Abstract

We describe a methodology to maximize slow-light pulse delay subject to a constraint on the allowable pulse distortion. We show that optimizing over a larger number of physical variables can increase the distortion-constrained delay. We demonstrate these concepts by comparing the optimum slow-light pulse delay achievable using a single Lorentzian gain line with that achievable using a pair of closely-spaced gain lines. We predict that distortion management using a gain doublet can provide approximately a factor of 2 increase in slow-light pulse delay as compared with the optimum single-line delay. Experimental results employing Bril-louin gain in optical fiber confirm our theoretical predictions.

© 2005 Optical Society of America

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  1. R. W. Boyd and D. J. Gauthier , “ ‘Slow’ and ‘Fast’ Light ,” in Progress in Optics , Vol. 43 , E. Wolf , ed. ( Elsevier, Amsterdam , 2002 ), pp. 497 – 530 .
    [CrossRef]
  2. Y. A. Vlasov , S. Petit , G. Klein , B. Hönerlage , and C. Hirlimann , “ Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal ,” Phys. Rev. E   60 , 1030 – 1035 ( 1999 ).
    [CrossRef]
  3. J. E. Heebner , R. W. Boyd , and Q. Park , “ Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide ,” Phys. Rev. E   65 , 036619 ( 2002 ).
    [CrossRef]
  4. Y. Xu , R. K. Lee , and A. Yariv , “ Scattering theory analysis of waveguide-resonator coupling ,” Phys. Rev. E   62 , 7389 – 7404 ( 2000 ).
    [CrossRef]
  5. A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled resonator optical waveguide: a proposal and analysis ,” Opt. Lett.   24 , 711 – 713 ( 1999 ).
    [CrossRef]
  6. R. W. Boyd , D. J. Gauthier , A. L. Gaeta , and A. E. Willner , “ Maximum time delay achievable on propagation through a slow-light medium ,” Phys. Rev. A   71 , 023801 ( 2005 ).
    [CrossRef]
  7. H. Cao , A. Dogariu , and L. J. Wang , “ Negative group delay and pulse compression in superluminal pulse propagation ,” IEEE J. Sel. Top. Quantum Electron.   9 , 52 – 58 ( 2003 ).
    [CrossRef]
  8. B. Macke and B. Ségard , “ Propagation of light-pulses at a negative group-velocity ,” European Phys. J. D   23 , 125 – 141 ( 2003 ).
    [CrossRef]
  9. M. Bashkansky , G. Beadie , Z. Dutton , F. K. Fatemi , J. Reintjes , and M. Steiner , “ Slow-light dynamics of large-bandwidth pulses in warm rubidium vapor ,” Phys. Rev. A   72 , 033819 ( 2005 ).
    [CrossRef]
  10. Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
    [CrossRef] [PubMed]
  11. K. Y. Song , M. G. Herráez , and L. Thévenaz , “ Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering ,” Opt. Express   13 , 82 – 88 ( 2005 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-82 .
    [CrossRef] [PubMed]
  12. K. Y. Song , M. G. Herráez , and L. Thévenaz , “ Long optically controlled delays in optical fibers ,” Opt. Lett.   30 , 1782 – 1784 ( 2005 ).
    [CrossRef] [PubMed]
  13. Z. Zhu , D.J. Gauthier , Y. Okawachi , J.E. Sharping , A.L. Gaeta , R.W. Boyd , and A.E. Willner , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” to appear in J. Opt. Soc. Am. B   22 ( 2005 ).
  14. A. V. Oppenheim and A. S. Willsky , Signals and Systems, 2nd Ed . ( Prentice Hall, Upper Saddle River , 1997 ).
  15. Y. Chen , G. Pasrija , B. Farhang-Boroujeny , and S. Blair , “ Engineering the nonlinear phase shift ,” Opt. Lett.   28 1945 – 1947 ( 2003 ).
    [CrossRef] [PubMed]
  16. G. Lenz , B. J. Eggleton , C. K. Madsen , and R. E. Slusher , “ Optical delay lines based on optical filters ,” IEEE J. Quantum Electron.   37 525 – 532 ( 2001 ).
    [CrossRef]
  17. J. E. Heebner , P. Chak , S. Pereira , J. E. Sipe , and R. W. Boyd , “ Distributed and localized feedback in microresonator sequences for linear and nonlinear optics ,” J. Opt. Soc. Am. B ,   21 1818 – 1832 ( 2004 ).
    [CrossRef]
  18. M. Nikles , L. Thévenaz , and P. A. Robert , “ Brillouin gain spectrum characterization in single-mode optical fibers ,” J. Lightwave Technol.   15 , 1842 – 1851 ( 1997 ).
    [CrossRef]
  19. Z. Dutton , M. Bashkansky , M. Steiner , and J. Reintjes , “ Channelization architecture for wide-band slow light in atomic vapors ,” SPIE   5735 , 115 – 129 ( 2005 ).
    [CrossRef]
  20. Q. Sun , Y. V. Rostovtsev , J. P. Dowling , M. O. Scully , and M. S. Zhubairy , “ Optically controlled delays for broadband pulses ,” Phys. Rev. A   72 031802(R) ( 2005 ).
    [CrossRef]

