Abstract

We present a holographic system that can be used to manipulate the group velocity of light pulses. The proposed structure is based on the multiplexing of two sequential holographic volume gratings, one in transmission and the other in reflection geometry, where one of the recording beams must be the same for both structures. As in other systems such as grating induced transparency (GIT) or coupled-resonator-induced transparency (CRIT), by using the coupled wave theory it is shown that this holographic structure represents a classical analogue of the electromagnetically induced transparency (EIT). Analytical expressions were obtained for the transmittance induced at the forbidden band (spectral hole) and conditions where the group velocity was slowed down were analyzed. Moreover, the propagation of Gaussian pulses is analyzed for this system by obtaining, after further approximations, analytical expressions for the distortion of the transmitted field. As a result, we demonstrate the conditions where the transmitted pulse is slowed down and its shape is only slightly distorted. Finally, by comparing with the exact solutions obtained, the range of validity of all the analytical formulae was verified, demonstrating that the error is very low.

©2011 Optical Society of America

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  1. R. Boyd, O. Hess, C. Denz, and E. Paspalkalis, “Slow light,” J. Opt. 12(10), 100301 (2010).
    [Crossref]
  2. J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B 22, 1062–1074 (2005).
    [Crossref]
  3. F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
    [Crossref]
  4. Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light fourier transform interferometer,” Phys. Rev. Lett. 99(24), 240801 (2007).
    [Crossref]
  5. Z. M. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32(8), 915–917 (2007).
    [Crossref] [PubMed]
  6. R. Boyd and D. J. Gauthier, ““Slow” and “fast” light,” in Progress in Optics, E. Wolf, ed., (Elsevier, 2002) vol. 43, chap. 6, pp. 497–530.
    [Crossref]
  7. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
    [Crossref]
  8. A. Kasapi, M. Jain, G. y. Yin, and S. E. Harris, “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
    [Crossref] [PubMed]
  9. M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75(2), 457–472 (2003).
    [Crossref]
  10. L. V. Hau, “Optical information processing in Bose-Einstein condensates,” Nat. Photonics 2(8), 451–453 (2008).
    [Crossref]
  11. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003).
    [Crossref] [PubMed]
  12. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90(11), 113903 (2003).
    [Crossref] [PubMed]
  13. R. M. Camacho, M. V. Pack, and J. C. Howell, “Low-distortion slow light using two absorption resonances,” Phys. Rev. A 73(6), 063812 (2006).
    [Crossref]
  14. R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
    [Crossref] [PubMed]
  15. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
    [Crossref] [PubMed]
  16. T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
    [Crossref]
  17. M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501 (2010).
    [Crossref]
  18. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
    [Crossref]
  19. D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
    [Crossref]
  20. Z. M. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol. 25(1), 201–206 (2007).
    [Crossref]
  21. L. Thevenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008).
    [Crossref]
  22. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
    [Crossref]
  23. M. F. Yanik, W. Suh, Z. Wang, and S. H. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93(23), 233903 (2004).
    [Crossref] [PubMed]
  24. K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency.” Phys. Rev. Lett. 98(21), 213904 (2007).
    [Crossref] [PubMed]
  25. H. C. Liu and A. Yariv, “Grating induced transparency (GIT) and the dark mode in optical waveguides,” Opt. Express 17(14), 11710–11718 (2009).
    [Crossref] [PubMed]
  26. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2945 (1969).
  27. B. Macke and B. Segard, “Propagation of light-pulses at a negative group-velocity,” Eur. Phys. J. D 23, 125–141 (2003).
    [Crossref]

2010 (2)

R. Boyd, O. Hess, C. Denz, and E. Paspalkalis, “Slow light,” J. Opt. 12(10), 100301 (2010).
[Crossref]

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501 (2010).
[Crossref]

2009 (1)

2008 (3)

L. Thevenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008).
[Crossref]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

L. V. Hau, “Optical information processing in Bose-Einstein condensates,” Nat. Photonics 2(8), 451–453 (2008).
[Crossref]

2007 (6)

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[Crossref]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light fourier transform interferometer,” Phys. Rev. Lett. 99(24), 240801 (2007).
[Crossref]

Z. M. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32(8), 915–917 (2007).
[Crossref] [PubMed]

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[Crossref] [PubMed]

Z. M. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS slow light in an optical fiber,” J. Lightwave Technol. 25(1), 201–206 (2007).
[Crossref]

