Abstract

Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.

© 2002 Optical Society of America

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  9. P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
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  25. N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
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  34. S. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
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  35. S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
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  36. H. G. Winful and V. Perlin, “Raman gap solitons,” Phys. Rev. Lett. 84, 3586–3589 (2000).
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  37. C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
    [CrossRef]
  38. G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1640 (1999).
    [CrossRef]
  39. M. Lukin and A. Imamoǧlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
  41. A. Imamoǧlu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).
    [CrossRef]

2000 (5)

P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
[CrossRef]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

H. G. Winful and V. Perlin, “Raman gap solitons,” Phys. Rev. Lett. 84, 3586–3589 (2000).
[CrossRef] [PubMed]

M. Lukin and A. Imamoǧlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef] [PubMed]

1999 (4)

S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1640 (1999).
[CrossRef]

T. Opatrný, B. Malomed, and G. Kurizki, “Dark and bright solitons in resonantly absorbing gratings,” Phys. Rev. E 60, 6137–6149 (1999).
[CrossRef]

1998 (4)

A. Kozhekin and G. Kurizki, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

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

H. Kimble, “Strong interaction of single atoms and photons in cavity QED,” Phys. Scr. 76, 127–137 (1998).
[CrossRef]

N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
[CrossRef]

1997 (2)

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

A. Imamoǧlu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).
[CrossRef]

1996 (3)

H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[CrossRef] [PubMed]

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

1995 (3)

Z. Cheng and G. Kurizki, “Optical ‘multiexcitons’: quantum gap solitons in nonlinear Bragg reflectors,” Phys. Rev. Lett. 75, 3430–3433 (1995).
[CrossRef] [PubMed]

A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

B. Mantsyzov, “Gap 2π pulse with an inhomogeneously broadened line and an oscillating solitary wave,” Phys. Rev. A 51, 4939–4943 (1995).
[CrossRef] [PubMed]

1994 (3)

A. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and induced atomic decay in photonic band structures,” J. Mod. Opt. 41, 353–384 (1994).
[CrossRef]

M. Scalora, J. Dowling, C. Bowden, and M. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

1993 (1)

J. Feng and F. Kneubuhl, “Solitons in a periodic structure with Kerr nonlinearity,” IEEE J. Quantum Electron. 29, 590 (1993).
[CrossRef]

1991 (2)

S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (2)

D. Christodoulides and R. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989).
[CrossRef] [PubMed]

A. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–40 (1989).
[CrossRef]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

1982 (1)

1969 (1)

S. McCall and E. Hahn, “Self-induced transparency,” Phys. Rev. 183, 457–485 (1969).
[CrossRef]

1967 (1)

S. McCall and E. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

Aceves, A.

A. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–40 (1989).
[CrossRef]

Aközbek, N.

N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
[CrossRef]

Bay, S.

P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
[CrossRef]

Blaauboer, M.

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

Bloemer, M.

M. Scalora, J. Dowling, C. Bowden, and M. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

Boggs, B.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Bowden, C.

M. Scalora, J. Dowling, C. Bowden, and M. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Bowden, C. M.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

Brommer, K. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Cheng, Z.

Z. Cheng and G. Kurizki, “Optical ‘multiexcitons’: quantum gap solitons in nonlinear Bragg reflectors,” Phys. Rev. Lett. 75, 3430–3433 (1995).
[CrossRef] [PubMed]

Christodoulides, D.

D. Christodoulides and R. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989).
[CrossRef] [PubMed]

de Sterke, C.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Deutsch, M.

A. Imamoǧlu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).
[CrossRef]

Dowling, J.

M. Scalora, J. Dowling, C. Bowden, and M. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

Dowling, J. P.

M. Scalora, J. P. Dowling, C. M. Bowden, and M. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

Eggleton, B.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Fan, S.

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

Feng, J.

J. Feng and F. Kneubuhl, “Solitons in a periodic structure with Kerr nonlinearity,” IEEE J. Quantum Electron. 29, 590 (1993).
[CrossRef]

Gibbs, H.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1640 (1999).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Greiner, C.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Hahn, E.

