Abstract

We predict transparent superluminal pulse propagation in coresonant coupled optical resonators when a gain element is placed in the resonator closest to the excitation waveguide, provided that the structure is overcoupled, but the resonator farthest from the excitation waveguide is undercoupled sufficiently to avoid lasing at the split modes. The effective steady-state absorptive and dispersive response of coupled resonators are derived, and the coupled-mode approximation is used to determine the conditions for transparent superluminal pulse propagation in these systems. In addition, we find that the effect of pulse compression is minimized when the structure is critically coupled.

© 2005 Optical Society of America

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  1. L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, "Tunable delay line with interacting whispering-gallery-mode resonators," Opt. Lett. 29, 626-628 (2004).
    [CrossRef] [PubMed]
  2. J. K. S. Poon, J. Scheuer, Y. Xu, and A. Yariv, "Designing coupled-resonator optical waveguide delay lines," J. Opt. Soc. Am. B 21, 1665-1673 (2004).
    [CrossRef]
  3. M. F. Yanik and S. Fan, "Stopping light all optically," Phys. Rev. Lett. 92, 083901 (2004).
    [CrossRef] [PubMed]
  4. 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]
  5. R. J. C. Spreeuw and J. P. Woerdman, "Photon band structure in a Sagnac fiber-optic ring resonator," Phys. Rev. Lett. 61, 318-321 (1988).
    [CrossRef] [PubMed]
  6. R. J. C. Spreeuw, R. Centeno, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, "Mode coupling in a He-Ne ring laser with backscattering," Phys. Rev. A 42, 4315-4324 (1990).
    [CrossRef] [PubMed]
  7. S. A. Diddams, J. C. Diels, and B. Atherton, "Differential intracavity phase spectroscopy and its application to a three-level system in samarium," Phys. Rev. A 58, 2252-2264 (1998).
    [CrossRef]
  8. R. Quintero-Torres, M. Navarro, M. Ackerman, and J. C. Diels, "Scatterometer using a bidirectional ring laser," Opt. Commun. 241, 179-183 (2004).
    [CrossRef]
  9. T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64, 23805 (2001).
    [CrossRef]
  10. R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65, 2642-2645 (1990).
    [CrossRef] [PubMed]
  11. R. J. C. Spreeuw and J. P. Woerdman, "Optical atoms," Prog. Opt. 31, 263-319 (1993).
    [CrossRef]
  12. D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51, 646-654 (1995).
    [CrossRef] [PubMed]
  13. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 63804 (2004).
    [CrossRef]
  14. W. E. Lamb, Jr. and R. C. Retherford, "Fine structure of the hydrogen atom. Part II," Phys. Rev. 81, 222-232 (1951).
    [CrossRef]
  15. P. R. Hemmer and M. G. Prentiss, "Coupled-pendulum model of the stimulated resonance Raman effect," J. Opt. Soc. Am. B 5, 1613-1623 (1988).
    [CrossRef]
  16. G. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2001).
    [CrossRef]
  17. L. J. Wang, "Casual 'all-pass' filters and Kramers-Kronig relations," Opt. Commun. 213, 27-32 (2002).
    [CrossRef]
  18. J. E. Heebner and R. W. Boyd, "'Slow' and 'fast' light in resonator-coupled-waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
    [CrossRef]
  19. L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
    [CrossRef] [PubMed]
  20. A. Dogariu, A. Kuzmich, and L. J. Wang, "Transparent anomalous dispersion and superluminal light-pulse propagation at negative group velocity," Phys. Rev. A 63, 53806 (2001).
    [CrossRef]
  21. J. Capmany and M. A. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8, 1904-1919 (1990).
    [CrossRef]
  22. D. D. Smith, H. Chang, and K. A. Fuller, "Whispering-gallery mode splitting in coupled microresonators," J. Opt. Soc. Am. B 20, 1967-1974 (2003).
    [CrossRef]
  23. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 99-103 (2004).
    [CrossRef]
  24. H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984).
  25. 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]

2004 (7)

L. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, "Tunable delay line with interacting whispering-gallery-mode resonators," Opt. Lett. 29, 626-628 (2004).
[CrossRef] [PubMed]

J. K. S. Poon, J. Scheuer, Y. Xu, and A. Yariv, "Designing coupled-resonator optical waveguide delay lines," J. Opt. Soc. Am. B 21, 1665-1673 (2004).
[CrossRef]