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency.” Phys. Rev. Lett. 98(21), 213904 (2007).
[Crossref] [PubMed]

2006 (1)

R. M. Camacho, M. V. Pack, and J. C. Howell, “Low-distortion slow light using two absorption resonances,” Phys. Rev. A 73(6), 063812 (2006).
[Crossref]

2005 (2)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

J. B. Khurgin, “Optical buffers based on slow light in electromagnetically induced transparent media and coupled resonator structures: comparative analysis,” J. Opt. Soc. Am. B 22, 1062–1074 (2005).
[Crossref]

2004 (2)

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
[Crossref]

M. F. Yanik, W. Suh, Z. Wang, and S. H. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93(23), 233903 (2004).
[Crossref] [PubMed]

2003 (4)

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

M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75(2), 457–472 (2003).
[Crossref]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90(11), 113903 (2003).
[Crossref] [PubMed]

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24(11), 711–713 (1999).
[Crossref]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[Crossref]

1995 (1)

A. Kasapi, M. Jain, G. y. Yin, and S. E. Harris, “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref] [PubMed]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2945 (1969).

Ali-Khan, I.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[Crossref] [PubMed]

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90(11), 113903 (2003).
[Crossref] [PubMed]

Boyd, R.

R. Boyd, O. Hess, C. Denz, and E. Paspalkalis, “Slow light,” J. Opt. 12(10), 100301 (2010).
[Crossref]

R. Boyd and D. J. Gauthier, ““Slow” and “fast” light,” in Progress in Optics, E. Wolf, ed., (Elsevier, 2002) vol. 43, chap. 6, pp. 497–530.
[Crossref]

Boyd, R. W.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light fourier transform interferometer,” Phys. Rev. Lett. 99(24), 240801 (2007).
[Crossref]

Z. M. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32(8), 915–917 (2007).
[Crossref] [PubMed]

D. D. Smith, H. Chang, K. A. Fuller, A. T. Rosenberger, and R. W. Boyd, “Coupled-resonator-induced transparency,” Phys. Rev. A 69(6), 063804 (2004).
[Crossref]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90(11), 113903 (2003).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003).
[Crossref] [PubMed]

Broadbent, C. J.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[Crossref] [PubMed]

Camacho, R. M.

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[Crossref] [PubMed]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light fourier transform interferometer,” Phys. Rev. Lett. 99(24), 240801 (2007).
[Crossref]

R. M. Camacho, M. V. Pack, and J. C. Howell, “Low-distortion slow light using two absorption resonances,” Phys. Rev. A 73(6), 063812 (2006).
[Crossref]

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(6), 063804 (2004).
[Crossref]

Dawes, A. M. C.

Denz, C.

R. Boyd, O. Hess, C. Denz, and E. Paspalkalis, “Slow light,” J. Opt. 12(10), 100301 (2010).
[Crossref]

Dudley, C. C.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Fan, S. H.

M. F. Yanik, W. Suh, Z. Wang, and S. H. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93(23), 233903 (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(6), 063804 (2004).
[Crossref]

Gauthier, D. J.

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[Crossref]

A. Kasapi, M. Jain, G. y. Yin, and S. E. Harris, “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref] [PubMed]

Hau, L. V.

L. V. Hau, “Optical information processing in Bose-Einstein condensates,” Nat. Photonics 2(8), 451–453 (2008).
[Crossref]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Hess, O.

R. Boyd, O. Hess, C. Denz, and E. Paspalkalis, “Slow light,” J. Opt. 12(10), 100301 (2010).
[Crossref]

Howell, J. C.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light fourier transform interferometer,” Phys. Rev. Lett. 99(24), 240801 (2007).
[Crossref]

R. M. Camacho, C. J. Broadbent, I. Ali-Khan, and J. C. Howell, “All-optical delay of images using slow light,” Phys. Rev. Lett. 98, 043902 (2007).
[Crossref] [PubMed]

R. M. Camacho, M. V. Pack, and J. C. Howell, “Low-distortion slow light using two absorption resonances,” Phys. Rev. A 73(6), 063812 (2006).
[Crossref]

Jain, M.

A. Kasapi, M. Jain, G. y. Yin, and S. E. Harris, “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref] [PubMed]

Kasapi, A.