S. McCall and E. Hahn, “Self-induced transparency,” Phys. Rev. 183, 457–485 (1969).
[CrossRef]

S. McCall and E. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

Harris, S.

S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

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

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

Hau, L.

S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

Imamog?lu, A.

M. Lukin and A. Imamoǧlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef] [PubMed]

A. Imamoǧlu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).
[CrossRef]

Imamoglu, A.

Jahnke, F.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1640 (1999).
[CrossRef]

Joannopoulos, J.

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

Joannopoulos, J. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

John, S.

N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
[CrossRef]

S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Joseph, R.

D. Christodoulides and R. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989).
[CrossRef] [PubMed]

Khitrova, G.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1640 (1999).
[CrossRef]

Kimble, H.

H. Kimble, “Strong interaction of single atoms and photons in cavity QED,” Phys. Scr. 76, 127–137 (1998).
[CrossRef]

Kira, M.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1640 (1999).
[CrossRef]

Kneubuhl, F.

J. Feng and F. Kneubuhl, “Solitons in a periodic structure with Kerr nonlinearity,” IEEE J. Quantum Electron. 29, 590 (1993).
[CrossRef]

Koch, S.

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1640 (1999).
[CrossRef]

Kofman, A.

A. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and induced atomic decay in photonic band structures,” J. Mod. Opt. 41, 353–384 (1994).
[CrossRef]

Kozhekin, A.

A. Kozhekin and G. Kurizki, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

Krug, P.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Kurizki, G.

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

T. Opatrný, B. Malomed, and G. Kurizki, “Dark and bright solitons in resonantly absorbing gratings,” Phys. Rev. E 60, 6137–6149 (1999).
[CrossRef]

A. Kozhekin and G. Kurizki, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

Z. Cheng and G. Kurizki, “Optical ‘multiexcitons’: quantum gap solitons in nonlinear Bragg reflectors,” Phys. Rev. Lett. 75, 3430–3433 (1995).
[CrossRef] [PubMed]

A. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and induced atomic decay in photonic band structures,” J. Mod. Opt. 41, 353–384 (1994).
[CrossRef]

Lambropoulos, P.

P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
[CrossRef]

Loftus, T.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Lukin, M.

M. Lukin and A. Imamoǧlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef] [PubMed]

Malomed, B.

T. Opatrný, B. Malomed, and G. Kurizki, “Dark and bright solitons in resonantly absorbing gratings,” Phys. Rev. E 60, 6137–6149 (1999).
[CrossRef]

Malomed, B. A.

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

Mantsyzov, B.

B. Mantsyzov, “Gap 2π pulse with an inhomogeneously broadened line and an oscillating solitary wave,” Phys. Rev. A 51, 4939–4943 (1995).
[CrossRef] [PubMed]

McCall, S.

S. McCall and E. Hahn, “Self-induced transparency,” Phys. Rev. 183, 457–485 (1969).
[CrossRef]

S. McCall and E. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

Meade, R. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Mossberg, T.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Mossberg, T. W.

Nielsen, T. R.

P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
[CrossRef]

Nikolopoulos, G. M.

P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
[CrossRef]

Opatrný, T.

T. Opatrný, B. Malomed, and G. Kurizki, “Dark and bright solitons in resonantly absorbing gratings,” Phys. Rev. E 60, 6137–6149 (1999).
[CrossRef]

Perlin, V.

H. G. Winful and V. Perlin, “Raman gap solitons,” Phys. Rev. Lett. 84, 3586–3589 (2000).
[CrossRef] [PubMed]

Rappe, A. M.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Scalora, M.

M. Scalora, J. Dowling, C. Bowden, and M. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

M. Scalora, J. P. Dowling, C. M. Bowden, and M. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

Schmidt, H.

A. Imamoǧlu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).
[CrossRef]

H. Schmidt and A. Imamoğlu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[CrossRef] [PubMed]

Sherman, B.

A. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and induced atomic decay in photonic band structures,” J. Mod. Opt. 41, 353–384 (1994).
[CrossRef]

Silberberg, Y.

Sipe, J.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Slusher, R.

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

Villeneuve, P.

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

Wabnitz, S.

A. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–40 (1989).
[CrossRef]

Wang, J.

S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991).
[CrossRef]

Wang, T.

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Winful, H. G.

H. G. Winful and V. Perlin, “Raman gap solitons,” Phys. Rev. Lett. 84, 3586–3589 (2000).
[CrossRef] [PubMed]

Woods, G.

A. Imamoǧlu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yamamoto, Y.

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

IEEE J. Quantum Electron. (1)

J. Feng and F. Kneubuhl, “Solitons in a periodic structure with Kerr nonlinearity,” IEEE J. Quantum Electron. 29, 590 (1993).
[CrossRef]

J. Appl. Phys. (1)

M. Scalora, J. P. Dowling, C. M. Bowden, and M. Bloemer, “The photonic band edge optical diode,” J. Appl. Phys. 76, 2023–2026 (1994).
[CrossRef]

J. Mod. Opt. (1)

A. Kofman, G. Kurizki, and B. Sherman, “Spontaneous and induced atomic decay in photonic band structures,” J. Mod. Opt. 41, 353–384 (1994).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

A. Aceves and S. Wabnitz, “Self-induced transparency solitons in nonlinear refractive periodic media,” Phys. Lett. A 141, 37–40 (1989).
[CrossRef]

Phys. Rev. (1)

S. McCall and E. Hahn, “Self-induced transparency,” Phys. Rev. 183, 457–485 (1969).
[CrossRef]

Phys. Rev. A (2)

B. Mantsyzov, “Gap 2π pulse with an inhomogeneously broadened line and an oscillating solitary wave,” Phys. Rev. A 51, 4939–4943 (1995).
[CrossRef] [PubMed]

C. Greiner, B. Boggs, T. Loftus, T. Wang, and T. Mossberg, “Polarization-dependent Rabi frequency beats in the coherent response of Tm3+ in YAG,” Phys. Rev. A 60, R2657–R2660 (1999).
[CrossRef]

Phys. Rev. B (2)

S. John and J. Wang, “Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991).
[CrossRef]

P. Villeneuve, S. Fan, and J. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).
[CrossRef]

Phys. Rev. E (3)

T. Opatrný, B. Malomed, and G. Kurizki, “Dark and bright solitons in resonantly absorbing gratings,” Phys. Rev. E 60, 6137–6149 (1999).
[CrossRef]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E 62, R57–R59 (2000).
[CrossRef]

N. Aközbek and S. John, “Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,” Phys. Rev. E 58, 3876–3895 (1998).
[CrossRef]

Phys. Rev. Lett. (16)

B. Eggleton, R. Slusher, C. de Sterke, P. Krug, and J. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
[CrossRef] [PubMed]

S. McCall and E. Hahn, “Self-induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[CrossRef]

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

S. Harris and L. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

H. G. Winful and V. Perlin, “Raman gap solitons,” Phys. Rev. Lett. 84, 3586–3589 (2000).
[CrossRef] [PubMed]

M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84, 1906–1909 (2000).
[CrossRef] [PubMed]

D. Christodoulides and R. Joseph, “Slow Bragg solitons in nonlinear periodic structures,” Phys. Rev. Lett. 62, 1746–1749 (1989).
[CrossRef] [PubMed]

A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74, 5020–5023 (1995).
[CrossRef] [PubMed]

A. Kozhekin and G. Kurizki, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Z. Cheng and G. Kurizki, “Optical ‘multiexcitons’: quantum gap solitons in nonlinear Bragg reflectors,” Phys. Rev. Lett. 75, 3430–3433 (1995).
[CrossRef] [PubMed]

M. Scalora, J. Dowling, C. Bowden, and M. Bloemer, “Optical limiting and switching of ultrashort pulses in nonlinear photonic band gap materials,” Phys. Rev. Lett. 73, 1368–1371 (1994).
[CrossRef] [PubMed]

