Abstract

Spatial-temporal characteristics of ultrashort optical pulses in a resonantly absorbing Bragg reflector are numerically evaluated. The moving and stationary spatial-temporal gap solitons are shown to exist in the photonic structure for a finite spatially-distributed light field in a finite thickness sample. A practical method of trapping light pulses in the photonic structure is presented.

© 2005 Optical Society of America

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References

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  1. R. E. Slusher and B. J. Eggleton (editors), Nonlinear Photonic Crystals (Springer- Verlag, Berlin, Heidelberg, 2003).
  2. H. G. Winful, J. H. Marburger, and E. Garmire “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
    [CrossRef]
  3. A. V. Andreev, A. V. Balakin, and I. A. Ozheredov, et al. “Compression of femtosecond laser pulses in thin one-dimensional photonic crystals,” Phys. Rev. E 63, 016602-1-9 (2001).
    [CrossRef]
  4. F. Schreier and O. Bryngdahl “Femtosecond pulse shaping with a stratified diffractive structure,” Opt. Commun. 185, 227–231 (2000).
    [CrossRef]
  5. C. M. de Sterke and J. E. Sipe “Gap solitons,” Progress in Optics,  33, 205–259 (1994).
  6. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996).
    [CrossRef] [PubMed]
  7. W. N. Xiao, J. Y. Zhou, and J. P. Prineas “Storage of ultrashort optical pulses in a resonantly absorbing Bragg reflector,” Opt. Express,  11, 3277–3283 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-24-3277.
    [CrossRef] [PubMed]
  8. A. E. Kozhekin, G. Kurizki, and B. A. Malomed “Standing and Moving Gap Solitons in Resonantly Absorbing Gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
    [CrossRef]
  9. M. Blaauboer, G. Kurizki, and B. A. Malomed “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phy. Rev. E 62, 57–60 (2000).
    [CrossRef]
  10. G. Kurizki, A. E. Kozhekin, T. Opatrny, and 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]
  11. 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]
  12. X. Liu, K. Beckwitt, and F. Wise, “Transverse Instability of Optical Spatiotemporal Solitons in Quadratic Media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
    [CrossRef] [PubMed]
  13. B. A. Malomed, D. Mihalache, and F. Wise, et al. “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
    [CrossRef]
  14. J. W. Haus, B. Y. Soon, and M. Scalora, et al. “Spatio-temporal instabilities for counter-propagating waves in periodic media,” Opt. Express 10, 114–121 (2002), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-2-114.
    [PubMed]
  15. 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).
  16. B. I. Mantsyzov and R. A. Silnikov, “Unstable excited and stable oscillating gap 2π pulses,” J. Opt. Soc. Am. B 19, 2203–2207 (2002).
    [CrossRef]
  17. J. Y. Zhou, H. G. Shao, and J. Zhao, et al. “Storage and release of femtosecond laser pulses in a resonant photonic crystal,” Opt. Lett. 30, 1560–1562 (2005).
    [CrossRef] [PubMed]

2005 (2)

B. A. Malomed, D. Mihalache, and F. Wise, et al. “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[CrossRef]

J. Y. Zhou, H. G. Shao, and J. Zhao, et al. “Storage and release of femtosecond laser pulses in a resonant photonic crystal,” Opt. Lett. 30, 1560–1562 (2005).
[CrossRef] [PubMed]

2003 (1)

2002 (2)

2001 (2)

A. V. Andreev, A. V. Balakin, and I. A. Ozheredov, et al. “Compression of femtosecond laser pulses in thin one-dimensional photonic crystals,” Phys. Rev. E 63, 016602-1-9 (2001).
[CrossRef]

G. Kurizki, A. E. Kozhekin, T. Opatrny, and 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]

2000 (3)

M. Blaauboer, G. Kurizki, and B. A. Malomed “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phy. Rev. E 62, 57–60 (2000).
[CrossRef]

F. Schreier and O. Bryngdahl “Femtosecond pulse shaping with a stratified diffractive structure,” Opt. Commun. 185, 227–231 (2000).
[CrossRef]

X. Liu, K. Beckwitt, and F. Wise, “Transverse Instability of Optical Spatiotemporal Solitons in Quadratic Media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[CrossRef] [PubMed]

1998 (2)

A. E. Kozhekin, G. Kurizki, and B. A. Malomed “Standing and Moving Gap Solitons in Resonantly Absorbing Gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

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]

1996 (1)

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

1994 (1)

C. M. de Sterke and J. E. Sipe “Gap solitons,” Progress in Optics,  33, 205–259 (1994).

1986 (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).

