Abstract

Efficient nonlinear optical frequency conversion is proposed and theoretically demonstrated by use of stopped short light pulses in a doubly resonant Bragg reflector. The pump pulse is shown to decelerate and stop in the reflector, and the stopped pump field reinforces the interaction with stimulated Raman scattering. The temporal walk-off between the pump pulse and the generated Raman pulse can be substantially reduced with the doubly resonant Bragg structure. Numerical simulations show that the conversion from the picosecond pump pulse to Stokes wave can reach 85%.

© 2006 Optical Society of America

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References

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  1. Y. R. Shen, The Principles of Nonlinear Optic (John Wiley & Sons, Inc, 1984).
  2. J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, "Intensity and gain measurements on the stimulated Raman emission in liquid O2 and N2," Phys. Rev. 180,61-68 (1969).
    [CrossRef]
  3. T. Hoffmann and F. K. Tittel, "Wideband-tunable high-power radiation by SRS of a XeF(C→A) excimer laser," IEEE J. Quantum Electron. 29,970-974 (1993).
    [CrossRef]
  4. C. HeadleyIII and G. P. Agrawal, "Unified description of ultrafast stimulated Raman scattering in optical fibers," J. Opt. Soc. Am. B 13,2170-2177 (1996).
    [CrossRef]
  5. 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]
  6. R. H. Goodman, R. E. Slusher, and M. I. Weinstein, "Stopping light on a defect," J. Opt. Soc. Am. B 19,1635-1652 (2002).
    [CrossRef]
  7. H. G. Winful and V. Perlin, "Raman gap solitons," Phys. Rev. Lett. 84,3586-3589 (2000).
    [CrossRef] [PubMed]
  8. W. C. K. Mak, B. A. Malomed, and P. L. Chu, "Formation of a standing-light pulse through collision of gap solitons," Phys. Rev. E 68,026609 (2003).
    [CrossRef]
  9. M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426,638-641 (2003).
    [CrossRef] [PubMed]
  10. A. André and M. D. Lukin, "Manipulating light pulses via dynamically controlled photonic band gap," Phys. Rev. Lett. 89, 143602 (2002).
    [CrossRef] [PubMed]
  11. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency," Phys. Rev. Lett. 93,233903 (2004).
    [CrossRef] [PubMed]
  12. M. F. Yanik and S. Fan, "Time reversal of light with linear optics and modulators," Phys. Rev. Lett. 93,173903 (2004).
    [CrossRef] [PubMed]
  13. C. Conti, G. Assanto and S. Trillo, "Gap solitons and slow light," J. Nonlinear Opt. Phys. Mater. 11,239-259 (2002).
    [CrossRef]
  14. G. Kurizki, A. E. Kozhekin, T. Opatrny, and B. A. Malomed, "Optical solitons in periodic media with resonant and off-resonant nonlinearities," Prog. Opt. 42,93-140 (2001).
    [CrossRef]
  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, J. Zhao, X. Yu, and K. S. Wong, "Storage and release of femtosecond laser pulses in a resonant photonic crystal," Opt. Lett. 30,1560-1562 (2005).
    [CrossRef] [PubMed]
  18. 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]
  19. J. Zhu, J. Y. Zhou, and J. Cheng, "Moving and stationary spatial-temporal solitons in a resonantly absorbing Bragg reflector," Opt. Express 13, 7133-7138 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-7133.
    [CrossRef] [PubMed]
  20. D. Rand, K. Steiglitz, and P. R. Prucnal, "Multicomponent gap solitons in superposed grating structure," Opt. Lett. 30, 1695-1697 (2005).
    [CrossRef] [PubMed]
  21. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, "Raman response function of silica-core fibers," J. Opt. Soc. Am. B 6,1159-1166 (1989).
    [CrossRef]
  22. C. M. de Sterke, K. R. Jackson, and B. D. Robert, "Nonlinear coupled-mode equations on a finite interval: a numerical procedure," J. Opt. Soc. Am. B 8,403-412 (1991).
    [CrossRef]
  23. 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 periodic structures," Phys. Rev. B 61,13863-13872 (2000).
    [CrossRef]