2005 (8)

R. W. Boyd , D. J. Gauthier , A. L. Gaeta , and A. E. Willner , “ Maximum time delay achievable on propagation through a slow-light medium ,” Phys. Rev. A   71 , 023801 ( 2005 ).
[CrossRef]

M. Bashkansky , G. Beadie , Z. Dutton , F. K. Fatemi , J. Reintjes , and M. Steiner , “ Slow-light dynamics of large-bandwidth pulses in warm rubidium vapor ,” Phys. Rev. A   72 , 033819 ( 2005 ).
[CrossRef]

Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
[CrossRef] [PubMed]

K. Y. Song , M. G. Herráez , and L. Thévenaz , “ Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering ,” Opt. Express   13 , 82 – 88 ( 2005 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-1-82 .
[CrossRef] [PubMed]

K. Y. Song , M. G. Herráez , and L. Thévenaz , “ Long optically controlled delays in optical fibers ,” Opt. Lett.   30 , 1782 – 1784 ( 2005 ).
[CrossRef] [PubMed]

Z. Zhu , D.J. Gauthier , Y. Okawachi , J.E. Sharping , A.L. Gaeta , R.W. Boyd , and A.E. Willner , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” to appear in J. Opt. Soc. Am. B   22 ( 2005 ).

Z. Dutton , M. Bashkansky , M. Steiner , and J. Reintjes , “ Channelization architecture for wide-band slow light in atomic vapors ,” SPIE   5735 , 115 – 129 ( 2005 ).
[CrossRef]

Q. Sun , Y. V. Rostovtsev , J. P. Dowling , M. O. Scully , and M. S. Zhubairy , “ Optically controlled delays for broadband pulses ,” Phys. Rev. A   72 031802(R) ( 2005 ).
[CrossRef]

2004 (1)

2003 (3)

Y. Chen , G. Pasrija , B. Farhang-Boroujeny , and S. Blair , “ Engineering the nonlinear phase shift ,” Opt. Lett.   28 1945 – 1947 ( 2003 ).
[CrossRef] [PubMed]

H. Cao , A. Dogariu , and L. J. Wang , “ Negative group delay and pulse compression in superluminal pulse propagation ,” IEEE J. Sel. Top. Quantum Electron.   9 , 52 – 58 ( 2003 ).
[CrossRef]

B. Macke and B. Ségard , “ Propagation of light-pulses at a negative group-velocity ,” European Phys. J. D   23 , 125 – 141 ( 2003 ).
[CrossRef]

2002 (1)

J. E. Heebner , R. W. Boyd , and Q. Park , “ Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide ,” Phys. Rev. E   65 , 036619 ( 2002 ).
[CrossRef]

2001 (1)

