Abstract

We investigate the group velocity of light in a one-dimensional volume-index grating inside a photorefractive LiNbO3 crystal. The slowdown of the group electromagnetic propagation is observed experimentally by tuning of the wave number of the optical beam close to the outside edge of the forbidden bandgap. We obtain a large group index of up to 7.5 in a 3.5-cm crystal sample. The group index is compared with the result of a theoretical derivation. The results are presented and discussed.

© 2000 Optical Society of America

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References

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  1. See, e.g., C. Kittel, Quantum Theory of Solids (Wiley, New York, 1968).
  2. See, e.g., P. St. J. Russell, J. Mod. Opt. 38, 1599 (1991).
    [CrossRef]
  3. See, e.g., P. Yeh, Optics of Layered Media (Wiley, New York, 1993).
  4. J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
    [CrossRef]
  5. M. Scalora, R. J. Flynn, S. B. Reinhardt, and R. L. Fork, Phys. Rev. E 54, 1078 (1996).
    [CrossRef]
  6. B. J. Eggleton, R. E. Slusher, C. M. de Sterice, P. A. Krug, and K. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
    [CrossRef] [PubMed]
  7. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, J. Opt. Soc. Am. B 16, 587 (1998).
    [CrossRef]
  8. C. P. Kuo, U. Osterberg, C. T. Seaton, G. I. Stegeman, and K. O. Hill, Opt. Lett. 13, 1032 (1988).
    [CrossRef] [PubMed]
  9. F. Oquellette, Appl. Opt. 29, 4826 (1990).
    [CrossRef]

1998 (1)

1996 (2)

M. Scalora, R. J. Flynn, S. B. Reinhardt, and R. L. Fork, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterice, P. A. Krug, and K. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

1994 (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

1991 (1)

See, e.g., P. St. J. Russell, J. Mod. Opt. 38, 1599 (1991).
[CrossRef]

1990 (1)

1988 (1)

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

de Sterice, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterice, P. A. Krug, and K. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

de Sterke, C. M.

Dowling, J. P.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, J. Opt. Soc. Am. B 16, 587 (1998).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterice, P. A. Krug, and K. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Flynn, R. J.

M. Scalora, R. J. Flynn, S. B. Reinhardt, and R. L. Fork, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Fork, R. L.

M. Scalora, R. J. Flynn, S. B. Reinhardt, and R. L. Fork, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Hill, K. O.

Kittel, C.

See, e.g., C. Kittel, Quantum Theory of Solids (Wiley, New York, 1968).

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterice, P. A. Krug, and K. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Kuo, C. P.

Oquellette, F.

Osterberg, U.

Reinhardt, S. B.

M. Scalora, R. J. Flynn, S. B. Reinhardt, and R. L. Fork, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Russell, P. St. J.

See, e.g., P. St. J. Russell, J. Mod. Opt. 38, 1599 (1991).
[CrossRef]

Scalora, M.

M. Scalora, R. J. Flynn, S. B. Reinhardt, and R. L. Fork, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

Seaton, C. T.

Sipe, K. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterice, P. A. Krug, and K. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Slusher, R. E.

B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, J. Opt. Soc. Am. B 16, 587 (1998).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterice, P. A. Krug, and K. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Stegeman, G. I.

Yeh, P.

See, e.g., P. Yeh, Optics of Layered Media (Wiley, New York, 1993).

Appl. Opt. (1)

J. Appl. Phys. (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, J. Appl. Phys. 75, 1896 (1994).
[CrossRef]

J. Mod. Opt. (1)

See, e.g., P. St. J. Russell, J. Mod. Opt. 38, 1599 (1991).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. E (1)

M. Scalora, R. J. Flynn, S. B. Reinhardt, and R. L. Fork, Phys. Rev. E 54, 1078 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

B. J. Eggleton, R. E. Slusher, C. M. de Sterice, P. A. Krug, and K. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Other (2)

See, e.g., P. Yeh, Optics of Layered Media (Wiley, New York, 1993).

See, e.g., C. Kittel, Quantum Theory of Solids (Wiley, New York, 1968).

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Figures (4)

Fig. 1
Fig. 1

Calculated transmission (dotted curve) and effective group velocity (solid curve) of a periodic medium.

Fig. 2
Fig. 2

Schematic of the experimental setup: BS’s, beam splitters; AO, acousto-optic Bragg cell; M1–M6, mirrors; Osc., oscilloscope; D1, D2, detectors.

Fig. 3
Fig. 3

Measured intensity of the transmitted probe beam for three cases: (a) without the grating and (b), (c) angle detuning corresponding to the first transmission maximum outside the bandgap (b) before and (c) after saturation of grating recording. In (a)–(c), the top signal is the reference beam detected by D1, and the bottom signal is the probe beam detected by D2.

Fig. 4
Fig. 4

Measured reflectivity (circles) and group-delay time (squares) as functions of angle detuning. The solid curve was obtained by fitting of the experimental data with the theoretical analysis. The fitting parameters are shown in the legend (α, absorption coefficient; n, refractive index; L, interaction length).

Equations (7)

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ϕ=πΛL+tan-1Δk2s tanh sL,
Δk=2nωc-2πΛ,
s=κ2-Δk/221/2,
κ=πn1/λ,
Vg=vgΔk/22-κ2 cosh2 sLΔk/22-κ2 sinh sLsL cosh sL,
Vg=vgκLtanh κL,
Vg=vgπ2κ2L2+π2,

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