2005 (2)

2004 (2)

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency," Phys. Rev. Lett. 93,233903 (2004).
[CrossRef] [PubMed]

M. F. Yanik and S. Fan, "Time reversal of light with linear optics and modulators," Phys. Rev. Lett. 93,173903 (2004).
[CrossRef] [PubMed]

2003 (3)

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]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, "Formation of a standing-light pulse through collision of gap solitons," Phys. Rev. E 68,026609 (2003).
[CrossRef]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426,638-641 (2003).
[CrossRef] [PubMed]

2002 (4)

A. André and M. D. Lukin, "Manipulating light pulses via dynamically controlled photonic band gap," Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

R. H. Goodman, R. E. Slusher, and M. I. Weinstein, "Stopping light on a defect," J. Opt. Soc. Am. B 19,1635-1652 (2002).
[CrossRef]

C. Conti, G. Assanto and S. Trillo, "Gap solitons and slow light," J. Nonlinear Opt. Phys. Mater. 11,239-259 (2002).
[CrossRef]

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]

2001 (1)

G. Kurizki, A. E. Kozhekin, T. Opatrny, and B. A. Malomed, "Optical solitons in periodic media with resonant and off-resonant nonlinearities," Prog. Opt. 42,93-140 (2001).
[CrossRef]

2000 (2)

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

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 periodic structures," Phys. Rev. B 61,13863-13872 (2000).
[CrossRef]

1996 (2)

C. HeadleyIII and G. P. Agrawal, "Unified description of ultrafast stimulated Raman scattering in optical fibers," J. Opt. Soc. Am. B 13,2170-2177 (1996).
[CrossRef]

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]

1993 (1)

T. Hoffmann and F. K. Tittel, "Wideband-tunable high-power radiation by SRS of a XeF(C→A) excimer laser," IEEE J. Quantum Electron. 29,970-974 (1993).
[CrossRef]

1991 (1)

1989 (1)

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).

1969 (1)

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, "Intensity and gain measurements on the stimulated Raman emission in liquid O2 and N2," Phys. Rev. 180,61-68 (1969).
[CrossRef]

Agrawal, G. P.

André, A.

A. André and M. D. Lukin, "Manipulating light pulses via dynamically controlled photonic band gap," Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Assanto, G.

C. Conti, G. Assanto and S. Trillo, "Gap solitons and slow light," J. Nonlinear Opt. Phys. Mater. 11,239-259 (2002).
[CrossRef]

Bajcsy, M.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426,638-641 (2003).
[CrossRef] [PubMed]

Chu, P. L.

W. C. K. Mak, B. A. Malomed, and P. L. Chu, "Formation of a standing-light pulse through collision of gap solitons," Phys. Rev. E 68,026609 (2003).
[CrossRef]

Conti, C.

C. Conti, G. Assanto and S. Trillo, "Gap solitons and slow light," J. Nonlinear Opt. Phys. Mater. 11,239-259 (2002).
[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, K. R. Jackson, and B. D. Robert, "Nonlinear coupled-mode equations on a finite interval: a numerical procedure," J. Opt. Soc. Am. B 8,403-412 (1991).
[CrossRef]

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]

Ell, C.

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 periodic structures," Phys. Rev. B 61,13863-13872 (2000).
[CrossRef]

Fan, S.

M. F. Yanik and S. Fan, "Time reversal of light with linear optics and modulators," Phys. Rev. Lett. 93,173903 (2004).
[CrossRef] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency," Phys. Rev. Lett. 93,233903 (2004).
[CrossRef] [PubMed]

Gibbs, H. M.

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 periodic structures," Phys. Rev. B 61,13863-13872 (2000).
[CrossRef]

Goodman, R. H.

Gordon, J. P.

Grun, J. B.

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, "Intensity and gain measurements on the stimulated Raman emission in liquid O2 and N2," Phys. Rev. 180,61-68 (1969).
[CrossRef]

Haus, H. A.

Headley, C.

Hoffmann, T.