G. Lenz , B. J. Eggleton , C. K. Madsen , and R. E. Slusher , “ Optical delay lines based on optical filters ,” IEEE J. Quantum Electron.   37 525 – 532 ( 2001 ).
[CrossRef]

2000 (1)

Y. Xu , R. K. Lee , and A. Yariv , “ Scattering theory analysis of waveguide-resonator coupling ,” Phys. Rev. E   62 , 7389 – 7404 ( 2000 ).
[CrossRef]

1999 (2)

A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled resonator optical waveguide: a proposal and analysis ,” Opt. Lett.   24 , 711 – 713 ( 1999 ).
[CrossRef]

Y. A. Vlasov , S. Petit , G. Klein , B. Hönerlage , and C. Hirlimann , “ Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal ,” Phys. Rev. E   60 , 1030 – 1035 ( 1999 ).
[CrossRef]

1997 (1)

M. Nikles , L. Thévenaz , and P. A. Robert , “ Brillouin gain spectrum characterization in single-mode optical fibers ,” J. Lightwave Technol.   15 , 1842 – 1851 ( 1997 ).
[CrossRef]

Bashkansky, M.

M. Bashkansky , G. Beadie , Z. Dutton , F. K. Fatemi , J. Reintjes , and M. Steiner , “ Slow-light dynamics of large-bandwidth pulses in warm rubidium vapor ,” Phys. Rev. A   72 , 033819 ( 2005 ).
[CrossRef]

Z. Dutton , M. Bashkansky , M. Steiner , and J. Reintjes , “ Channelization architecture for wide-band slow light in atomic vapors ,” SPIE   5735 , 115 – 129 ( 2005 ).
[CrossRef]

Beadie, G.

M. Bashkansky , G. Beadie , Z. Dutton , F. K. Fatemi , J. Reintjes , and M. Steiner , “ Slow-light dynamics of large-bandwidth pulses in warm rubidium vapor ,” Phys. Rev. A   72 , 033819 ( 2005 ).
[CrossRef]

Bigelow, M. S.

Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
[CrossRef] [PubMed]

Blair, S.

Boyd, R. W.

Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
[CrossRef] [PubMed]

R. W. Boyd , D. J. Gauthier , A. L. Gaeta , and A. E. Willner , “ Maximum time delay achievable on propagation through a slow-light medium ,” Phys. Rev. A   71 , 023801 ( 2005 ).
[CrossRef]

J. E. Heebner , P. Chak , S. Pereira , J. E. Sipe , and R. W. Boyd , “ Distributed and localized feedback in microresonator sequences for linear and nonlinear optics ,” J. Opt. Soc. Am. B ,   21 1818 – 1832 ( 2004 ).
[CrossRef]

J. E. Heebner , R. W. Boyd , and Q. Park , “ Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide ,” Phys. Rev. E   65 , 036619 ( 2002 ).
[CrossRef]

R. W. Boyd and D. J. Gauthier , “ ‘Slow’ and ‘Fast’ Light ,” in Progress in Optics , Vol. 43 , E. Wolf , ed. ( Elsevier, Amsterdam , 2002 ), pp. 497 – 530 .
[CrossRef]

Boyd, R.W.

Z. Zhu , D.J. Gauthier , Y. Okawachi , J.E. Sharping , A.L. Gaeta , R.W. Boyd , and A.E. Willner , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” to appear in J. Opt. Soc. Am. B   22 ( 2005 ).

Cao, H.

H. Cao , A. Dogariu , and L. J. Wang , “ Negative group delay and pulse compression in superluminal pulse propagation ,” IEEE J. Sel. Top. Quantum Electron.   9 , 52 – 58 ( 2003 ).
[CrossRef]

Chak, P.

Chen, Y.

Dogariu, A.

H. Cao , A. Dogariu , and L. J. Wang , “ Negative group delay and pulse compression in superluminal pulse propagation ,” IEEE J. Sel. Top. Quantum Electron.   9 , 52 – 58 ( 2003 ).
[CrossRef]

Dowling, J. P.

