of cold atoms,” Opt. Express 18, 4538–4546 (2010).
[CrossRef]

Cui, C. Li.

C. Li. Cui, J. K. Jia, Y. Zhang, Y. Xue, H. L. Xu, and J. H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B 44, 215504 (2011).
[CrossRef]

de Araujo, L. E. E.

Ding, Y.

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
[CrossRef]

Du, S. W.

S. W. Du, “Atomic-resonance-enhanced nonlinear optical frequency conversion with entangled photon pairs,” Phys. Rev. A 83, 033807 (2011).
[CrossRef]

Dutta, B. K.

B. K. Dutta and P. K. Mahapatra, “Electromagetically induced grating in a three-level ladder-type system driven by a strong standing wave pump and weak probe field,” J. Phys. B 39, 1145–1157 (2006).

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65, 022314 (2002).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

Gao, J. W.

J. W. Gao, J. H. Wu, N. Ba, C. L. Cui, and X. X. Tian, “Efficient all-optical routing using dynamically induced transparency windows and photonic band gaps,” Phys. Rev. A 81, 013804 (2010).
[CrossRef]

C. L. Cui, J. H. Wu, J. W. Gao, Y. Zhang, and N. Ba, “Double photonic bandgaps dynamically induced in a tripod system of cold atoms,” Opt. Express 18, 4538–4546 (2010).
[CrossRef]

Gao, J. Y.

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[CrossRef]

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
[CrossRef]

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

W. H. Xu, J. H. Wu, and J. Y. Gao, “Large index of refraction without absorption via decay-induced coherence in a three-level V system,” Eur. Phys. J. D 30, 137–141 (2004).
[CrossRef]

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Lambda system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

Gong, S. Q.

Y. P. Niu and S. Q. Gong, “Enhancing Kerr nonlinearity via spontaneously generated coherence,” Phys. Rev. A 73, 053811 (2006).
[CrossRef]

Ham, B. S.

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[CrossRef]

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

Hu, X. M.

X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Jia, J. K.

C. Li. Cui, J. K. Jia, Y. Zhang, Y. Xue, H. L. Xu, and J. H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B 44, 215504 (2011).
[CrossRef]

Jiang, L.

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[CrossRef]

Jiang, Y.

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[CrossRef]

Kapale, K. T.

K. T. Kapale, M. O. Scully, S. Y. Zhu, and M. S. Zubairy, “Quenching of spontaneous emission through interference of incoherent pump processes,” Phys. Rev. A 67, 023804 (2003).
[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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

Kim, K.

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

Knight, P. L.

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

Kou, J.

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[CrossRef]

Kozlov, V. V.

V. V. Kozlov, Y. Rostovtsev, and M. O. Scully, “Whispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
[CrossRef]

La Rocca, G. C.

J. H. Wu, G. C. La Rocca, and M. Artoni, “Controlled light-pulse propagation in driven color center in diamond,” Phys. Rev. B 77, 113106 (2008).
[CrossRef]

M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef]

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Lee, C. P.

S. Y. Zhu, R. C. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
[CrossRef]

Li, A. J.

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
[CrossRef]

Li, Y. Q.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

Ling, H. Y.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

Lo, H. Y.

H. Y. Lo, P. C. Su, and Y. F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

Lukin, M. D.

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65, 022314 (2002).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

Ma, S. M.

Mahapatra, P. K.

B. K. Dutta and P. K. Mahapatra, “Electromagetically induced grating in a three-level ladder-type system driven by a strong standing wave pump and weak probe field,” J. Phys. B 39, 1145–1157 (2006).

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Menon, S.

S. Menon and G. S. Argarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Lambda system,” Phys. Rev. A 57, 4014–4018 (1998).
[CrossRef]

Niu, Y. P.

Y. P. Niu and S. Q. Gong, “Enhancing Kerr nonlinearity via spontaneously generated coherence,” Phys. Rev. A 73, 053811 (2006).
[CrossRef]

Paspalakis, E.

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

Peng, J. S.

X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

Raczynski, A.

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Polariton picture of light propagation and storing in a tripod system,” Opt. Commun. 260, 73–80 (2006).
[CrossRef]

Rostovtsev, Y.

V. V. Kozlov, Y. Rostovtsev, and M. O. Scully, “Whispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
[CrossRef]

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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

Rzepecka, M.

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Polariton picture of light propagation and storing in a tripod system,” Opt. Commun. 260, 73–80 (2006).
[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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

Scully, M. O.