M. F. Yanik and S. Fan, "Stopping light all optically," Phys. Rev. Lett. 92, 083901 (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]

R. Quintero-Torres, M. Navarro, M. Ackerman, and J. C. Diels, "Scatterometer using a bidirectional ring laser," Opt. Commun. 241, 179-183 (2004).
[CrossRef]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 63804 (2004).
[CrossRef]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 99-103 (2004).
[CrossRef]

2003 (2)

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]

D. D. Smith, H. Chang, and K. A. Fuller, "Whispering-gallery mode splitting in coupled microresonators," J. Opt. Soc. Am. B 20, 1967-1974 (2003).
[CrossRef]

2002 (2)

L. J. Wang, "Casual 'all-pass' filters and Kramers-Kronig relations," Opt. Commun. 213, 27-32 (2002).
[CrossRef]

J. E. Heebner and R. W. Boyd, "'Slow' and 'fast' light in resonator-coupled-waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
[CrossRef]

2001 (3)

G. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2001).
[CrossRef]

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64, 23805 (2001).
[CrossRef]

A. Dogariu, A. Kuzmich, and L. J. Wang, "Transparent anomalous dispersion and superluminal light-pulse propagation at negative group velocity," Phys. Rev. A 63, 53806 (2001).
[CrossRef]

2000 (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

1998 (1)

S. A. Diddams, J. C. Diels, and B. Atherton, "Differential intracavity phase spectroscopy and its application to a three-level system in samarium," Phys. Rev. A 58, 2252-2264 (1998).
[CrossRef]

1995 (1)

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51, 646-654 (1995).
[CrossRef] [PubMed]

1993 (1)

R. J. C. Spreeuw and J. P. Woerdman, "Optical atoms," Prog. Opt. 31, 263-319 (1993).
[CrossRef]

1990 (3)

R. J. C. Spreeuw, R. Centeno, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, "Mode coupling in a He-Ne ring laser with backscattering," Phys. Rev. A 42, 4315-4324 (1990).
[CrossRef] [PubMed]

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65, 2642-2645 (1990).
[CrossRef] [PubMed]

J. Capmany and M. A. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

1988 (2)

R. J. C. Spreeuw and J. P. Woerdman, "Photon band structure in a Sagnac fiber-optic ring resonator," Phys. Rev. Lett. 61, 318-321 (1988).
[CrossRef] [PubMed]

P. R. Hemmer and M. G. Prentiss, "Coupled-pendulum model of the stimulated resonance Raman effect," J. Opt. Soc. Am. B 5, 1613-1623 (1988).
[CrossRef]

1951 (1)

W. E. Lamb, Jr. and R. C. Retherford, "Fine structure of the hydrogen atom. Part II," Phys. Rev. 81, 222-232 (1951).
[CrossRef]

Ackerman, M.

R. Quintero-Torres, M. Navarro, M. Ackerman, and J. C. Diels, "Scatterometer using a bidirectional ring laser," Opt. Commun. 241, 179-183 (2004).
[CrossRef]

Atherton, B.

S. A. Diddams, J. C. Diels, and B. Atherton, "Differential intracavity phase spectroscopy and its application to a three-level system in samarium," Phys. Rev. A 58, 2252-2264 (1998).
[CrossRef]

Beijersbergen, M. W.

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65, 2642-2645 (1990).
[CrossRef] [PubMed]

Bouwmeester, D.

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51, 646-654 (1995).
[CrossRef] [PubMed]

Boyd, R. W.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 63804 (2004).
[CrossRef]

J. E. Heebner and R. W. Boyd, "'Slow' and 'fast' light in resonator-coupled-waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
[CrossRef]

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]

Capmany, J.

J. Capmany and M. A. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

Centeno, R.

R. J. C. Spreeuw, R. Centeno, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, "Mode coupling in a He-Ne ring laser with backscattering," Phys. Rev. A 42, 4315-4324 (1990).
[CrossRef] [PubMed]

Chang, H.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 63804 (2004).
[CrossRef]

D. D. Smith, H. Chang, and K. A. Fuller, "Whispering-gallery mode splitting in coupled microresonators," J. Opt. Soc. Am. B 20, 1967-1974 (2003).
[CrossRef]

Dekker, N. H.

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51, 646-654 (1995).
[CrossRef] [PubMed]

Diddams, S. A.