Q. Sun , Y. V. Rostovtsev , J. P. Dowling , M. O. Scully , and M. S. Zhubairy , “ Optically controlled delays for broadband pulses ,” Phys. Rev. A   72 031802(R) ( 2005 ).
[CrossRef]

Dutton, Z.

Z. Dutton , M. Bashkansky , M. Steiner , and J. Reintjes , “ Channelization architecture for wide-band slow light in atomic vapors ,” SPIE   5735 , 115 – 129 ( 2005 ).
[CrossRef]

M. Bashkansky , G. Beadie , Z. Dutton , F. K. Fatemi , J. Reintjes , and M. Steiner , “ Slow-light dynamics of large-bandwidth pulses in warm rubidium vapor ,” Phys. Rev. A   72 , 033819 ( 2005 ).
[CrossRef]

Eggleton, B. J.

G. Lenz , B. J. Eggleton , C. K. Madsen , and R. E. Slusher , “ Optical delay lines based on optical filters ,” IEEE J. Quantum Electron.   37 525 – 532 ( 2001 ).
[CrossRef]

Farhang-Boroujeny, B.

Fatemi, F. K.

M. Bashkansky , G. Beadie , Z. Dutton , F. K. Fatemi , J. Reintjes , and M. Steiner , “ Slow-light dynamics of large-bandwidth pulses in warm rubidium vapor ,” Phys. Rev. A   72 , 033819 ( 2005 ).
[CrossRef]

Gaeta, A. L.

Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
[CrossRef] [PubMed]

R. W. Boyd , D. J. Gauthier , A. L. Gaeta , and A. E. Willner , “ Maximum time delay achievable on propagation through a slow-light medium ,” Phys. Rev. A   71 , 023801 ( 2005 ).
[CrossRef]

Gaeta, A.L.

Z. Zhu , D.J. Gauthier , Y. Okawachi , J.E. Sharping , A.L. Gaeta , R.W. Boyd , and A.E. Willner , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” to appear in J. Opt. Soc. Am. B   22 ( 2005 ).

Gauthier, D. J.

R. W. Boyd , D. J. Gauthier , A. L. Gaeta , and A. E. Willner , “ Maximum time delay achievable on propagation through a slow-light medium ,” Phys. Rev. A   71 , 023801 ( 2005 ).
[CrossRef]

Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier , “ ‘Slow’ and ‘Fast’ Light ,” in Progress in Optics , Vol. 43 , E. Wolf , ed. ( Elsevier, Amsterdam , 2002 ), pp. 497 – 530 .
[CrossRef]

Gauthier, D.J.

Z. Zhu , D.J. Gauthier , Y. Okawachi , J.E. Sharping , A.L. Gaeta , R.W. Boyd , and A.E. Willner , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” to appear in J. Opt. Soc. Am. B   22 ( 2005 ).

Heebner, J. E.

J. E. Heebner , P. Chak , S. Pereira , J. E. Sipe , and R. W. Boyd , “ Distributed and localized feedback in microresonator sequences for linear and nonlinear optics ,” J. Opt. Soc. Am. B ,   21 1818 – 1832 ( 2004 ).
[CrossRef]

J. E. Heebner , R. W. Boyd , and Q. Park , “ Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide ,” Phys. Rev. E   65 , 036619 ( 2002 ).
[CrossRef]

Herráez, M. G.

Hirlimann, C.

Y. A. Vlasov , S. Petit , G. Klein , B. Hönerlage , and C. Hirlimann , “ Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal ,” Phys. Rev. E   60 , 1030 – 1035 ( 1999 ).
[CrossRef]

Hönerlage, B.

Y. A. Vlasov , S. Petit , G. Klein , B. Hönerlage , and C. Hirlimann , “ Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal ,” Phys. Rev. E   60 , 1030 – 1035 ( 1999 ).
[CrossRef]

Klein, G.

