Abstract

A practical method of slowing and stopping an incident ultra-short light pulse with a resonantly absorbing Bragg reflector is demonstrated numerically. It is shown that an incident laser pulse with suitable pulse area evolves from a given pulse waveform into a stable, spatially-localized oscillating or standing gap soliton. We show that multiple gap solitons can be simultaneously spatially localized, resulting in efficient optical energy conversion and storage in the resonantly absorbing Bragg structure as atomically coherent states.

© 2003 Optical Society of America

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References

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  25. A. Andre and M.D. Lukin, �??Manupulating light pulses via dynamically controlled photonic band gap,�?? Phys. Rev. Lett. 89, 143602 (2002).
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  26. S. Chi, B. Luo, H.Y. Tseng, �??Ultrashort Bragg soliton in a fiber Bragg grating,�?? Opt. Comm. 206, 115�??121 (2002)
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Appl. Phys. Lett. (1)

J.P. Prineas, J.Y. Zhou, J. Kuhl, H. M. Gibbs, G. Khitrova, S. W. Koch, A. Knorr, �??Ultrafast ac Stark effect switching of active photonic bandgap from Bragg-periodic semiconductor quantum wells,�?? Appl. Phys. Lett. 81, 4332 (2002).
[CrossRef]

J. Nonlinear Opt. Phys. & Mat. (1)

C. Conti, G. Assanto and S. Trillo, �??Gap solitons and slow light,�?? J. Nonlinear Opt. Phys. & Mat. 11, 239�??259 (2002).
[CrossRef]

J. Opt. Soc. Am B (1)

B. I. Mantsyzov and R. A. Silnikov, �??Unstable excited and stable oscillating gap 2�? pulses,�?? J. Opt. Soc. Am B19, 2203-2207 (2002).

JETP Letters (2)

B. I. Mantsyzov and R. A. Sil�??nikov, �??Oscillating gap 2�? pulse in resonantly absorbing lattice,�?? JETP Letters 74, 456�??459 (2001).
[CrossRef]

V. G. Arkhipkin and I. V. Timofeev, �??Electromagnetically induced transparency: writing, storing, and reading short optical pulses,�?? JETP Letters 76, 66 (2002).
[CrossRef]

Opt. Comm. (1)

S. Chi, B. Luo, H.Y. Tseng, �??Ultrashort Bragg soliton in a fiber Bragg grating,�?? Opt. Comm. 206, 115�??121 (2002)
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (1)

S.L. McCall and E.L. Hahn, Phys. Rev. 183, 457 (1969)
[CrossRef]

Phys. Rev. A (1)

B. I. Mantsyzov, �??Gap 2�? pulse with an inhomogeneously broadened line and an oscillating solitary wave,�?? Phys. Rev. A 51, 4939 (1995).
[CrossRef] [PubMed]

Phys. Rev. B (1)

J. P. Prineas, C. Ell, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, �??Exciton-polariton eigenmodes in light-coupled In0.04Ga0.96As/GaAs semiconductor multiple quantum-well structures,�?? Phys. Rev. B, 61, 13863 (2000).
[CrossRef]

Phys. Rev. E (2)

N. Akozbek and S. John, �??Self-induced transparency solitary waves in a doped nonlinear photonic band gap material,�?? Phys. Rev. E 58, 3876 (1998).
[CrossRef]

J. Cheng, J. Y. Zhou, �??Effects of the near-dipole-dipole interaction on gap solitons in resonantly absorbing gratings,�?? Phys. Rev. E 66, 036606 (2002).
[CrossRef]

Phys. Rev. Lett. (8)

A. Andre and M.D. Lukin, �??Manupulating light pulses via dynamically controlled photonic band gap,�?? Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, �??Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,�?? Phys. Rev. Lett. 76, 4199 (1996).
[CrossRef] [PubMed]