T. Hoffmann and F. K. Tittel, "Wideband-tunable high-power radiation by SRS of a XeF(C→A) excimer laser," IEEE J. Quantum Electron. 29,970-974 (1993).
[CrossRef]

Jackson, K. R.

Khitrova, G.

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 periodic structures," Phys. Rev. B 61,13863-13872 (2000).
[CrossRef]

Koch, S. W.

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 periodic structures," Phys. Rev. B 61,13863-13872 (2000).
[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," Prog. Opt. 42,93-140 (2001).
[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," Prog. Opt. 42,93-140 (2001).
[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).

Lee, E. S.

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 periodic structures," Phys. Rev. B 61,13863-13872 (2000).
[CrossRef]

Lukin, M. D.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426,638-641 (2003).
[CrossRef] [PubMed]

A. André and M. D. Lukin, "Manipulating light pulses via dynamically controlled photonic band gap," Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

Mak, W. C. K.

W. C. K. Mak, B. A. Malomed, and P. L. Chu, "Formation of a standing-light pulse through collision of gap solitons," Phys. Rev. E 68,026609 (2003).
[CrossRef]

Malomed, B. A.

W. C. K. Mak, B. A. Malomed, and P. L. Chu, "Formation of a standing-light pulse through collision of gap solitons," Phys. Rev. E 68,026609 (2003).
[CrossRef]

G. Kurizki, A. E. Kozhekin, T. Opatrny, and B. A. Malomed, "Optical solitons in periodic media with resonant and off-resonant nonlinearities," Prog. Opt. 42,93-140 (2001).
[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).

McQuillan, A. K.

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, "Intensity and gain measurements on the stimulated Raman emission in liquid O2 and N2," Phys. Rev. 180,61-68 (1969).
[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," Prog. Opt. 42,93-140 (2001).
[CrossRef]

Perlin, V.

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

Prineas, J. P.

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]

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 periodic structures," Phys. Rev. B 61,13863-13872 (2000).
[CrossRef]

Prucnal, P. R.

Rand, D.

Robert, B. D.

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]

Slusher, R. E.

R. H. Goodman, R. E. Slusher, and M. I. Weinstein, "Stopping light on a defect," J. Opt. Soc. Am. B 19,1635-1652 (2002).
[CrossRef]

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]

Steiglitz, K.

Stoicheff, B. P.

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, "Intensity and gain measurements on the stimulated Raman emission in liquid O2 and N2," Phys. Rev. 180,61-68 (1969).
[CrossRef]

Stolen, R. H.

Suh, W.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency," Phys. Rev. Lett. 93,233903 (2004).
[CrossRef] [PubMed]

Tittel, F. K.

T. Hoffmann and F. K. Tittel, "Wideband-tunable high-power radiation by SRS of a XeF(C→A) excimer laser," IEEE J. Quantum Electron. 29,970-974 (1993).
[CrossRef]

Tomlinson, W. J.

Trillo, S.

C. Conti, G. Assanto and S. Trillo, "Gap solitons and slow light," J. Nonlinear Opt. Phys. Mater. 11,239-259 (2002).
[CrossRef]

Wang, Z.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency," Phys. Rev. Lett. 93,233903 (2004).
[CrossRef] [PubMed]

Weinstein, M. I.

Winful, H. G.

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

Wong, K. S.

Xiao, W. N.

Yanik, M. F.

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency," Phys. Rev. Lett. 93,233903 (2004).
[CrossRef] [PubMed]

M. F. Yanik and S. Fan, "Time reversal of light with linear optics and modulators," Phys. Rev. Lett. 93,173903 (2004).
[CrossRef] [PubMed]

Yu, X.

Zhao, J.

Zhou, J. Y.