Y. A. Vlasov , S. Petit , G. Klein , B. Hönerlage , and C. Hirlimann , “ Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal ,” Phys. Rev. E   60 , 1030 – 1035 ( 1999 ).
[CrossRef]

Lee, R. K.

Y. Xu , R. K. Lee , and A. Yariv , “ Scattering theory analysis of waveguide-resonator coupling ,” Phys. Rev. E   62 , 7389 – 7404 ( 2000 ).
[CrossRef]

A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled resonator optical waveguide: a proposal and analysis ,” Opt. Lett.   24 , 711 – 713 ( 1999 ).
[CrossRef]

Lenz, G.

G. Lenz , B. J. Eggleton , C. K. Madsen , and R. E. Slusher , “ Optical delay lines based on optical filters ,” IEEE J. Quantum Electron.   37 525 – 532 ( 2001 ).
[CrossRef]

Macke, B.

B. Macke and B. Ségard , “ Propagation of light-pulses at a negative group-velocity ,” European Phys. J. D   23 , 125 – 141 ( 2003 ).
[CrossRef]

Madsen, C. K.

G. Lenz , B. J. Eggleton , C. K. Madsen , and R. E. Slusher , “ Optical delay lines based on optical filters ,” IEEE J. Quantum Electron.   37 525 – 532 ( 2001 ).
[CrossRef]

Nikles, M.

M. Nikles , L. Thévenaz , and P. A. Robert , “ Brillouin gain spectrum characterization in single-mode optical fibers ,” J. Lightwave Technol.   15 , 1842 – 1851 ( 1997 ).
[CrossRef]

Okawachi, Y.

Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
[CrossRef] [PubMed]

Z. Zhu , D.J. Gauthier , Y. Okawachi , J.E. Sharping , A.L. Gaeta , R.W. Boyd , and A.E. Willner , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” to appear in J. Opt. Soc. Am. B   22 ( 2005 ).

Oppenheim, A. V.

A. V. Oppenheim and A. S. Willsky , Signals and Systems, 2nd Ed . ( Prentice Hall, Upper Saddle River , 1997 ).

Park, Q.

J. E. Heebner , R. W. Boyd , and Q. Park , “ Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide ,” Phys. Rev. E   65 , 036619 ( 2002 ).
[CrossRef]

Pasrija, G.

Pereira, S.

Petit, S.

Y. A. Vlasov , S. Petit , G. Klein , B. Hönerlage , and C. Hirlimann , “ Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal ,” Phys. Rev. E   60 , 1030 – 1035 ( 1999 ).
[CrossRef]

Reintjes, J.

M. Bashkansky , G. Beadie , Z. Dutton , F. K. Fatemi , J. Reintjes , and M. Steiner , “ Slow-light dynamics of large-bandwidth pulses in warm rubidium vapor ,” Phys. Rev. A   72 , 033819 ( 2005 ).
[CrossRef]

Z. Dutton , M. Bashkansky , M. Steiner , and J. Reintjes , “ Channelization architecture for wide-band slow light in atomic vapors ,” SPIE   5735 , 115 – 129 ( 2005 ).
[CrossRef]

Robert, P. A.

M. Nikles , L. Thévenaz , and P. A. Robert , “ Brillouin gain spectrum characterization in single-mode optical fibers ,” J. Lightwave Technol.   15 , 1842 – 1851 ( 1997 ).
[CrossRef]

Rostovtsev, Y. V.

Q. Sun , Y. V. Rostovtsev , J. P. Dowling , M. O. Scully , and M. S. Zhubairy , “ Optically controlled delays for broadband pulses ,” Phys. Rev. A   72 031802(R) ( 2005 ).
[CrossRef]

Scherer, A.

Schweinsberg, A.

Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
[CrossRef] [PubMed]

Scully, M. O.

Q. Sun , Y. V. Rostovtsev , J. P. Dowling , M. O. Scully , and M. S. Zhubairy , “ Optically controlled delays for broadband pulses ,” Phys. Rev. A   72 031802(R) ( 2005 ).
[CrossRef]

Ségard, B.