V. V. Kozlov, Y. Rostovtsev, and M. O. Scully, “Whispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
[CrossRef]

K. T. Kapale, M. O. Scully, S. Y. Zhu, and M. S. Zubairy, “Quenching of spontaneous emission through interference of incoherent pump processes,” Phys. Rev. A 67, 023804 (2003).
[CrossRef]

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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
[CrossRef]

Shin, S. G.

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

Silvestri, L.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Su, P. C.

H. Y. Lo, P. C. Su, and Y. F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

Tian, X. X.

J. W. Gao, J. H. Wu, N. Ba, C. L. Cui, and X. X. Tian, “Efficient all-optical routing using dynamically induced transparency windows and photonic band gaps,” Phys. Rev. A 81, 013804 (2010).
[CrossRef]

Wan, R. G.

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[CrossRef]

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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

Wu, J. H.

C. Li. Cui, J. K. Jia, Y. Zhang, Y. Xue, H. L. Xu, and J. H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B 44, 215504 (2011).
[CrossRef]

J. W. Gao, J. H. Wu, N. Ba, C. L. Cui, and X. X. Tian, “Efficient all-optical routing using dynamically induced transparency windows and photonic band gaps,” Phys. Rev. A 81, 013804 (2010).
[CrossRef]

C. L. Cui, J. H. Wu, J. W. Gao, Y. Zhang, and N. Ba, “Double photonic bandgaps dynamically induced in a tripod system of cold atoms,” Opt. Express 18, 4538–4546 (2010).
[CrossRef]

J. H. Wu, G. C. La Rocca, and M. Artoni, “Controlled light-pulse propagation in driven color center in diamond,” Phys. Rev. B 77, 113106 (2008).
[CrossRef]

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
[CrossRef]

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

W. H. Xu, J. H. Wu, and J. Y. Gao, “Large index of refraction without absorption via decay-induced coherence in a three-level V system,” Eur. Phys. J. D 30, 137–141 (2004).
[CrossRef]

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Lambda system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

Xiao, M.

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

Xiao, Z. H.

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

Xu, H.

Xu, H. L.

C. Li. Cui, J. K. Jia, Y. Zhang, Y. Xue, H. L. Xu, and J. H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B 44, 215504 (2011).
[CrossRef]

Xu, J. H.

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

Xu, W. H.

W. H. Xu, J. H. Wu, and J. Y. Gao, “Large index of refraction without absorption via decay-induced coherence in a three-level V system,” Eur. Phys. J. D 30, 137–141 (2004).
[CrossRef]

Xue, Y.

C. Li. Cui, J. K. Jia, Y. Zhang, Y. Xue, H. L. Xu, and J. H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B 44, 215504 (2011).
[CrossRef]

Yamamoto, Y.

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

Zaremba, J.

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Polariton picture of light propagation and storing in a tripod system,” Opt. Commun. 260, 73–80 (2006).
[CrossRef]

Zhang, Y.

C. Li. Cui, J. K. Jia, Y. Zhang, Y. Xue, H. L. Xu, and J. H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B 44, 215504 (2011).
[CrossRef]

C. L. Cui, J. H. Wu, J. W. Gao, Y. Zhang, and N. Ba, “Double photonic bandgaps dynamically induced in a tripod system of cold atoms,” Opt. Express 18, 4538–4546 (2010).
[CrossRef]

Zhao, Y. C.

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
[CrossRef]

Zhu, S. Y.

K. T. Kapale, M. O. Scully, S. Y. Zhu, and M. S. Zubairy, “Quenching of spontaneous emission through interference of incoherent pump processes,” Phys. Rev. A 67, 023804 (2003).
[CrossRef]

S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
[CrossRef]

S. Y. Zhu, R. C. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
[CrossRef]

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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

Zielinska-Kaniasty, S.

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Polariton picture of light propagation and storing in a tripod system,” Opt. Commun. 260, 73–80 (2006).
[CrossRef]

Zubairy, M. S.

K. T. Kapale, M. O. Scully, S. Y. Zhu, and M. S. Zubairy, “Quenching of spontaneous emission through interference of incoherent pump processes,” Phys. Rev. A 67, 023804 (2003).
[CrossRef]

Eur. Phys. J. D (1)

W. H. Xu, J. H. Wu, and J. Y. Gao, “Large index of refraction without absorption via decay-induced coherence in a three-level V system,” Eur. Phys. J. D 30, 137–141 (2004).
[CrossRef]

J. Phys. B (4)

X. M. Hu and J. S. Peng, “Quantum interference from spontaneous decay in Lambda systems: realization in the dressed-state picture,” J. Phys. B 33, 921–931 (2000).
[CrossRef]

C. Li. Cui, J. K. Jia, Y. Zhang, Y. Xue, H. L. Xu, and J. H. Wu, “Resonant gain suppression and quantum destructive interference in a three-level open V system,” J. Phys. B 44, 215504 (2011).
[CrossRef]

B. K. Dutta and P. K. Mahapatra, “Electromagetically induced grating in a three-level ladder-type system driven by a strong standing wave pump and weak probe field,” J. Phys. B 39, 1145–1157 (2006).

