Abstract

There are two standard methods for controlling the group velocity of light. One makes use of the dispersive properties associated with the resonance structure of a material medium. The other makes use of structural resonances, such as those that occur in photonic crystals. Both procedures have proved useful in a variety of situations. In this work we contrast these two approaches, especially in terms of issues such as the kinematics of energy flow though the system and the resulting implications for the behavior of nonlinear optical processes in these situations. Stated differently, this paper addresses the question of when nonlinear optical processes are enhanced through use of slow-light interactions and when they are not.

© 2011 Optical Society of America

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  9. Especially intriguing are the consequences of Eq. (5) for circumstances under which the group velocity vg becomes negative, implying a negative value of the Poynting vector magnitude S. In such circumstances, it is considered more useful to describe the situation in terms of an energy velocity rather than a group velocity. Details can be found in [3]. A negative value of the energy velocity would imply the flow of energy back toward the source. Some authors have argued that negative values of the energy velocity are physically meaningful [50], whereas others do not [3]. At present, there seems to be no complete understanding of this issue.
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    [CrossRef]
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    [CrossRef]
  29. H. Gersen, T. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
    [CrossRef]
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    [CrossRef]
  31. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
    [CrossRef]
  32. L. O’Faolain, T. P. White, D. O’Brien, X. Yuan, M. D. Settle, and T. F. Krauss, “Dependence of extrinsic loss on group velocity in photonic crystal waveguides,” Opt. Express 15, 13129–13138 (2007).
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  34. H. G. Winful, “Pulse compression in optical fiber filters,” Appl. Phys. Lett. 46, 527–529 (1985).
    [CrossRef]
  35. H. G. Winful, “Delay time and the Hartman effect in quantum tunneling,” Phys. Rev. Lett. 91, 260401 (2003).
    [CrossRef]
  36. H. G. Winful, “The meaning of group delay in barrier tunnelling: a re-examination of superluminal group velocities,” New J. Phys. 8, 101 (2006).
    [CrossRef]
  37. C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990).
    [CrossRef]
  38. S. Longhi, M. Marana, M. Belmonte, and P. Laporta, “Superluminal pulse propagation in linear and nonlinear photonic grating structures,” IEEE J. Sel. Top. Quantum Electron. 9, 4–16 (2003).
    [CrossRef]
  39. C. Monat, M. de Sterke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt. 12, 104003 (2010).
    [CrossRef]
  40. S. Chin, I. Dicaire, J. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thvenaz, “Material slow light does not enhance Beer–Lambert absorption,” in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2009), paper SMA3.
  41. I. Dicaire, S. Chin, and L. Thvenaz, “Structural slow light can enhance Beer–Lambert absorption,” in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SLWC2.
  42. N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E 64, 056604 (2001).
    [CrossRef]
  43. P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photon. 4, 862–868 (2010).
    [CrossRef]
  44. C. Husko, S. Combri, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides,” Opt. Express 17, 22442–22451 (2009).
    [CrossRef]
  45. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
    [CrossRef]
  46. M. Santagiustina, C. G. Someda, G. Vadala, S. Combri, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express 18, 21024–21028 (2010).
    [CrossRef]
  47. J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011).
    [CrossRef]
  48. C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
    [CrossRef]
  49. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation,” Nat. Photon. 3, 206–210 (2009).
    [CrossRef]
  50. E. A. Bolda, J. C. Garrison, and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain line,” Phys. Rev. A 49, 2938–2947 (1994).
    [CrossRef]

2011 (2)

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow light medium,” Science 333, 65–67 (2011).
[CrossRef]

J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations,” Opt. Express 19, 4458–4463 (2011).
[CrossRef]

2010 (8)

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
[CrossRef]

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[CrossRef]

R. Boyd, O. Hess, C. Denz, and E. Palpalakis, eds., “Slow lights,” J. Opt. 12, 100301 (2010).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

C. Monat, M. de Sterke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt. 12, 104003 (2010).
[CrossRef]

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photon. 4, 862–868 (2010).
[CrossRef]

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
[CrossRef]

M. Santagiustina, C. G. Someda, G. Vadala, S. Combri, and A. De Rossi, “Theory of slow light enhanced four-wave mixing in photonic crystal waveguides,” Opt. Express 18, 21024–21028 (2010).
[CrossRef]

2009 (3)

C. Husko, S. Combri, Q. V. Tran, F. Raineri, C. W. Wong, and A. De Rossi, “Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides,” Opt. Express 17, 22442–22451 (2009).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation,” Nat. Photon. 3, 206–210 (2009).
[CrossRef]

2008 (2)

2007 (1)

2006 (2)

H. G. Winful, “The meaning of group delay in barrier tunnelling: a re-examination of superluminal group velocities,” New J. Phys. 8, 101 (2006).
[CrossRef]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897 (2006).
[CrossRef]

2005 (4)