B. Macke and B. Ségard , “ Propagation of light-pulses at a negative group-velocity ,” European Phys. J. D   23 , 125 – 141 ( 2003 ).
[CrossRef]

Sharping, J. E.

Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
[CrossRef] [PubMed]

Sharping, J.E.

Z. Zhu , D.J. Gauthier , Y. Okawachi , J.E. Sharping , A.L. Gaeta , R.W. Boyd , and A.E. Willner , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” to appear in J. Opt. Soc. Am. B   22 ( 2005 ).

Sipe, J. E.

Slusher, R. E.

G. Lenz , B. J. Eggleton , C. K. Madsen , and R. E. Slusher , “ Optical delay lines based on optical filters ,” IEEE J. Quantum Electron.   37 525 – 532 ( 2001 ).
[CrossRef]

Song, K. Y.

Steiner, M.

Z. Dutton , M. Bashkansky , M. Steiner , and J. Reintjes , “ Channelization architecture for wide-band slow light in atomic vapors ,” SPIE   5735 , 115 – 129 ( 2005 ).
[CrossRef]

M. Bashkansky , G. Beadie , Z. Dutton , F. K. Fatemi , J. Reintjes , and M. Steiner , “ Slow-light dynamics of large-bandwidth pulses in warm rubidium vapor ,” Phys. Rev. A   72 , 033819 ( 2005 ).
[CrossRef]

Sun, Q.

Q. Sun , Y. V. Rostovtsev , J. P. Dowling , M. O. Scully , and M. S. Zhubairy , “ Optically controlled delays for broadband pulses ,” Phys. Rev. A   72 031802(R) ( 2005 ).
[CrossRef]

Thévenaz, L.

Vlasov, Y. A.

Y. A. Vlasov , S. Petit , G. Klein , B. Hönerlage , and C. Hirlimann , “ Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal ,” Phys. Rev. E   60 , 1030 – 1035 ( 1999 ).
[CrossRef]

Wang, L. J.

H. Cao , A. Dogariu , and L. J. Wang , “ Negative group delay and pulse compression in superluminal pulse propagation ,” IEEE J. Sel. Top. Quantum Electron.   9 , 52 – 58 ( 2003 ).
[CrossRef]

Willner, A. E.

R. W. Boyd , D. J. Gauthier , A. L. Gaeta , and A. E. Willner , “ Maximum time delay achievable on propagation through a slow-light medium ,” Phys. Rev. A   71 , 023801 ( 2005 ).
[CrossRef]

Willner, A.E.

Z. Zhu , D.J. Gauthier , Y. Okawachi , J.E. Sharping , A.L. Gaeta , R.W. Boyd , and A.E. Willner , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” to appear in J. Opt. Soc. Am. B   22 ( 2005 ).

Willsky, A. S.

A. V. Oppenheim and A. S. Willsky , Signals and Systems, 2nd Ed . ( Prentice Hall, Upper Saddle River , 1997 ).

Xu, Y.

Y. Xu , R. K. Lee , and A. Yariv , “ Scattering theory analysis of waveguide-resonator coupling ,” Phys. Rev. E   62 , 7389 – 7404 ( 2000 ).
[CrossRef]

A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled resonator optical waveguide: a proposal and analysis ,” Opt. Lett.   24 , 711 – 713 ( 1999 ).
[CrossRef]

Yariv, A.

Y. Xu , R. K. Lee , and A. Yariv , “ Scattering theory analysis of waveguide-resonator coupling ,” Phys. Rev. E   62 , 7389 – 7404 ( 2000 ).
[CrossRef]

A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled resonator optical waveguide: a proposal and analysis ,” Opt. Lett.   24 , 711 – 713 ( 1999 ).
[CrossRef]

Zhu, Z.

Z. Zhu , D.J. Gauthier , Y. Okawachi , J.E. Sharping , A.L. Gaeta , R.W. Boyd , and A.E. Willner , “ Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber ,” to appear in J. Opt. Soc. Am. B   22 ( 2005 ).

