Abstract

We describe volume holograms written in photorefractive crystals in which the writing beams experience two-beam coupling. We obtain analytic expressions for the diffraction efficiency of a weak reading beam that has a different polarization from the writing beams. Good agreement is obtained between experimental and theoretical results.

© 1991 Optical Society of America

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References

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  1. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  2. P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
    [Crossref]
  3. R. Saxena, F. Vachss, I. McMichael, P. Yeh, J. Opt. Soc. Am. B 7, 1210 (1990).
    [Crossref]
  4. N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [Crossref]
  5. J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 885 (1984).
    [Crossref]
  6. J. H. Hong, P. Yeh, D. Psaltis, D. Brady, Opt. Lett. 15, 344 (1990).
    [Crossref] [PubMed]
  7. J. Feinberg, R. W. Hellwarth, Opt. Lett. 5, 519 (1980).
    [Crossref] [PubMed]
  8. J. Feinberg, Opt. Lett. 7, 486 (1982).
    [Crossref] [PubMed]
  9. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 52, 1297 (1980).
    [Crossref]
  10. R. M. Pierce, R. S. Cudney, G. D. Bacher, J. Feinberg, Opt. Lett. 15, 414 (1990).
    [Crossref] [PubMed]

1990 (3)

1989 (1)

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
[Crossref]

1984 (1)

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 885 (1984).
[Crossref]

1982 (1)

1980 (2)

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 52, 1297 (1980).
[Crossref]

J. Feinberg, R. W. Hellwarth, Opt. Lett. 5, 519 (1980).
[Crossref] [PubMed]

1979 (1)

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Bacher, G. D.

Brady, D.

Cudney, R. S.

Feinberg, J.

Heaton, J. M.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 885 (1984).
[Crossref]

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 52, 1297 (1980).
[Crossref]

Hellwarth, R. W.

J. Feinberg, R. W. Hellwarth, Opt. Lett. 5, 519 (1980).
[Crossref] [PubMed]

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 52, 1297 (1980).
[Crossref]

Hong, J. H.

Khuktarev, N. V.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Markov, V. B.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

McMichael, I.

Mills, P. A.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 885 (1984).
[Crossref]

Odulov, S. G.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

Paige, E. G. S.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 885 (1984).
[Crossref]

Pierce, R. M.

Psaltis, D.

Saxena, R.

Solymar, L.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 885 (1984).
[Crossref]

Soskin, M. S.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 52, 1297 (1980).
[Crossref]

Vachss, F.

Vinetskii, V. L.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

Wilson, T.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 885 (1984).
[Crossref]

Yeh, P.

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Ferroelectrics (1)

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

IEEE J. Quantum Electron. (1)

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
[Crossref]

J. Appl. Phys. (1)

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 52, 1297 (1980).
[Crossref]

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

Opt. Acta (1)

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, T. Wilson, Opt. Acta 31, 885 (1984).
[Crossref]

Opt. Lett. (4)

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Figures (4)

Fig. 1
Fig. 1

Nonuniform amplitude of the photorefractive grating for different values of the beam ratio β during writing. The two-beam coupling constant Γ is equal to 20 cm−1.

Fig. 2
Fig. 2

Diffraction efficiency η as a function of the beam ratio β during writing. The grating thickness d is equal to 0.5 cm, and absorption effects are neglected (α = 0). E-write/E-read curve, Γ = 2κ = 20 cm−1; O-write/E-read curve, Γ = 1 cm−1, 2κ = 20 cm−1; Kogelnik curve, Γ = 0, 2κ = 20 cm−1. (E denotes extraordinary polarization, O denotes ordinary polarization.)

Fig. 3
Fig. 3

Experimental setup for the reading hologram written by coupled beams.

Fig. 4
Fig. 4

Experimental data for the diffraction efficiency η as a function of the beam ratio β during writing. The solid curves are obtained by fitting each data set to the theoretical expression given in Eq. (8). (a) E-write/E-read case, (b) O-write/E-read case.

Equations (8)

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n 1 ( x ) = Δ n cos ( K g x ) ,
η = sin 2 ( π Δ n d λ R cos θ R ) ,
Δ n ( z ) = Δ n s 2 [ I 1 W ( z ) I 2 W ( z ) ] 1 / 2 I 1 W ( z ) + I 2 W ( z ) = 2 Δ n s [ ( 1 + β e Γ z ) ( 1 + e - Γ z β ) ] 1 / 2 ,
d A 1 R d z = - α R 2 cos θ R A 1 R - i π λ R cos θ R × Δ n s ( β e Γ z / 2 + e - Γ z / 2 β ) A 2 R , d A 2 R d z = - α R 2 cos θ R A 2 R - i π λ R cos θ R × Δ n s ( β e Γ z / 2 + e - Γ z / 2 β ) A 1 R ,
B i R ( z ) = A i R ( z ) exp ( α R z 2 cos θ R ) , i = 1 , 2 ,
z = 2 Γ tan - 1 [ exp ( Γ z β 2 ) ] ,
d B 1 R d z = - i κ B 2 R , d B 2 R d z = - i κ B 1 R ,
η = | A 2 R ( d ) A 0 | 2 = exp ( - α R d cos θ R ) × sin 2 { 2 κ Γ [ tan - 1 ( e Γ d / 2 β ) - tan - 1 ( β ) ] } .

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