Y. Vlasov, M. O’Boyle, H. F. Harmann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[CrossRef]

M. L. Povinelli, S. Johnson, and J. D. Joannopoulos, “Slow-light, band-edge waveguides for tunable time delays,” Opt. Express 13, 7145–7159 (2005).
[CrossRef]

H. Gersen, T. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef]

S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, “Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity,” Phys. Rev. Lett. 94, 033903 (2005).
[CrossRef]

2003 (4)

H. G. Winful, “Delay time and the Hartman effect in quantum tunneling,” Phys. Rev. Lett. 91, 260401 (2003).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultra-slow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef]

S. Longhi, M. Marana, M. Belmonte, and P. Laporta, “Superluminal pulse propagation in linear and nonlinear photonic grating structures,” IEEE J. Sel. Top. Quantum Electron. 9, 4–16 (2003).
[CrossRef]

2002 (1)

2001 (2)

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E 64, 056604 (2001).
[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef]

2000 (1)

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

1999 (3)

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

1996 (1)

T. F. Krauss, R. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

1994 (1)

E. A. Bolda, J. C. Garrison, and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain line,” Phys. Rev. A 49, 2938–2947 (1994).
[CrossRef]

1990 (2)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990).
[CrossRef]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

1985 (1)

H. G. Winful, “Pulse compression in optical fiber filters,” Appl. Phys. Lett. 46, 527–529 (1985).
[CrossRef]

1982 (1)

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[CrossRef]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nature Photonics 2, 465–473 (2008).
[CrossRef]

Barsi, C.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897 (2006).
[CrossRef]

Beggs, D. M.

L. O’Faolain, S. A. Schulz, D. M. Beggs, T. P. White, M. Spasenovic, L. Kuipers, F. Morichetti, A. Melloni, S. Mazoyer, J. P. Hugonin, P. Lalanne, and T. F. Krauss, “Loss engineered slow light waveguides,” Opt. Express 18, 27627–27638 (2010).
[CrossRef]

S. A. Schulz, L. O’Faolain, D. M. Beggs, T. P. White, A. Melloni, and T. F. Krauss, “Dispersion engineered slow light in photonic crystals: a comparison,” J. Opt. 12, 104004 (2010).
[CrossRef]

Behroozi, C.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Belmonte, M.

S. Longhi, M. Marana, M. Belmonte, and P. Laporta, “Superluminal pulse propagation in linear and nonlinear photonic grating structures,” IEEE J. Sel. Top. Quantum Electron. 9, 4–16 (2003).
[CrossRef]

Beugnot, J.

S. Chin, I. Dicaire, J. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thvenaz, “Material slow light does not enhance Beer–Lambert absorption,” in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2009), paper SMA3.

Bhat, N. A. R.

N. A. R. Bhat and J. E. Sipe, “Optical pulse propagation in nonlinear photonic crystals,” Phys. Rev. E 64, 056604 (2001).
[CrossRef]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultra-slow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef]

Bogaerts, W.

H. Gersen, T. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[CrossRef]

Bolda, E. A.

E. A. Bolda, J. C. Garrison, and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain line,” Phys. Rev. A 49, 2938–2947 (1994).
[CrossRef]

Boyd, R. W.

S. Franke-Arnold, G. Gibson, R. W. Boyd, and M. J. Padgett, “Rotary photon drag enhanced by a slow light medium,” Science 333, 65–67 (2011).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
[CrossRef]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895–897 (2006).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301, 200–202 (2003).
[CrossRef]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultra-slow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef]

R. W. Boyd and D. J. Gauthier, Slow and Fast Light, Progress in Optics (Elsevier, 2002), pp. 497–530.

Brand, S.

T. F. Krauss, R. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Chiao, R. Y.

E. A. Bolda, J. C. Garrison, and R. Y. Chiao, “Optical pulse propagation at negative group velocities due to a nearby gain line,” Phys. Rev. A 49, 2938–2947 (1994).
[CrossRef]

Chin, S.

I. Dicaire, S. Chin, and L. Thvenaz, “Structural slow light can enhance Beer–Lambert absorption,” in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SLWC2.

S. Chin, I. Dicaire, J. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thvenaz, “Material slow light does not enhance Beer–Lambert absorption,” in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2009), paper SMA3.

Chu, S.

S. Chu and S. Wong, “Linear pulse propagation in an absorbing medium,” Phys. Rev. Lett. 48, 738–741 (1982).
[CrossRef]

Colman, P.

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photon. 4, 862–868 (2010).
[CrossRef]

Combri, S.

Combrie, S.

P. Colman, C. Husko, S. Combrie, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photon. 4, 862–868 (2010).
[CrossRef]

Corcoran, B.

De La Rue, R.

T. F. Krauss, R. De La Rue, and S. Brand, “Two-dimensional photonic-bandgap structures operating at near-infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

De Rossi, A.

de Sterke, C. M.

C. M. de Sterke and J. E. Sipe, “Coupled modes and the nonlinear Schrödinger equation,” Phys. Rev. A 42, 550–555 (1990).
[CrossRef]

de Sterke, M.

