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Optical precursors were first studied by Sommerfield and Brillouin in 1914 to resolve the apparent contradictions between fast light propagation and the theory of relativity. They showed theoretically that the front edge of a step-modulated pulse does not interact with the medium and always travels at c because the dispersive material has a finite response time to the optical pulse. The past experimental studies of precursors in classical pulse propagation were always focused on an opaque medium with single or multiple Lorentz absorption lines. In these cases, the precursor signal cannot be separated from the main pulse or otherwise the main field is absorbed. However, the electromagnetically induced transparency (EIT) technique was successfully used to separate precursors from the main pulse due to the slow-light effect in cold atoms. The EIT refers to the absorption suppression or elimination of a probe field through atomic coherence in a certain medium dressed by a strong coupling field. In this paper, a four-level double-lambda atomic system with two upper states coupled to the excited state is explored to separate optical precursors from a square-modulated laser pulse with the effect of spontaneously generated coherence (SGC). The SGC effect occurs in the process of spontaneous emission, in which the atom decays from closely placed upper levels to a single ground level. The quantum interference between the decay channels takes place, which leads to decay induced transparency, thus enhancing the Kerr nonlinearity and amplification without inversion. With the assistance of spontaneously generated coherence, an EIT window appears with steep normal dispersion when the trigger field is far from resonance. Then we can obtain the optical precursors which are separated from the main pulse due to the slow-light effects in the EIT window. In the absence of SGC, the main pulse is absorbed by an opaque medium with Lorentz absorptive lines, so the slow-light effect could not take place. In addition, we obtain the stacked optical precursors with the input probe field amplitude or phase modulated by designing a series of square pulses. For the amplitude modulation case, the peak power reaches about 4.5 times that of the input pulse. With the phase modulation we obtain a transient pulse with a peak power of 14 times that of the input, as a result of constructive interference between the stacked precursors and main field. We expect these findings to be instructive in devising optical devices for optical communication, detection and medical imaging among other applications.
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Keywords:
- atomic coherence /
- electromagnetically induced transparency /
- spontaneously generated coherence
[1] Harris S E 1997 Phys. Today 50 36
[2] Fleischhauer M, Imamoglu A, Marangos J P 2005 Rev. Mod. Phys. 77 633
[3] Hau L V, Harris S E, Dutton Z, Behroozi C H 1999 Nature 397 594
[4] Turukhin A V, Sudarshanam V S, Shahriar M S, Musser J A, Ham B S, Hemmer P R 2001 Phys. Rev. Lett. 88 023602
[5] Jiang Q C, Liu C, Liu J H, Zhang J X 2015 Acta Phys. Sin. 64 094208 (in Chinese) [姜其畅, 刘超, 刘晋宏, 张俊香 2015 64 094208]
[6] Liu C, Dutton Z, Behroozi C H, Hau L V 2001 Nature 409 490
[7] Bajcsy M, Zibrov A S, Lukin M D 2003 Nature 426 638
[8] Longdell J J, Fraval E, Sellars M J, Manson N B 2005 Phys. Rev. Lett. 95 063601
[9] Zhang X H, Bao Q Q, Zhang Y, Su M C, Cui C L, Wu J H 2012 Chin. Phys. B 21 054209
[10] Yan Y, Li S J, Tian L, Wang H 2016 Acta Phys. Sin. 65 014205 (in Chinese) [闫妍, 李淑静, 田龙, 王海 2016 65 014205]
[11] Wang X X, Sun J X, Sun Y H, Li A J, Chen Y, Zhang X J, Kang Z H, Wang L, Wang H H, Gao J Y 2015 Chin. Phys. B 24 074204
[12] Wang L, Luo M X, Sun J X, Sun Y H, Chen Y, Wei X G, Kang Z H, Wang H H, Gao J Y 2015 Chin. Phys. B 24 064205
[13] Menon S, Argarwal G S 1998 Phys. Rev. A 57 4014
[14] Paspalakis E, Knight P L L 1998 Phys. Rev. Lett. 81 293
[15] Wu J H, Gao J Y 2002 Phys. Rev. A 65 063807
[16] Zhang B, Liu Z X, Xu W C 2013 Acta Phys. Sin. 62 164207 (in Chinese) [张冰, 刘志学, 徐万超 2013 62 164207]
[17] Zhu S Y, Chan R C F, Lee C P 1995 Phys. Rev. A 52 710
[18] Xu W H, Wu J H, Gao J Y 2004 Eur. Phys. J. D 30 137
[19] Wan R G, Kou J, Jiang L, Jiang Y, Gao J Y 2011 Phys. Rev. A 83 033824