Z. H. Xiao, S. G. Shin, and K. Kim, “An electromagnetically induced grating by microwave modulation,” J. Phys. B 43, 161004 (2010).
[CrossRef]

Nature (London) (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature (London) 397, 594–598 (1999).
[CrossRef]

Opt. Commun. (1)

A. Raczynski, M. Rzepecka, J. Zaremba, and S. Zielinska-Kaniasty, “Polariton picture of light propagation and storing in a tripod system,” Opt. Commun. 260, 73–80 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (13)

R. G. Wan, J. Kou, L. Jiang, Y. Jiang, and J. Y. Gao, “Electromagnetically induced grating via enhanced nonlinear modulation by spontaneously generated coherence,” Phys. Rev. A 83, 033824 (2011).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: dark-state polaritons,” Phys. Rev. A 65, 022314 (2002).
[CrossRef]

J. W. Gao, J. H. Wu, N. Ba, C. L. Cui, and X. X. Tian, “Efficient all-optical routing using dynamically induced transparency windows and photonic band gaps,” Phys. Rev. A 81, 013804 (2010).
[CrossRef]

H. Y. Ling, Y. Q. Li, and M. Xiao, “Electromagnetically induced grating: homogeneously broadened medium,” Phys. Rev. A 57, 1338–1344 (1998).
[CrossRef]

S. Menon and G. S. Argarwal, “Effects of spontaneously generated coherence on the pump-probe response of a Lambda system,” Phys. Rev. A 57, 4014–4018 (1998).
[CrossRef]

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Lambda system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

S. Y. Zhu, R. C. F. Chan, and C. P. Lee, “Spontaneous emission from a three-level atom,” Phys. Rev. A 52, 710–716 (1995).
[CrossRef]

H. Y. Lo, P. C. Su, and Y. F. Chen, “Low-light-level cross-phase modulation by quantum interference,” Phys. Rev. A 81, 053829 (2010).
[CrossRef]

S. W. Du, “Atomic-resonance-enhanced nonlinear optical frequency conversion with entangled photon pairs,” Phys. Rev. A 83, 033807 (2011).
[CrossRef]

J. H. Wu, A. J. Li, Y. Ding, Y. C. Zhao, and J. Y. Gao, “Control of spontaneous emission from a coherently driven four-level atom,” Phys. Rev. A 72, 023802 (2005).
[CrossRef]

Y. P. Niu and S. Q. Gong, “Enhancing Kerr nonlinearity via spontaneously generated coherence,” Phys. Rev. A 73, 053811 (2006).
[CrossRef]

K. T. Kapale, M. O. Scully, S. Y. Zhu, and M. S. Zubairy, “Quenching of spontaneous emission through interference of incoherent pump processes,” Phys. Rev. A 67, 023804 (2003).
[CrossRef]

V. V. Kozlov, Y. Rostovtsev, and M. O. Scully, “Whispering-gallery-mode analysis of phase-matched doubly resonant second-harmonic generation,” Phys. Rev. A 74, 063804 (2006).
[CrossRef]

Phys. Rev. B (1)

J. H. Wu, G. C. La Rocca, and M. Artoni, “Controlled light-pulse propagation in driven color center in diamond,” Phys. Rev. B 77, 113106 (2008).
[CrossRef]

Phys. Rev. Lett. (7)

M. Artoni and G. C. La Rocca, “Optically tunable photonic stop bands in homogeneous absorbing media,” Phys. Rev. Lett. 96, 073905 (2006).
[CrossRef]

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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).

J. H. Wu, J. Y. Gao, J. H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani, “Ultrafast all optical switching via tunable Fano interference,” Phys. Rev. Lett. 95, 057401 (2005).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

S. Y. Zhu and M. O. Scully, “Spectral line elimination and spontaneous emission cancellation via quantum interference,” Phys. Rev. Lett. 76, 388–391 (1996).
[CrossRef]

E. Paspalakis and P. L. Knight, “Phase control of spontaneous emission,” Phys. Rev. Lett. 81, 293–296 (1998).
[CrossRef]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

(a) Schematic diagram of a four-level atomic system with SGC effect driven by an SW coupling field and a probe field. (b) Arrangement of the probe (coupling) electric field E⃗p (E⃗c) and relevant dipole moments d⃗41 and d⃗31 (d⃗42 and d⃗32). (c) Sketch of the probe and coupling field propagating through the atomic sample.