M. Lukin and A. Imamoǧlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef] [PubMed]

A. Imamoǧlu, H. Schmidt, G. Woods, and M. Deutsch, “Strongly interacting photons in a nonlinear cavity,” Phys. Rev. Lett. 79, 1467–1470 (1997).
[CrossRef]

Phys. Scr. (1)

H. Kimble, “Strong interaction of single atoms and photons in cavity QED,” Phys. Scr. 76, 127–137 (1998).
[CrossRef]

Phys. Today (1)

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

Rep. Prog. Phys. (1)

P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, “Fundamental quantum optics in structured reservoirs,” Rep. Prog. Phys. 63, 455–503 (2000).
[CrossRef]

Rev. Mod. Phys. (1)

G. Khitrova, H. Gibbs, F. Jahnke, M. Kira, and S. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1640 (1999).
[CrossRef]

Other (6)

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, Princeton, N.J., 1995).

G. Kurizki, A. Kozhekin, T. Opatrny, and B. Malomed, “Optical solitons in periodic media with resonant and off-resonant nonlinearities,” in Progress in Optics E. Wolf, ed. (Elsevier, North-Holland, 2001), Vol. 42, pp. 93–146.

See the Photonic Band-Gap Bibliography, J. Dowling, H. Everitt, and E. Yablonovitch, eds., at http://home.earthlink.net/ ˜jpdowling/pbgbib.html.

M. Scully and M. Zubairy, in Quantum Optics (Cambridge University, Cambridge, 1997), Chap. 7.

C. de Sterke and J. E. Sipe, “Gap solitons,” in Progress in Optics E. Wolf, ed. (Elsevier, North-Holland, 1997), Vol. 33, Chap. 3, pp. 205–259.

A. Newell and J. Moloney, Nonlinear Optics (Addison-Wesley, Reading, Mass., 1992).

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Figures (7)

Fig. 1
Fig. 1

Schematic description of the periodic RABR and of the decomposition of the electric field E into modes Σ+ and Σ-. The shading represents regions with different indices of refraction; the darker the shading, the larger n is. The black regions correspond to the TLA layers. The localization of the field envelope over ∼20 structure periods is shown for the sake of visualization; in reality, the field is localized over a hundred or more periods.

Fig. 2
Fig. 2

RABR dispersion curves at η=0.5 and δ=-0.2. The solid curves show the dispersion branches corresponding to the ‘bare’ (noninteracting) grating, and the dashed and dash-dotted lines stand for the dispersion branches of the grating ‘dressed’ by the active medium. The frequency bands that support the standing dark and bright solitons are shaded.

Fig. 3
Fig. 3

Pulses obtained as a result of ‘pushing’ a zero-velocity RABR soliton (dashed curves): (a) push, characterized by the initial multiplier exp(-ipζ) after a sufficiently long evolution (τ=400) (solid curves). δ=0, η=4, χ=-4.4, and p=0.1. (b) idem, but for p=0.5.

Fig. 4
Fig. 4

Forward-propagating electric field of the two-dimensional ‘light bullet’ in the Bragg reflector, |EF|, versus time τ and transverse coordinate x, after having propagated the distance z=1000. The parameters are η=0.1, δ=0.2, C=0.1, and Ө0=-1000. The field is scaled by the constant /4τ0μn0.

Fig. 5
Fig. 5

(a) Schematic representation of the atomic system interaction with a strong driving field on the transition |2|3 and weak fields Ea and Eb on the transitions |1|2 and |3|4, respectively. (b) Absorption and dispersion spectra of the Ea field in the absence (solid curve) or presence (dashed curve) of the Eb field.

Fig. 6
Fig. 6

(a) Schematic representation of the field–atom system: The probe field Ea exhibits EIT on the transition |1|2, in the presence of the driving field Ed on the transition |3|2. The control field Eb exhibits a SIT GS on the transitions |5|6. The transition |3|4 serves to cross couple the two fields. Initially only the states |1〉 and |5〉 are populated. (b) Polarizations and propagation directions of the fields involved in the transitions above.