Zibrov, A. S.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426,638-641 (2003).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

T. Hoffmann and F. K. Tittel, "Wideband-tunable high-power radiation by SRS of a XeF(C→A) excimer laser," IEEE J. Quantum Electron. 29,970-974 (1993).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

C. Conti, G. Assanto and S. Trillo, "Gap solitons and slow light," J. Nonlinear Opt. Phys. Mater. 11,239-259 (2002).
[CrossRef]

J. Opt. Soc. Am. B (5)

Nature (1)

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, "Stationary pulses of light in an atomic medium," Nature 426,638-641 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

J. B. Grun, A. K. McQuillan, and B. P. Stoicheff, "Intensity and gain measurements on the stimulated Raman emission in liquid O2 and N2," Phys. Rev. 180,61-68 (1969).
[CrossRef]

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 periodic structures," Phys. Rev. B 61,13863-13872 (2000).
[CrossRef]

Phys. Rev. E (1)

W. C. K. Mak, B. A. Malomed, and P. L. Chu, "Formation of a standing-light pulse through collision of gap solitons," Phys. Rev. E 68,026609 (2003).
[CrossRef]

Phys. Rev. Lett. (5)

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. André and M. D. Lukin, "Manipulating light pulses via dynamically controlled photonic band gap," Phys. Rev. Lett. 89, 143602 (2002).
[CrossRef] [PubMed]

M. F. Yanik, W. Suh, Z. Wang, and S. Fan, "Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency," Phys. Rev. Lett. 93,233903 (2004).
[CrossRef] [PubMed]

M. F. Yanik and S. Fan, "Time reversal of light with linear optics and modulators," Phys. Rev. Lett. 93,173903 (2004).
[CrossRef] [PubMed]

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

Prog. Opt. (1)

G. Kurizki, A. E. Kozhekin, T. Opatrny, and B. A. Malomed, "Optical solitons in periodic media with resonant and off-resonant nonlinearities," Prog. Opt. 42,93-140 (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)

J. Zhu, J. Y. Zhou, and J. Cheng, "Moving and stationary spatial-temporal solitons in a resonantly absorbing Bragg reflector," Opt. Express 13, 7133-7138 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-7133.
[CrossRef] [PubMed]

Y. R. Shen, The Principles of Nonlinear Optic (John Wiley & Sons, Inc, 1984).

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Figures (3)

Fig. 1.
Fig. 1.

Evolution of (a) the population inversion n and (b) the energy density (|+p|2+|p|2) of the pump pulse in DRBR without SRS but with optical Kerr effect. Here τ 0 = 1.5τc , ∑0 = 2.1507, K = 4.5 and Δ = 0.

Fig. 2.
Fig. 2.

Evolution of the energy density of (a) the pump pulse (|+p,s|2+|p|2) and (b) the Stokes pulse (|+s|2+|s|2) in DRBR with SRS. Here Gp = 1 × 10-2, Gs = 9.5 × 10-3 and other parameters are the same as in Fig. 1.

Fig. 3.
Fig. 3.

The energy density of the Stokes pulse output from right-hand side (|+s(ζ = 6)|2) of DRBR. The same Stokes pulse output from left-hand side (|s(ζ = 0)|2) is not shown. The parameters are the same as in Fig. 2.

Equations (10)

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I s = I SN exp ( g R L p L ) = I SN exp ( g R I p c n 0 t ) .
± Σ p ± ζ + Σ p ± τ = i Γ p Σ p ± [ Σ p ± 2 + 2 Σ p 2 + ( 2 f R ) ( Σ s + 2 + 2 Σ s 2 ) ]
G p 2 Σ p ± ( Σ s + 2 + Σ s 2 ) + P ,
± Σ s ± ζ + Σ s ± τ = i Γ s Σ s ± [ Σ s ± 2 + 2 Σ s 2 + ( 2 f R ) ( Σ p + 2 + 2 Σ p 2 ) ]
+ G s 2 Σ s ± ( Σ p + 2 + Σ p 2 ) + i K Σ s ∓; + i Δ Σ s ± ,
P τ = ( Σ p + + Σ p ) n ,
n τ = Re [ ( Σ p + + Σ p ) P * ] .
W p , s = 1 4 ħ ω p ρ ( Σ p , s + 2 + Σ p , s 2 ) ,
I p , s ± = ε 0 c n 0 2 ħ 2 4 μ 2 τ c 2 Σ p , s ± 2 .
Σ s ± 2 = Σ SN ± 2 exp ( G s Σ p ± 2 τ ) ,

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