S. A. Diddams, J. C. Diels, and B. Atherton, "Differential intracavity phase spectroscopy and its application to a three-level system in samarium," Phys. Rev. A 58, 2252-2264 (1998).
[CrossRef]

Diels, J. C.

R. Quintero-Torres, M. Navarro, M. Ackerman, and J. C. Diels, "Scatterometer using a bidirectional ring laser," Opt. Commun. 241, 179-183 (2004).
[CrossRef]

S. A. Diddams, J. C. Diels, and B. Atherton, "Differential intracavity phase spectroscopy and its application to a three-level system in samarium," Phys. Rev. A 58, 2252-2264 (1998).
[CrossRef]

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]

A. Dogariu, A. Kuzmich, and L. J. Wang, "Transparent anomalous dispersion and superluminal light-pulse propagation at negative group velocity," Phys. Rev. A 63, 53806 (2001).
[CrossRef]

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

Dorsselaer, F. E. v.

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51, 646-654 (1995).
[CrossRef] [PubMed]

Eliel, E. R.

R. J. C. Spreeuw, R. Centeno, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, "Mode coupling in a He-Ne ring laser with backscattering," Phys. Rev. A 42, 4315-4324 (1990).
[CrossRef] [PubMed]

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65, 2642-2645 (1990).
[CrossRef] [PubMed]

Fan, S.

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, "Stopping light all optically," Phys. Rev. Lett. 92, 083901 (2004).
[CrossRef] [PubMed]

Fuller, K. A.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 63804 (2004).
[CrossRef]

D. D. Smith, H. Chang, and K. A. Fuller, "Whispering-gallery mode splitting in coupled microresonators," J. Opt. Soc. Am. B 20, 1967-1974 (2003).
[CrossRef]

Garrido Alzar, G. L.

G. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2001).
[CrossRef]

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984).

Heebner, J. E.

J. E. Heebner and R. W. Boyd, "'Slow' and 'fast' light in resonator-coupled-waveguides," J. Mod. Opt. 49, 2629-2636 (2002).
[CrossRef]

Hemmer, P. R.

Huang, Y.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 99-103 (2004).
[CrossRef]

Ilchenko, V. S.

Kuzmich, A.

A. Dogariu, A. Kuzmich, and L. J. Wang, "Transparent anomalous dispersion and superluminal light-pulse propagation at negative group velocity," Phys. Rev. A 63, 53806 (2001).
[CrossRef]

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

Lamb, W. E.

W. E. Lamb, Jr. and R. C. Retherford, "Fine structure of the hydrogen atom. Part II," Phys. Rev. 81, 222-232 (1951).
[CrossRef]

Maleki, L.

Martinez, M. A. G.

G. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2001).
[CrossRef]

Matsko, A. B.

Mookherjea, S.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 99-103 (2004).
[CrossRef]

Muriel, M. A.

J. Capmany and M. A. Muriel, "A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing," J. Lightwave Technol. 8, 1904-1919 (1990).
[CrossRef]

Navarro, M.

R. Quintero-Torres, M. Navarro, M. Ackerman, and J. C. Diels, "Scatterometer using a bidirectional ring laser," Opt. Commun. 241, 179-183 (2004).
[CrossRef]

Nussenzveig, P.

G. L. Garrido Alzar, M. A. G. Martinez, and P. Nussenzveig, "Classical analog of electromagnetically induced transparency," Am. J. Phys. 70, 37-41 (2001).
[CrossRef]

Opatrny, T.

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64, 23805 (2001).
[CrossRef]

Paloczi, G. T.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 99-103 (2004).
[CrossRef]

Poon, J. K. S.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 99-103 (2004).
[CrossRef]

J. K. S. Poon, J. Scheuer, Y. Xu, and A. Yariv, "Designing coupled-resonator optical waveguide delay lines," J. Opt. Soc. Am. B 21, 1665-1673 (2004).
[CrossRef]

Prentiss, M. G.

Quintero-Torres, R.

R. Quintero-Torres, M. Navarro, M. Ackerman, and J. C. Diels, "Scatterometer using a bidirectional ring laser," Opt. Commun. 241, 179-183 (2004).
[CrossRef]

Retherford, R. C.

W. E. Lamb, Jr. and R. C. Retherford, "Fine structure of the hydrogen atom. Part II," Phys. Rev. 81, 222-232 (1951).
[CrossRef]

Rosenberger, A. T.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 63804 (2004).
[CrossRef]

Savchenkov, A. A.