A. Kasapi, M. Jain, G. y. Yin, and S. E. Harris, “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref] [PubMed]

Khurgin, J. B.

Kobayashi, N.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency.” Phys. Rev. Lett. 98(21), 213904 (2007).
[Crossref] [PubMed]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2945 (1969).

Lee, R. K.

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Observation of ultraslow light propagation in a ruby crystal at room temperature,” Phys. Rev. Lett. 90(11), 113903 (2003).
[Crossref] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, “Superluminal and slow light propagation in a room-temperature solid,” Science 301(5630), 200–202 (2003).
[Crossref] [PubMed]

Liu, H. C.

Lukin, M. D.

M. D. Lukin, “Colloquium: Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75(2), 457–472 (2003).
[Crossref]

Macke, B.

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

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

Notomi, M.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501 (2010).
[Crossref]

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

Pack, M. V.

R. M. Camacho, M. V. Pack, and J. C. Howell, “Low-distortion slow light using two absorption resonances,” Phys. Rev. A 73(6), 063812 (2006).
[Crossref]

Paspalkalis, E.

R. Boyd, O. Hess, C. Denz, and E. Paspalkalis, “Slow light,” J. Opt. 12(10), 100301 (2010).
[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(6), 063804 (2004).
[Crossref]

Scherer, A.

Segard, B.

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

Sekaric, L.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[Crossref]

Shi, Z.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light fourier transform interferometer,” Phys. Rev. Lett. 99(24), 240801 (2007).
[Crossref]

Shi, Z. M.

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(6), 063804 (2004).
[Crossref]

Suh, W.

M. F. Yanik, W. Suh, Z. Wang, and S. H. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93(23), 233903 (2004).
[Crossref] [PubMed]

Thevenaz, L.

L. Thevenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008).
[Crossref]

Tomita, M.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency.” Phys. Rev. Lett. 98(21), 213904 (2007).
[Crossref] [PubMed]

Totsuka, K.

K. Totsuka, N. Kobayashi, and M. Tomita, “Slow light in coupled-resonator-induced transparency.” Phys. Rev. Lett. 98(21), 213904 (2007).
[Crossref] [PubMed]

Vlasov, Y.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[Crossref]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

Vudyasetu, P. K.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light fourier transform interferometer,” Phys. Rev. Lett. 99(24), 240801 (2007).
[Crossref]

Wang, Z.

M. F. Yanik, W. Suh, Z. Wang, and S. H. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93(23), 233903 (2004).
[Crossref] [PubMed]

Willner, A. E.

Xia, F. N.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[Crossref]

Xu, Y.

Yanik, M. F.

M. F. Yanik, W. Suh, Z. Wang, and S. H. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. 93(23), 233903 (2004).
[Crossref] [PubMed]

Yariv, A.

Yin, G. y.

A. Kasapi, M. Jain, G. y. Yin, and S. E. Harris, “Electromagnetically induced transparency - propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref] [PubMed]

Zhang, L.

Zhu, Z. M.

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48(9), 2909–2945 (1969).

Eur. Phys. J. D (1)

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

J. Lightwave Technol. (1)

J. Opt. (1)

R. Boyd, O. Hess, C. Denz, and E. Paspalkalis, “Slow light,” J. Opt. 12(10), 100301 (2010).
[Crossref]

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

Nat. Photonics (4)

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[Crossref]

L. V. Hau, “Optical information processing in Bose-Einstein condensates,” Nat. Photonics 2(8), 451–453 (2008).
[Crossref]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

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[Crossref]

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Scheme of the multiplexing of volume holographic gratings.

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Fig. 2
Fig. 2

Index group (np , p = s, w) normalized to refractive index n as a function of recording angle θp .

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Fig. 3
Fig. 3

L1 as a function of group index ns.

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Fig. 4
Fig. 4

T as a function of detuning δω. Inset curves (blue) shows the relative error of our approximated function (25) in comparison with exact result given by Eq. (16).

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Fig. 5
Fig. 5

Phase as a function of detuning δω. Inset curve shows the relative error of our approximated function (25) in comparison with exact result given by Eq. (16).

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Fig. 6
Fig. 6

Intensity of incident pulse (brown) and time-delayed pulses obtained using equation 35 and approximations (25) (blue) or (37)–(38) (pink) as a function of time. Inset curve shows the relative error in comparison with exact solution.