C. Monat, M. de Sterke, and B. J. Eggleton, “Slow light enhanced nonlinear optics in periodic structures,” J. Opt. 12, 104003 (2010).
[CrossRef]

Dicaire, I.

S. Chin, I. Dicaire, J. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thvenaz, “Material slow light does not enhance Beer–Lambert absorption,” in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2009), paper SMA3.

I. Dicaire, S. Chin, and L. Thvenaz, “Structural slow light can enhance Beer–Lambert absorption,” in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SLWC2.

Dogariu, A.

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

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Ebnali-Heidari, M.

Eggleton, B. J.

C. Monat, M. Ebnali-Heidari, C. Grillet, B. Corcoran, B. J. Eggleton, T. P. White, L. O’Faolain, J. Li, and T. F. Krauss, “Four-wave mixing in slow light engineered silicon photonic crystal waveguides,” Opt. Express 18, 22915–22927 (2010).
[CrossRef]

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[CrossRef]

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[CrossRef]

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Other (10)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed.(Princeton University, 2008).

P. W. Milonni, Fast Light, Slow Light, and Left-Handed Light (Institute of Physics Publishing, 2005).

J. B. Khurgin and R. S. Tucker, eds., Slow Light: Science and Applications (CRC, 2008).

R. W. Boyd and D. J. Gauthier, Slow and Fast Light, Progress in Optics (Elsevier, 2002), pp. 497–530.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1960).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall, 1984). See especially Section 11.3.

Especially intriguing are the consequences of Eq. (5) for circumstances under which the group velocity vg becomes negative, implying a negative value of the Poynting vector magnitude S. In such circumstances, it is considered more useful to describe the situation in terms of an energy velocity rather than a group velocity. Details can be found in [3]. A negative value of the energy velocity would imply the flow of energy back toward the source. Some authors have argued that negative values of the energy velocity are physically meaningful [50], whereas others do not [3]. At present, there seems to be no complete understanding of this issue.

Z. Shi, “Fundamentals and applications of slow light,” PhD Dissertation (University of Rochester, 2010).

S. Chin, I. Dicaire, J. Beugnot, S. Foaleng-Mafang, M. Gonzalez-Herraez, and L. Thvenaz, “Material slow light does not enhance Beer–Lambert absorption,” in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2009), paper SMA3.

I. Dicaire, S. Chin, and L. Thvenaz, “Structural slow light can enhance Beer–Lambert absorption,” in Slow and Fast Light, OSA Technical Digest (CD) (Optical Society of America, 2011), paper SLWC2.

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Figures (9)

Fig. 1.
Fig. 1.

Origin of slow and fast light for an isolated absorption resonance (a) and gain resonance (b).

Fig. 2.
Fig. 2.

Origin of slow and fast light for a dip in a gain feature (a) and an absorption feature (b).

Fig. 3.
Fig. 3.

(top) Schematic illustration of the pulse compression that occurs when light enters a slow-light medium. (bottom) Pulse expansion occurs for the case of a fast-light medium. In each case the pulse is represented in terms of its energy density u.

Fig. 4.
Fig. 4.

A representative slow-light structure in the form on a line-defect photonic-crystal structure. Reproduced with permission from [23].

Fig. 5.
Fig. 5.

(a) Dispersion diagram of a typical line-defect photonic-crystal waveguide. (b) Mode index determined from the dispersion diagram of part (a). (c) Reduced group index (ngn) for this structure. Note that while the group index is very large, it changes rapidly with wavelength, which is undesirable for many applications. Much current work is aimed at developing dispersion-engineered PhC waveguides that minimize this effect. Reproduced with permission from [24].

Fig. 6.
Fig. 6.

Schematic illustration of the origin of slow light in a Bragg grating structure. Reproduced with permission from [33].

Fig. 7.
Fig. 7.

Dispersion relation of a FBG as given by Eq. (10).

Fig. 8.
Fig. 8.

Dependence of either the normalized group delay or the normalized stored energy of a FBG structure on the detuning of the incident light field from the Bragg frequency ωB. Reproduced with permission from [36].

Fig. 9.
Fig. 9.

(a) Power transmission through a FBG as a function of detuning from the Bragg resonance. (b) Group delay through this structure. Reproduced with permission from [38].

Equations (12)

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

vg=c/ng,
ng=n+ωdndω.
u=12nngϵ0|E|2
S=12ncϵ0|E|2.
S=uvg=u(c/ng)
EFz+1vEFt=iκEBe2iΔβz
EBz1vEBt=iκEFe2iΔβz,
EF(z)=E0[γcoshγ(zL)+i(Ω/v)sinhγ(zL)]/g
EB(z)=iE0[κsinhγ(zL)]/g
(Ω/v)2=q2+κ2.
U=U0[(κ/γ)2(tanhγL)/γL(Ω/γv)2sech2γL1+(Ω/γv)2tanh2γL],
Γ=(3S22)S2γ0,

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