M. Hübner, J. Prineas, C. Ell, P. Brick, E.S. Lee, G. Khitrova, H.M. Gibbs, and S.W. Koch, �??Optical lattices achieved by excitons in periodic quantum well structures,�?? Phys. Rev. Lett. 83, 2841 (1999).
[CrossRef]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, �??Storage of light in atomic vapor,�?? Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, �??Bragg grating solitons,�?? Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

W. Chen and D. L. Mills, �??Gap solitons and the nonlinear optical response of superlattices,�?? Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

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

A. E. Kozhekin and G. Kurizki, �??Standing and moving gap solitons in resonantly absorbing gratings,�?? Phys. Rev. Lett. 81, 3647 (1998).
[CrossRef]

Phys. Solid State (1)

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, �??Bragg reflection of light from quantum wells�?? Fiz. Tverd. Tela (St. Petersburg) 36, 2118 (1994) [Phys. Solid State 36, 1156 (1994)].

Progress in Optics (1)

G. Kurizki, A. E. Kozhekin, T. Opatrny, B. A. Malomed, �??Optical solitons in periodic media with resonant and off-resonant nonlinearities,�?? Progress in Optics 42, ed. E. Wolf, 93�??140 (2001).
[CrossRef]

Sov. Phys. JETP (1)

B. I. Mantsyzov and R. N. Kuz�??min, �??Coherent interaction of light with a discrete periodic resonant medium,�?? Sov. Phys. JETP 64, 37�??44 (1986).

Other (2)

R. E. Slusher and B. J. Eggleton (editors), Nonlinear Photonic Crystals (Springer-Verlag, Berlin, Heidelberg, 2003).

P. Meystre and M. Sagent III, Elements of Quantum Optics (Springer-Verlag, World Publishing Corp., 1992).

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Figures (4)

Fig. 1.
Fig. 1.

Contour plot for the inversion n(x, t) for varying pulse amplitudes Ω0+. Time t is on vertical axis, position in the structure x is on the axis, and n is out of the page. The black corresponds to n=1, i.e. population inversion, and the white to n=-1, two-level systems in ground state. Thus the dark line tracks the localized excitation through the structure in spacetime. (a) Ω0+=1.5;(b) Ω0+=3.6; (c) Ω0+=4.3; (d) Ω0+=8.4.τ 0=0.5 for all plots. The incident pulses all have sech profiles.

Fig. 2.
Fig. 2.

Distributions for n(x), P(x), Ω0±(x) at t=90 within the structure in Fig. 1(b).

Fig. 3.
Fig. 3.

(a):Stability of a decelerating soliton against an added stochastic perturbation. Plot layout is the same as described in Fig. 1. All parameters are the same as in Fig. 1 except for the added stochastic perturbation. (b)The effects of the transverse and longitude relaxations on the existence of a decelerating soliton; here T 1=T 2=100τc and initial conditions are the same as in Fig. 1 except that Ω0+=4.0.

Fig. 4.
Fig. 4.

Collisions of two serially incident sech pulses. Plot layout is the same as described in Fig. 1. (a): Ω +(t)=3.6sech[(t-10)/0.5]+3.6sech[(t-30)/0.5]; (b): Ω +(t)=3.6sech[(t-10)/0.5]+4.5sech[(t-50)/0.5].

Equations (5)

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P ( x , t ) = Ω t ± ( x , t ) ± Ω x ± ( x , t ) ,
P t ( x , t ) = n ( x , t ) ( Ω + ( x , t ) + Ω ( x , t ) ) ,
n t ( x , t ) = Re ( P * ( x , t ) ( Ω + ( x , t ) + Ω ( x , t ) ) ) ,
Ω + ( x = 0 , t ) = Ω 0 + ( t ) , Ω ( x = l , t ) = 0 ,
Ω ± ( x , t = 0 ) = 0 , P ( x , t = 0 ) = 0 , n ( x , t = 0 ) = 1 .

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