1979 (1)

H. G. Winful, J. H. Marburger, and E. Garmire “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Akozbek, N.

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]

Andreev, A. V.

A. V. Andreev, A. V. Balakin, and I. A. Ozheredov, et al. “Compression of femtosecond laser pulses in thin one-dimensional photonic crystals,” Phys. Rev. E 63, 016602-1-9 (2001).
[CrossRef]

Balakin, A. V.

A. V. Andreev, A. V. Balakin, and I. A. Ozheredov, et al. “Compression of femtosecond laser pulses in thin one-dimensional photonic crystals,” Phys. Rev. E 63, 016602-1-9 (2001).
[CrossRef]

Beckwitt, K.

X. Liu, K. Beckwitt, and F. Wise, “Transverse Instability of Optical Spatiotemporal Solitons in Quadratic Media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[CrossRef] [PubMed]

Blaauboer, M.

M. Blaauboer, G. Kurizki, and B. A. Malomed “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phy. Rev. E 62, 57–60 (2000).
[CrossRef]

Bryngdahl, O.

F. Schreier and O. Bryngdahl “Femtosecond pulse shaping with a stratified diffractive structure,” Opt. Commun. 185, 227–231 (2000).
[CrossRef]

de Sterke, C. M.

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

C. M. de Sterke and J. E. Sipe “Gap solitons,” Progress in Optics,  33, 205–259 (1994).

Eggleton, B. J.

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

Garmire, E.

H. G. Winful, J. H. Marburger, and E. Garmire “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Haus, J. W.

John, S.

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]

Kozhekin, A. E.

G. Kurizki, A. E. Kozhekin, T. Opatrny, and 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]

A. E. Kozhekin, G. Kurizki, and B. A. Malomed “Standing and Moving Gap Solitons in Resonantly Absorbing Gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

Krug, P. A.

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

Kurizki, G.

G. Kurizki, A. E. Kozhekin, T. Opatrny, and 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]

M. Blaauboer, G. Kurizki, and B. A. Malomed “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phy. Rev. E 62, 57–60 (2000).
[CrossRef]

A. E. Kozhekin, G. Kurizki, and B. A. Malomed “Standing and Moving Gap Solitons in Resonantly Absorbing Gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

Kuz’min, R. N.

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).

Liu, X.

X. Liu, K. Beckwitt, and F. Wise, “Transverse Instability of Optical Spatiotemporal Solitons in Quadratic Media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[CrossRef] [PubMed]

Malomed, B. A.

B. A. Malomed, D. Mihalache, and F. Wise, et al. “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[CrossRef]

G. Kurizki, A. E. Kozhekin, T. Opatrny, and 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]

M. Blaauboer, G. Kurizki, and B. A. Malomed “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phy. Rev. E 62, 57–60 (2000).
[CrossRef]

A. E. Kozhekin, G. Kurizki, and B. A. Malomed “Standing and Moving Gap Solitons in Resonantly Absorbing Gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

Mantsyzov, B. I.

B. I. Mantsyzov and R. A. Silnikov, “Unstable excited and stable oscillating gap 2π pulses,” J. Opt. Soc. Am. B 19, 2203–2207 (2002).
[CrossRef]

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).

Marburger, J. H.

H. G. Winful, J. H. Marburger, and E. Garmire “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Mihalache, D.

B. A. Malomed, D. Mihalache, and F. Wise, et al. “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[CrossRef]

Opatrny, T.

G. Kurizki, A. E. Kozhekin, T. Opatrny, and 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]

Ozheredov, I. A.

A. V. Andreev, A. V. Balakin, and I. A. Ozheredov, et al. “Compression of femtosecond laser pulses in thin one-dimensional photonic crystals,” Phys. Rev. E 63, 016602-1-9 (2001).
[CrossRef]

Prineas, J. P.

Scalora, M.

Schreier, F.