Scheuer, J.

J. K. S. Poon, J. Scheuer, Y. Xu, and A. Yariv, "Designing coupled-resonator optical waveguide delay lines," J. Opt. Soc. Am. B 21, 1665-1673 (2004).
[CrossRef]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 99-103 (2004).
[CrossRef]

Schrama, C. A.

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51, 646-654 (1995).
[CrossRef] [PubMed]

Smith, D. D.

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, "Coupled-resonator-induced transparency," Phys. Rev. A 69, 63804 (2004).
[CrossRef]

D. D. Smith, H. Chang, and K. A. Fuller, "Whispering-gallery mode splitting in coupled microresonators," J. Opt. Soc. Am. B 20, 1967-1974 (2003).
[CrossRef]

Spreeuw, R. J. C.

R. J. C. Spreeuw and J. P. Woerdman, "Optical atoms," Prog. Opt. 31, 263-319 (1993).
[CrossRef]

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65, 2642-2645 (1990).
[CrossRef] [PubMed]

R. J. C. Spreeuw, R. Centeno, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, "Mode coupling in a He-Ne ring laser with backscattering," Phys. Rev. A 42, 4315-4324 (1990).
[CrossRef] [PubMed]

R. J. C. Spreeuw and J. P. Woerdman, "Photon band structure in a Sagnac fiber-optic ring resonator," Phys. Rev. Lett. 61, 318-321 (1988).
[CrossRef] [PubMed]

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]

van Druten, N. J.

R. J. C. Spreeuw, R. Centeno, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, "Mode coupling in a He-Ne ring laser with backscattering," Phys. Rev. A 42, 4315-4324 (1990).
[CrossRef] [PubMed]

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65, 2642-2645 (1990).
[CrossRef] [PubMed]

Visser, P. M.

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51, 646-654 (1995).
[CrossRef] [PubMed]

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]

L. J. Wang, "Casual 'all-pass' filters and Kramers-Kronig relations," Opt. Commun. 213, 27-32 (2002).
[CrossRef]

A. Dogariu, A. Kuzmich, and L. J. Wang, "Transparent anomalous dispersion and superluminal light-pulse propagation at negative group velocity," Phys. Rev. A 63, 53806 (2001).
[CrossRef]

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

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]

Welsch, D. G.

T. Opatrny and D. G. Welsch, "Coupled cavities for enhancing the cross-phase-modulation in electromagnetically induced transparency," Phys. Rev. A 64, 23805 (2001).
[CrossRef]

Woerdman, J. P.

D. Bouwmeester, N. H. Dekker, F. E. v. Dorsselaer, C. A. Schrama, P. M. Visser, and J. P. Woerdman, "Observation of Landau-Zener dynamics in classical optical systems," Phys. Rev. A 51, 646-654 (1995).
[CrossRef] [PubMed]

R. J. C. Spreeuw and J. P. Woerdman, "Optical atoms," Prog. Opt. 31, 263-319 (1993).
[CrossRef]

R. J. C. Spreeuw, N. J. van Druten, M. W. Beijersbergen, E. R. Eliel, and J. P. Woerdman, "Classical realization of a strongly driven two-level system," Phys. Rev. Lett. 65, 2642-2645 (1990).
[CrossRef] [PubMed]

R. J. C. Spreeuw, R. Centeno, N. J. van Druten, E. R. Eliel, and J. P. Woerdman, "Mode coupling in a He-Ne ring laser with backscattering," Phys. Rev. A 42, 4315-4324 (1990).
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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).
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[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic of two coupled optical resonators in an all-pass configuration.

Fig. 2
Fig. 2

Parametric phasor (Argand) diagram of the complex electric field transmission for a single overcoupled resonator (dotted curve) and two coupled resonators, overcoupled and amplified to transparency (dashed curve). Fast light occurs for the solid portion of the curve, i.e., for frequencies between the dispersion reversals (indicated by the tangents from the origin). The plots start at the dot ( ϕ = 0 ) and proceed counterclockwise as indicated around the loop over a range of 2 π .