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Equations (40)

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ε = ε 0 + ε 1   Cos ( K 1 . r ) + ε 2 Cos ( K 2 . r )
K 1 = n ω o c ( Sin ( θ r ) − Sin ( θ s ) ,   0 ,   Cos ( θ r ) − Cos ( θ s ) )
K 2 = n ω o c ( Sin ( θ s ) − Sin ( θ w ) ,   0 ,   Cos ( θ s ) − Cos ( θ w ) )
∂ 2 E ∂ x 2 + ∂ 2 E ∂ z 2 + ( ω c ) 2   ε E = 0
E = R ( z )   exp ( − j K R . r ) + S ( z )   exp ( − j K S . r ) + W ( z ) exp ( − j   K W . r )
K S = K R − K 1 ,   K W = K S − K 2
K R = n ω c ( Sin ( θ ) ,   0 ,   Cos ( θ ) )
K S = n c ( ω   Sin ( θ ) − ω o ( Sin ( θ r ) − Sin ( θ s ) ) ,   0 ,   ω   Cos ( θ ) −   ω o ( Cos ( θ r ) − Cos ( θ s ) ) )
K W = n c ( ω   Sin ( θ ) − ω o ( Sin ( θ r ) − Sin ( θ w ) ) ,   0 ,   ω   Cos ( θ ) − ω o ( Cos ( θ r ) − Cos ( θ w ) ) )
d d z ( R ( z ) S ( z ) W ( z ) ) = − j ( 0 κ 1 c r 0 κ 1 c s ϑ s c s κ 2 c s 0 κ 2 c w ϑ w c w )       ( R ( z ) S ( z ) W ( z ) )
κ i = ε i ω 4 c n with i = ( 1 ,   2 ) ϑ p = β 2 − | K p | 2 2 β with p = ( s ,   w ) c q = K Q z 2 β with q = ( r ,   s ,   w )
κ ¯ i = ε i ω o 4 c n with i = ( 1 ,   2 ) ϑ ¯ p = n δ ω c ( 1 − Cos ( θ p ) ) with p = ( s ,   w ) c ¯ q = Cos ( θ q ) with q = ( r ,   s ,   w ) ;
d d z ( R ( z ) S ( z ) W ( z ) ) = A ( R ( z ) S ( z ) W ( z ) ) = − j ( 0 c r c s ν 1 c r 0 c r c s ν 1 c s ξ s c w c s ν 2 c s 0 c w c s ν 2 c w ξ w )       ( R ( z ) S ( z ) W ( z ) )
n p = n ( S e c ( θ p ) − 1 ) with   p = ( s ,   w ) ν 1 = κ ¯ 1 2 ( n s n + 1 ) ν 2 = κ ¯ 2 2 ( n s n + 1 ) ( n w n + 1 ) ξ p = ϑ p c p = δ ω c n p w i t h   p = ( s ,   w )
R ( z ) = ∑ i = 0 2 C i exp ( x i   z )
t = R ( L ) = ∑ i = 0 2 C i exp ( x i   L )
P = − x 3 − j ( ξ s + ξ w ) x 2 + ( ξ s ξ w − ν 1 − ν 2 ) x − j ν 1 ξ w
C 0 = Γ 12 Γ 01 − Γ 02 + Γ 12 C 1 = − Γ 02 Γ 01 − Γ 02 + Γ 12 C 2 = Γ 01 Γ 01 − Γ 02 + Γ 12
Γ ip = exp ( L ( x i + x p ) ) Ω ip         w i t h         Ω ip = ( x i − x p )   ( − ν 1 + x i x p )
t = ν 1 + ν 2 ν 2 + ν 1 Cos ( L ν 1 + ν 2 )
t = exp ( j ψ ) ρ 01 2 + ρ 02 2 + ρ 12 2 − 2   ( ρ 01 ρ 02 Cos ( ϕ 21 ) − ρ 01 ρ 12 Cos ( ϕ 20 ) + ρ 02 ρ 12 Cos ( ϕ 01 ) )