Fig. 7
Fig. 7

Schematic representation of the level scheme suitable for EIT in the presence of a Raman GS (only the relevant levels are shown).

Equations (45)

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2θζτ˜=-sin θ
τ˜=(t-n0z/c)/τ0,ζ=n0z/(cτ0),
τ0=n0μ2πωcϱ0
Ω(ζ, τ˜)=(τ0)-1A0 sech[β(ζ-vτ˜)],
E(z, t)=(μτ0)-1{Re[Σ+(z, t)exp(-iωct)]cos kcz-Im[Σ-(z, t)exp(-iωct)]sin kcz}.
exp(ikcz2j)=1,exp(ikcz2j+1)=-1,
Pτ=-iδP+Σ+w,
wτ=-Re(Σ+P*).
w=1-|P|2.
2Σ+τ2-2Σ+ζ2=η2Σ++2i(η-δ)P-21-|P|2Σ+,
2Σ-τ2-2Σ-ζ2=-η2Σ--2Pζ,
Pτ=-iδP-1-|P|2Σ+,
Σ+=A exp[i(κζ-χτ)],Σ-=B exp[i(κζ-χτ)],
w=-1,P=C exp[i(κζ-χτ)],
(χ2-κ2-η2)(χ-δ)×{(χ-δ)[χ2-κ2-(2+η2)]+2(η-δ)}=0.
χ0=η,χ0,±=-(η-δ)/2±2+(η+δ)2/2,
χ=±k,χ=δ+2(η-δ)k-2.
η=η0δ/2+1+δ2/4,
Σ+=exp(-iχτ)S(ζ),P=i exp(-iχτ)P(ζ),
d2Sdζ2=(η2-χ2)S-2S(η-χ)sign(χ-δ)(χ-δ)2+S2.
χ1,21/2[δ-η(η+δ)2+8]
S(ζ)=2|χ-δ|R(ζ)[1-R2(ζ)]-1,
|ζ|=2χ-δχ-η(1-R02)-1/2tan-1R02-R21-R02+(2R0)-1lnR0+R02-R2R,
Smax=4R0/|χ+η|.
A+(χ2-η2)A=2P,
S2|χ-δ|R0 sech2χ-ηχ-δR0ζ.
2iχ0(χ0-δ)2-η+δ(χ0-δ)2τ+2ζ2+χ0-η(χ0-δ)3|S|2S=η2-χ02+2χ0-ηχ0-δS.
-i3Σ+τx2+i3Σ-ζx2+2Σ+τ2-2Σ+ζ2+η2Σ+x2+η2Σ+-2Pτ-2iηP=0,
-i3Σ-τx2+i3Σ+ζx2+2Σ-τ2-2Σ-ζ2-η2Σ-x2+η2Σ-+2Pζ=0,
Σ+=A0sech Ө1 sech Ө2 exp[i(κζ-χτ)+iπ/4],
Σ-=Σ+/v,
P=sech Ө1 sech Ө2(tanh Ө1+tanh Ө2)2+δ-η4ηC4[(tanh Ө1-tanh Ө2)2-2(sech2 Ө1+sech2 Ө2)]21/2×exp[i(κζ-χτ)+iν],
w=(1-|P|2)1/2,
A0=2δ/η-1,β=δ/η+1,
v=-(δ-η)/(δ+η),κ=-δ2-η2,
χ=δ.
δ/η-1C2,
δ/η-1C21.
ϕa=Re(αa)z-α0γ2|Ωb|22Δb|Ωd|2z,
Im(αa)=-γ4 Re(αa)2ΔbRe(αa),
Im(αa,b)=α0γ2|Ωb,a|2γ4|Ωd|2;
vg(a)2|Ωd|2α0γ3c/n0
ΩSIT(z, t)=Ωb sechtvg(b)-z2β,
θb=-ΩSITdt=Ωbvg(b)αbπ,
vg(b)=Ωb2αb.

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