[20] Ba N, Wang L, Wu X Y, Liu X J, Wang H H, Cui C L, Li A J 2013 Appl. Opt. 52 4264
[21] Yao Y P, Zhang T Y, Kou J, Wan R G 2013 Phys. Lett. A 377 1416
[22] Sommerfeld A 1914 Ann. Phys. 349 177
[23] Brillouin L 1914 Ann. Phys. 349 203
[24] Falcon E, Laroche C, Fauve S 2003 Phys. Rev. Lett. 91 064502
[25] Jeong H, Dawes A M C, Gauthier D J 2006 Phys. Rev. Lett. 96 143901
[26] Lynch F J, Holland R E, Hamermesh M 1960 Phy. Rev. 120 513
[27] Pleshko P, Palocz I 1969 Phys. Rev. Lett 22 1201
[28] Varoquaux E, Williams G A, Avenel O 1986 Phys. Rev. B 34 7617
[29] Choi S H, sterberg U L 2004 Phys. Rev. Lett. 92 193903
[30] Wei D, Chen J F, Loy M M T, Wong G K L, Du S W 2009 Phys. Rev. Lett. 103 093602
[31] Chen J F, Jeong H, Feng L, Loy M M T, Wong G K L, Du S W 2010 Phys. Rev. Lett. 104 223602
[32] Jeong H, Du S W 2009 Phys. Rev. A 79 011802
[33] Chen J F, Wang S, Wei D, Loy M M T, Wong G K L, Du S W 2010 Phys. Rev. A 81 033844
[34] Du S, Belthangady C, Kolchin P, Ying G Y, Harris S E 2008 Opt. Lett. 33 2149
[35] Peng Y D, Niu Y P, Qi Y H, Yao H F, Gong S Q 2011 Phys. Rev. A 83 013812
[36] Peng Y D, Yang A H, Li D H, Zhao X H, Jiang L, Zhang L Y 2013 J. Mod. Opt. 60 1343
[37] Richard A, John P, Richard M 1989 J. Opt. Soc. Am. A 6 1441
[38] Bao Q Q, Fang B, Yang X, Cui C L, Wu J H 2014 J. Opt. Soc. Am. B 31 62
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[1] Harris S E 1997 Phys. Today 50 36
[2] Fleischhauer M, Imamoglu A, Marangos J P 2005 Rev. Mod. Phys. 77 633
[3] Hau L V, Harris S E, Dutton Z, Behroozi C H 1999 Nature 397 594
[4] Turukhin A V, Sudarshanam V S, Shahriar M S, Musser J A, Ham B S, Hemmer P R 2001 Phys. Rev. Lett. 88 023602
[5] Jiang Q C, Liu C, Liu J H, Zhang J X 2015 Acta Phys. Sin. 64 094208 (in Chinese) [姜其畅, 刘超, 刘晋宏, 张俊香 2015 64 094208]
[6] Liu C, Dutton Z, Behroozi C H, Hau L V 2001 Nature 409 490
[7] Bajcsy M, Zibrov A S, Lukin M D 2003 Nature 426 638
[8] Longdell J J, Fraval E, Sellars M J, Manson N B 2005 Phys. Rev. Lett. 95 063601
[9] Zhang X H, Bao Q Q, Zhang Y, Su M C, Cui C L, Wu J H 2012 Chin. Phys. B 21 054209
[10] Yan Y, Li S J, Tian L, Wang H 2016 Acta Phys. Sin. 65 014205 (in Chinese) [闫妍, 李淑静, 田龙, 王海 2016 65 014205]
[11] Wang X X, Sun J X, Sun Y H, Li A J, Chen Y, Zhang X J, Kang Z H, Wang L, Wang H H, Gao J Y 2015 Chin. Phys. B 24 074204
[12] Wang L, Luo M X, Sun J X, Sun Y H, Chen Y, Wei X G, Kang Z H, Wang H H, Gao J Y 2015 Chin. Phys. B 24 064205
[13] Menon S, Argarwal G S 1998 Phys. Rev. A 57 4014
[14] Paspalakis E, Knight P L L 1998 Phys. Rev. Lett. 81 293
[15] Wu J H, Gao J Y 2002 Phys. Rev. A 65 063807
[16] Zhang B, Liu Z X, Xu W C 2013 Acta Phys. Sin. 62 164207 (in Chinese) [张冰, 刘志学, 徐万超 2013 62 164207]
[17] Zhu S Y, Chan R C F, Lee C P 1995 Phys. Rev. A 52 710
[18] Xu W H, Wu J H, Gao J Y 2004 Eur. Phys. J. D 30 137
[19] Wan R G, Kou J, Jiang L, Jiang Y, Gao J Y 2011 Phys. Rev. A 83 033824
[20] Ba N, Wang L, Wu X Y, Liu X J, Wang H H, Cui C L, Li A J 2013 Appl. Opt. 52 4264
[21] Yao Y P, Zhang T Y, Kou J, Wan R G 2013 Phys. Lett. A 377 1416
[22] Sommerfeld A 1914 Ann. Phys. 349 177
[23] Brillouin L 1914 Ann. Phys. 349 203
[24] Falcon E, Laroche C, Fauve S 2003 Phys. Rev. Lett. 91 064502
[25] Jeong H, Dawes A M C, Gauthier D J 2006 Phys. Rev. Lett. 96 143901
[26] Lynch F J, Holland R E, Hamermesh M 1960 Phy. Rev. 120 513
[27] Pleshko P, Palocz I 1969 Phys. Rev. Lett 22 1201
[28] Varoquaux E, Williams G A, Avenel O 1986 Phys. Rev. B 34 7617
[29] Choi S H, sterberg U L 2004 Phys. Rev. Lett. 92 193903
[30] Wei D, Chen J F, Loy M M T, Wong G K L, Du S W 2009 Phys. Rev. Lett. 103 093602
[31] Chen J F, Jeong H, Feng L, Loy M M T, Wong G K L, Du S W 2010 Phys. Rev. Lett. 104 223602
[32] Jeong H, Du S W 2009 Phys. Rev. A 79 011802
[33] Chen J F, Wang S, Wei D, Loy M M T, Wong G K L, Du S W 2010 Phys. Rev. A 81 033844
[34] Du S, Belthangady C, Kolchin P, Ying G Y, Harris S E 2008 Opt. Lett. 33 2149
[35] Peng Y D, Niu Y P, Qi Y H, Yao H F, Gong S Q 2011 Phys. Rev. A 83 013812
[36] Peng Y D, Yang A H, Li D H, Zhao X H, Jiang L, Zhang L Y 2013 J. Mod. Opt. 60 1343
[37] Richard A, John P, Richard M 1989 J. Opt. Soc. Am. A 6 1441
[38] Bao Q Q, Fang B, Yang X, Cui C L, Wu J H 2014 J. Opt. Soc. Am. B 31 62
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