F. Schreier and O. Bryngdahl “Femtosecond pulse shaping with a stratified diffractive structure,” Opt. Commun. 185, 227–231 (2000).
[CrossRef]

Shao, H. G.

Silnikov, R. A.

Sipe, J. E.

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

C. M. de Sterke and J. E. Sipe “Gap solitons,” Progress in Optics,  33, 205–259 (1994).

Slusher, R. E.

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

Soon, B. Y.

Winful, H. G.

H. G. Winful, J. H. Marburger, and E. Garmire “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

Wise, F.

B. A. Malomed, D. Mihalache, and F. Wise, et al. “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[CrossRef]

X. Liu, K. Beckwitt, and F. Wise, “Transverse Instability of Optical Spatiotemporal Solitons in Quadratic Media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[CrossRef] [PubMed]

Xiao, W. N.

Zhao, J.

Zhou, J. Y.

Appl. Phys. Lett. (1)

H. G. Winful, J. H. Marburger, and E. Garmire “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (1)

B. A. Malomed, D. Mihalache, and F. Wise, et al. “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

F. Schreier and O. Bryngdahl “Femtosecond pulse shaping with a stratified diffractive structure,” Opt. Commun. 185, 227–231 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phy. Rev. E (1)

M. Blaauboer, G. Kurizki, and B. A. Malomed “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phy. Rev. E 62, 57–60 (2000).
[CrossRef]

Phys. Rev. E (2)

A. V. Andreev, A. V. Balakin, and I. A. Ozheredov, et al. “Compression of femtosecond laser pulses in thin one-dimensional photonic crystals,” Phys. Rev. E 63, 016602-1-9 (2001).
[CrossRef]

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]

Phys. Rev. Lett. (3)

X. Liu, K. Beckwitt, and F. Wise, “Transverse Instability of Optical Spatiotemporal Solitons in Quadratic Media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[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, 1627–1630 (1996).
[CrossRef] [PubMed]

A. E. Kozhekin, G. Kurizki, and B. A. Malomed “Standing and Moving Gap Solitons in Resonantly Absorbing Gratings,” Phys. Rev. Lett. 81, 3647–3650 (1998).
[CrossRef]

Progress in Optics (2)

G. Kurizki, A. E. Kozhekin, T. Opatrny, and 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]

C. M. de Sterke and J. E. Sipe “Gap solitons,” Progress in Optics,  33, 205–259 (1994).

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 (1)

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

Supplementary Material (3)

» Media 1: GIF (710 KB)     
» Media 2: GIF (693 KB)     
» Media 3: GIF (836 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Animation of the pulse evolution through an RPC with detuning χ = 0. The amplitude of the initial pulse is Ω0 = 0.5. The top panel is the forward-propagating pulse and the bottom panel is the back ward propagating pulse. The numbers in brackets denote the maximum value of the intensity in that plot (727 KB gif animation).

Fig. 2.
Fig. 2.

Animation of Gaussian pulse evolution through the RPC. Parameters are the same as Fig. 1 except for χ =1.4 and Ω0 = 5.5 (710 KB gif animation).

Fig. 3.
Fig. 3.

Full width of the half maximum of the forward pulse. Solid line: FWHM in the longitude direction; dotted line: FWHM in the transverse direction; space bracketed by the dash line: RPC structure.

Fig. 4.
Fig. 4.

The evolution of hyperbolic secant pulse through an RABR with detuning χ = -0.15 and initial amplitude Ω0 = 3.5 (856 KB gif animation).

Equations (9)

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

Ω + t = Ω z + i η Ω + P + i F 2 Ω +
Ω t = + Ω + z + i η Ω + + P + i F 2 Ω
P t = i δ P + ( Ω + + Ω ) w
w t = Re ( ( Ω + + Ω ) P * )
Ω + ( x , z , t = 0 ) = Ω 0 exp ( ( z z 0 ) 2 σ z 2 + i χ ( z z 0 ) ) exp ( x 2 σ x 2 )
Ω ( x , z , t = 0 ) = 0
P ( x , z , t = 0 ) = 0
w ( x , z , t = 0 ) = 1
Ω + ( x , z , t = 0 ) = Ω 0 sec h ( ( z z 0 ) σ z ) exp ( i χ ( z z 0 ) ) exp ( x 2 σ x 2 )

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