ρ ip = Ω ip Ω 01 − Ω 02 + Ω 12 ϕ ip = ( x i − x p ) L / j ψ = arctan ( ρ 01 Sin ( x 2 L / j ) − ρ 02 Sin ( x 1 L / j ) + ρ 12 Sin ( x 0 L / j ) ρ 01 Cos ( x 2 L / j ) − ρ 02 Cos ( x 1 L / j ) + ρ 12 Cos ( x 0 L / j ) )
x 0 = − j ξ w ν 1 ν 1 + ν 2 x 1 = − j 4 ( 2 ξ w ν 2 ν 1 + ν 2 + 4 ν 1 + ν 2 + ξ s ( 2 − ξ w ν 2 ( ν 1 + ν 2 ) ) 3 / 2 ) ) x 2 = j 4 ( − 2 ξ w ν 2 ν 1 + ν 2 + 4 ν 1 + ν 2 + ξ s ( − 2 − ξ w ν 2 ( ν 1 + ν 2 ) ) 3 / 2 ) )
t = ( ν 1 + ν 2 ) 5 / 2 exp ( − j π ν 1 ( 3 ξ w ν 2 + ξ s ( ν 1 + ν 2 ) ) ( ν 1 + ν 2 ) 5 / 2 ) ( ν 1 + ν 2 ) 5 + π 2 ( 2 ξ s ξ w ( 2 ν 1 − ν 2 ) ν 2 ( ν 1 + ν 2 ) − ξ w 2 ν 1 ν 2 ( ν 2 − 2 ν 1 ) 2 )
t ( ω ) = exp ( j τ d δ ω ) 1 + ( δ ω / γ ) 2 = exp ( j τ d ( ω − ω o ) ) 1 + ( ( ω − ω o ) / γ ) 2
τ d = 4 n 3 π ( n s n + ( n w + n ) ( 3 n w + n s ) α 2 ) ε 1 ω o n s + n ( α 2 ( n w + n ) + n ) 3 / 2
γ = ε 1 ω o n s + n ( α 2 ( n w + n ) + n ) 5 / 2 4 α π n 5 / 2 n w ( n + n w )   ( 2 n − ( n + n w ) α 2 )   ( 2 n ( n s − n w ) + ( n + n w )   ( 2 n s + n w ) α 2 )
α = η − n n w + n
τ d = 4 n 2 π ( − n s + ( n s + 3 n w ) η 2 ) ε 1 ω o − n ( n s + n )   ( η 2 − 1 )   ( η 2 − 1 ) 2
γ = ε 1 ω o n s + n ( η 2 − 1 ) 5 / 2 4 π n 3 / 2 − n w η 2 ( η 2 + 2 )   ( 2 n s ( η 2 − 1 ) ) + n w ( η 2 + 2 )
L 1 = 8 π c n ω o ε 1 − ( 1 + n s / n ) ( η 2 − 1 )
v g = L 1 τ d = 2 c ( η 2 − 1 ) 2 − n s + ( n s + 3 n w ) η 2
Φ inc ( t ) = exp ( − ( c t ) 2 2 ( W 0 n ) 2 )       Cos ( ω o t )
Φ ^ inc ( ω ) = ∫ − ∞ ∞ Φ inc ( t ) exp ( j ω t ) d ω = A π ( exp ( − A ( ω − ω o ) 2 ) + exp ( − A ( ω + ω o ) 2 ) )
Φ tr ( t ) = 1 2 π ∫ − ∞ ∞ ϕ ^ inc ( ω ) t ( ω ) exp ( − j ω t ) d ω
Φ tr ( t ) = 1 2 π ∫ − ∞ ∞ ϕ ^ inc ( ω ) exp ( j   τ d ( ω − ω o ) ) 1 + ( ( ω − ω o ) / γ ) 2 exp ( − j   ω   t ) d ω
t ( ω ) = exp ( j   τ d ( ω − ω o ) ) 1 + ( ( ω − ω o ) / γ ) 2 ≈ exp ( j   τ d ( ω − ω o ) ) ( 1 − 1 2 ( ( ω − ω o ) / γ ) 2 )
Φ tr ( t ) = exp ( − c 2 ( τ d − t ) 2 2 ( W 0 n ) 2   Cos ( ω o t )   ( c 4 ( τ d − t ) 2 − c 2 n 2 W 0 2 + 2 γ 2 n 4 W 0 4 ) ) 2 γ 2 n 4 W 0 4
D rms = ∫ − ∞ ∞ ( Φ tr e ( t ) − Φ inc e ( t − τ d ) ) 2 d t ∫ − ∞ ∞ Φ inc e ( t ) 2 d t
D rms = 3 c 2 4 γ 2 n 2 W 0 2

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