Fig. 2.
Fig. 2.

Linear susceptibility χ(1) (a) and (b), and the absorption of the transitions |3|1 (green lines) and |4|1 (blue lines) (c) and (d), versus the probe detuning Δp in the cases with (solid curve) and without (dashed curve) SGC. The relevant parameters are chosen as Γ31=Γ32=Γ41=Γ42=0.5γ, γ3=γ4=γ, γ2=0.002γ, γ=5.75MHz, and Δ=γ.

Fig. 3.
Fig. 3.

Nonlinear susceptibility χ(3) versus the probe detuning Δp in the cases with (solid curve) and without (dashed curve) SGC. The detuning of the coupling field is chosen as Δc=0 in (a) and (b), and Δc=6γ in (c) and (d). Other parameters are the same as in Fig. 2.

Fig. 4.
Fig. 4.

(a) Amplitude and (b) phase of the transmission function T(x) as a function of the space period x/Λ. The solid curve and dashed curve correspond, respectively, to the cases with and without SGC. (c) Diffraction intensity as a function of sinθ with SGC. (d) Diffraction intensity as a function of sinθ without SGC. Parameters are as follows: Δp=0, Ωc=0.1γ, M=5, Λ=4, and L=4z0. Other parameters are the same as in Figs. 3(a) and 3(b).

Fig. 5.
Fig. 5.

Zero-order diffraction intensity as a function of the probe detuning Δp. The solid curve and dashed curve correspond, respectively, to the cases with and without SGC. Other parameters are the same as in Fig. 4.

Fig. 6.
Fig. 6.

(a) Amplitude and (b) phase of the transmission function T(x) as a function of the space period x/Λ. The solid curve and dashed curve correspond, respectively, to the cases with and without SGC. (c) Diffraction intensity as a function of sinθ with SGC. (d) Diffraction intensity as a function of sinθ without SGC. The other parameters are the same as those in Fig. 4, except Δp=0.1γ.

Fig. 7.
Fig. 7.

(a) Amplitude and (b) phase of the transmission function T(x) as a function of the space period x/Λ. The solid curve and dashed curve correspond, respectively, to the cases with and without SGC. (c) Diffraction intensity as a function of sinθ with SGC. (d) Diffraction intensity as a function of sinθ without SGC. Parameters are as follows: Δp=0, Ωc=0.3γ, M=5, Λ=4, and L=300z0. Other parameters are the same as in Figs. 3(c) and 3(d).

Fig. 8.
Fig. 8.

Second-order diffraction intensity Ip(θ2) as a function of (a) Δc and (b) L. The other parameters are the same as in Fig. 7.

Fig. 9.
Fig. 9.

(a) Amplitude and (b) phase of the transmission function T(x) as a function of the space period x/Λ for different interaction lengths as L=300z0 (solid line) and L=360z0 (dashed line). (c) Diffraction pattern as a function sinθ of when L=300z0. (d) Diffraction pattern as a function sinθ of when L=360z0.

Fig. 10.
Fig. 10.

Four-level double-Λ system with SGC (left) and four-level system without SGC (right). The latter is equivalent to the former in the dressed-state representation of an additional coupling field Ωd.

Equations (9)

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

a˙1=iΩp1*a3+iqΩp1*a4,a˙2=i(ΔpΔc)a2+iΩc1*a3+ikΩc1*a4,a˙3=i(Δp+Δ)a3γ3a3+iΩp1a1+iΩc1a2γ43a4,a˙4=i(ΔpΔ)a4γ4a4+iqΩp1a1+ikΩc1a2γ43a3,
χp=Nd312ε0χ=Nd312ε0(χ(1)+χ(3)Ωc2),χ=δ(γ4+q2γ3i2qγ43)Ωc2(qk)2δ(γ432+γ3γ4)Ωc2(γ4+k2γ3i2kγ43),
χ(1)=γ4+q2γ3i2qγ43γ432+γ3γ4
χ(3)=1δ(γ432+γ3γ4)((γ4+q2γ3i2qγ43)(γ4+k2γ3i2kγ43)γ432+γ3γ4(qk)2),
Epz=iπε0λpP,
Epz=iχpEp,
T=eIm[χp]γLeiRe[χp]γL,
Ip(θ)=|F(θ)|2sin2(MπΛsinθ/λp)M2sin2(πΛsinθ/λp),
Ip(θ1)=|F(θ1)|2=|01Texp(i2πx)dx|2.

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