Fig. 3
Fig. 3

Transmittance (dashed curves) and dispersive response (solid curves) of coupled resonators as a function of the decay rate γ 2 in the second resonator ( γ 2 < 0 indicates the resonator contains an amplifying medium): (a) transmittance at resonance T 2 ( 0 ) , (b) transmittance at the split resonances T 2 ( δ ( sp ) ) , (c) the derivative of effective phase shift at resonance, and (d) the derivative of effective phase shift at the split resonances. The vertical lines indicate the critical coupling γ 2 ( cr ) (dashed lines) and lasing threshold γ 2 ( th ) (dotted lines). Note that the dispersion reverses at each of these points. The dot indicates the gain required for GAS. The parameters are γ 1 = 0.001 , γ 0 = 0.1 , and κ = 0.008 . Curve (e) indicates the sign of expression (14), positive (negative) indicating pulse compression (expansion).

Fig. 4
Fig. 4

Steady-state absorptive and dispersive responses of coupled resonators for GAS as a function of the detuning δ of the excitation: (a) the effective phase shift, ϕ 2 ( eff ) and (b) single-structure absorption coefficient, 2 ln τ 2 .

Fig. 5
Fig. 5

Numerical solution of the coupled-mode equations demonstrating the time advancement of a Gaussian pulse without loss or distortion after transmission across (a) a single coupled-resonator structure and (b) a sequence of nine such structures.

Fig. 6
Fig. 6

(a) and (b) Transmittance T 2 and (c) and (d) relative pulse compression factor C = ( 1 β 2 ) ρ 2 at ϕ = 0 for two different values of γ 0 : indistinguishable splitting γ 0 γ ( eff ) (dashed curves) and distinguishable splitting near critical coupling γ 0 = γ ( eff ) (solid curves). The dotted curve represents the distinguishability boundary. Variation of γ 0 does not change the gain γ 2 required for transparent GAS (as indicated by the solid vertical line) but does change the relative pulse compression, which varies linearly with γ 0 along any vertical line and linearly with γ 2 along any horizontal line. The relative pulse compression is minimized at critical coupling. The two vertical dashed–dotted lines indicate the lasing thresholds at ϕ = 0 .

Equations (14)

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τ 2 ( ϕ 1 , ϕ 2 ) = r 2 a 2 τ 1 exp ( i ϕ 2 ) 1 r 2 a 2 τ 1 exp ( i ϕ 2 ) = τ 2 exp [ i ϕ 2 ( eff ) ] ,
τ 1 ( ϕ 1 ) = r 1 a 1 exp ( i ϕ 1 ) 1 r 1 a 1 exp ( i ϕ 1 ) = τ 1 exp [ i ϕ 1 ( eff ) ]
d τ d ϕ = 1 τ [ τ d τ d ϕ ] = 0 ,
d ϕ ( eff ) d ϕ = 1 τ 2 τ d τ d ϕ = 0 or ,
a ̇ 1 ( t ) = i ω ̃ 1 a 1 ( t ) + i κ 2 a 2 ( t ) ,
a ̇ 2 ( t ) = ( i ω ̃ 2 γ 0 2 ) a 2 ( t ) + i κ 2 a 1 ( t ) + i γ 0 τ RT a 0 ( t ) ,
τ 2 ( δ ) = δ 2 + i [ ( γ 1 + γ 2 ) 2 γ 0 2 ] δ ( γ 1 2 ) ( γ ( eff ) γ 0 ) 2 δ 2 + i [ ( γ 1 + γ 2 ) 2 + γ 0 2 ] δ ( γ 1 2 ) ( γ ( eff ) + γ 0 ) 2 ,
τ 1 ( δ ) = δ + i ( γ 1 γ 0 ) 2 δ + i ( γ 1 + γ 0 ) 2 .
d ϕ 2 ( eff ) d δ δ = 0 = 4 γ 0 ( κ 2 γ 1 2 ) γ 1 2 [ ( γ ( eff ) ) 2 γ 0 2 ] ,
0 < κ 2 γ 1 2 < γ 1 γ 0 .
( 1 β 2 ) = C ρ 2 ,
τ t = τ i [ 1 + 1 τ i 2 d 2 d δ 2 ln 1 τ ( δ ) δ = 0 ] 1 2 = τ i β ,
C = γ ( eff ) ( κ 2 γ 1 2 ) 2 + γ 1 κ 2 [ γ 0 2 ( γ ( eff ) ) 2 ] γ 0 ( κ 2 γ 1 2 ) 2 .
d d δ [ τ d τ d δ ] δ = 0 > 0 ,

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