Zhu, Z. M.

Y. Okawachi , M. S. Bigelow , J. E. Sharping , Z. M. Zhu , A. Schweinsberg , D. J. Gauthier , R. W. Boyd , and A. L. Gaeta , “ Tunable all-optical delays via Brillouin slow light in an optical fiber ,” Phys. Rev. Lett.   94 , 153902 ( 2005 ).
[CrossRef] [PubMed]

Zhubairy, M. S.

Q. Sun , Y. V. Rostovtsev , J. P. Dowling , M. O. Scully , and M. S. Zhubairy , “ Optically controlled delays for broadband pulses ,” Phys. Rev. A   72 031802(R) ( 2005 ).
[CrossRef]

European Phys. J. D (1)

B. Macke and B. Ségard , “ Propagation of light-pulses at a negative group-velocity ,” European Phys. J. D   23 , 125 – 141 ( 2003 ).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Lenz , B. J. Eggleton , C. K. Madsen , and R. E. Slusher , “ Optical delay lines based on optical filters ,” IEEE J. Quantum Electron.   37 525 – 532 ( 2001 ).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

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

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Figures (3)

Fig. 1.
Fig. 1.

Gain and dispersion for a single Lorentzian line (solid) and a doublet with separation δ = δ/√3 (dashed). Also shown are the two constituent lines (dotted) that make up the doublet. (a) The gain exponent has a broad flat top (a result of setting k 2 = 0), although it is larger for the same value of the individual gain coefficients. (b) The central region of approximately linear dispersion is very similar for both systems near the center of the lines, but extends farther for the gain-doublet case.

Fig. 2.
Fig. 2.

Simulation and experimental results for both the single Lorentzian line (solid lines for simulation, circles for experimental results) and the doublet (dashed lines for simulation, squares for experimental results). (a) Relative delay. (b) Lorentzian line-center amplitude gain coefficients g 01 and g 02. Also shown is the center-frequency gain coefficient for the doublet g 2((ω 0) (dot-dashed). (c) Line separation for the doublet. The horizontal line indicates the value of δ/γ that leads to k 2 = 0

Fig. 3.
Fig. 3.

Experiment setup based on a fiber Brillouin amplifier. TL1, TL2: tunable lasers; IS1, IS2: isolators; FPC1, FPC2, FPC3: fiber polarization controllers; MZM1, MZM2: Mach-Zehnder modulators; FG1, FG2: function generators; EDFA: Erbium-doped fiber amplifier; C1, C2: circulators; SMF-28e: 500-m-long SMF-28e fiber (the SBS amplifier); PM: power meter.

Equations (12)

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A ω z = A ω 0 e ik ( ω ) z ,
k ( ω ) = k 0 + k 1 ( ω ω c ) ,
k ( ω ) = ω c n 0 + g 0 z ( γ ω ( ω 0 δ ) + + γ ω ( ω 0 + δ ) + ) ,
k 2 = 4 i g 0 γ 2 z 3 δ 2 γ 2 ( δ 2 + γ 2 ) 3 .
t g = z ( k 1 1 c ) = z c ( n 0 1 ) + 3 4 g 0 γ ,
t g = z c ( n 0 1 ) + g 0 γ .
D a = H max H min H max + H min ,
D p = 1 2 π max [ H ( ω ) ( t p ω + ϕ 0 ) ] ω 0 Δ b ω 0 + Δ b ,
H 1 ( ω ) = exp ( iz n 0 ω c ) × exp ( g 1 ( ω ) )
= exp ( iz n 0 ω c + g 01 ( ω ω 0 ) + ) .
H 2 ( ω ) = exp ( iz n 0 ω c ) × exp ( g 2 ( ω ) )
= exp ( iz n 0 ω c + g 02 ( ω ω 0 δ ) + + g 02 ( ω ω 0 δ ) + ) .

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