Abstract

We present the theory for photorefractive two-beam coupling without optical activity in cubic crystals rotated around the [110] axis. We also describe two-beam coupling experiments in InP:Fe that fit the theory closely. The 15.5% gain enhancement for grating wave vectors aligned along the 〈111〉 directions is demonstrated explicitly.

© 1990 Optical Society of America

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References

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  1. M. B. Klein, Opt. Lett. 9, 350 (1984).
    [CrossRef] [PubMed]
  2. G. Albanese, J. Kumar, W. H. Steier, Opt. Lett. 11, 650 (1986).
    [CrossRef] [PubMed]
  3. L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
    [CrossRef]
  4. K. Walsh, T. J. Hall, R. E. Burge, Opt. Lett. 12, 1026 (1987).
    [CrossRef] [PubMed]
  5. L. J. Cheng, P. Yeh, Opt. Lett. 13, 50 (1988).
    [CrossRef] [PubMed]
  6. B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, J. P. Huignard, Opt. Lett. 13, 327 (1988).
    [CrossRef] [PubMed]
  7. J. C. Fabre, J. M. C. Jonathan, G. Roosen, J. Opt. Soc. Am. B 5, 1730 (1988).
    [CrossRef]
  8. R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
    [CrossRef]
  9. B. Mainguet, Opt. Lett. 13, 657 (1988).
    [CrossRef] [PubMed]
  10. G. C. Valley, S. W. McCahon, M. B. Klein, J. Appl. Phys. 64, 6684 (1988).
    [CrossRef]
  11. P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
    [CrossRef]
  12. S. I. Stepanov, M. P. Petrov, in Photorefractive Materials and Their Applications I, Fundamental Phenomena, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 9, pp. 284–285.
  13. G. Khitrova, D. Rouède, N. V. Kukhtarev, H. M. Gibbs, Phys. Rev. Lett. 62, 1110 (1989);N. V. Kukhtarev, D. Rouède, G. Khitrova, H. M. Gibbs, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), postdeadline paper PB-2.
    [CrossRef] [PubMed]
  14. N. V. Kukhtarev, in Photorefractive Materials and Their Applications I, Fundamental Phenomena, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 4, pp. 99–129.
    [CrossRef]
  15. G. C. Valley, J. Appl. Phys. 59, 3363 (1986);F. P. Strohkendl, J. M. C. Jonathan, R. W. Hellwarth, Opt. Lett. 11, 312 (1986).
    [CrossRef] [PubMed]
  16. R. B. Bylsma, D. H. Olson, A. M. Glass, Opt. Lett. 13, 853 (1988).
    [CrossRef] [PubMed]
  17. G. D. Pettit, J. J. Turner, J. Appl. Phys. 36, 2081 (1965).
    [CrossRef]
  18. N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
    [CrossRef]
  19. We determined the effective trap density NE by measuring Γ versus the grating spacing Λ.
  20. A. M. Glass, M. B. Klein, G. C. Valley, Electron. Lett. 21, 220 (1985).
    [CrossRef]
  21. T. Takanohashi, K. Nakajima, J. Appl. Phys. 65, 3933 (1989).
    [CrossRef]

1989 (3)

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

G. Khitrova, D. Rouède, N. V. Kukhtarev, H. M. Gibbs, Phys. Rev. Lett. 62, 1110 (1989);N. V. Kukhtarev, D. Rouède, G. Khitrova, H. M. Gibbs, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), postdeadline paper PB-2.
[CrossRef] [PubMed]

T. Takanohashi, K. Nakajima, J. Appl. Phys. 65, 3933 (1989).
[CrossRef]

1988 (7)

1987 (1)

1986 (3)

G. Albanese, J. Kumar, W. H. Steier, Opt. Lett. 11, 650 (1986).
[CrossRef] [PubMed]

L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[CrossRef]

G. C. Valley, J. Appl. Phys. 59, 3363 (1986);F. P. Strohkendl, J. M. C. Jonathan, R. W. Hellwarth, Opt. Lett. 11, 312 (1986).
[CrossRef] [PubMed]

1985 (1)

A. M. Glass, M. B. Klein, G. C. Valley, Electron. Lett. 21, 220 (1985).
[CrossRef]

1984 (2)

N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
[CrossRef]

M. B. Klein, Opt. Lett. 9, 350 (1984).
[CrossRef] [PubMed]

1965 (1)

G. D. Pettit, J. J. Turner, J. Appl. Phys. 36, 2081 (1965).
[CrossRef]

Albanese, G.

Burge, R. E.

Bylsma, R. B.

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

R. B. Bylsma, D. H. Olson, A. M. Glass, Opt. Lett. 13, 853 (1988).
[CrossRef] [PubMed]

Cheng, L. J.

L. J. Cheng, P. Yeh, Opt. Lett. 13, 50 (1988).
[CrossRef] [PubMed]

L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[CrossRef]

Fabre, J. C.

Gibbs, H. M.

G. Khitrova, D. Rouède, N. V. Kukhtarev, H. M. Gibbs, Phys. Rev. Lett. 62, 1110 (1989);N. V. Kukhtarev, D. Rouède, G. Khitrova, H. M. Gibbs, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), postdeadline paper PB-2.
[CrossRef] [PubMed]

Glass, A. M.

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

R. B. Bylsma, D. H. Olson, A. M. Glass, Opt. Lett. 13, 853 (1988).
[CrossRef] [PubMed]

A. M. Glass, M. B. Klein, G. C. Valley, Electron. Lett. 21, 220 (1985).
[CrossRef]

Gravey, P.

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

Hall, T. J.

Herriau, J. P.

Huignard, J. P.

Imbert, B.

Jonathan, J. M. C.

Khitrova, G.

G. Khitrova, D. Rouède, N. V. Kukhtarev, H. M. Gibbs, Phys. Rev. Lett. 62, 1110 (1989);N. V. Kukhtarev, D. Rouède, G. Khitrova, H. M. Gibbs, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), postdeadline paper PB-2.
[CrossRef] [PubMed]

Klein, M. B.

G. C. Valley, S. W. McCahon, M. B. Klein, J. Appl. Phys. 64, 6684 (1988).
[CrossRef]

A. M. Glass, M. B. Klein, G. C. Valley, Electron. Lett. 21, 220 (1985).
[CrossRef]

M. B. Klein, Opt. Lett. 9, 350 (1984).
[CrossRef] [PubMed]

Kukhtarev, N. V.

G. Khitrova, D. Rouède, N. V. Kukhtarev, H. M. Gibbs, Phys. Rev. Lett. 62, 1110 (1989);N. V. Kukhtarev, D. Rouède, G. Khitrova, H. M. Gibbs, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), postdeadline paper PB-2.
[CrossRef] [PubMed]

N. V. Kukhtarev, in Photorefractive Materials and Their Applications I, Fundamental Phenomena, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 4, pp. 99–129.
[CrossRef]

Kumar, J.

Labandibar, J. Y.

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

Mainguet, B.

Mallick, S.

McCahon, S. W.

G. C. Valley, S. W. McCahon, M. B. Klein, J. Appl. Phys. 64, 6684 (1988).
[CrossRef]

Nakajima, K.

T. Takanohashi, K. Nakajima, J. Appl. Phys. 65, 3933 (1989).
[CrossRef]

Olson, D. H.

R. B. Bylsma, D. H. Olson, A. M. Glass, Opt. Lett. 13, 853 (1988).
[CrossRef] [PubMed]

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

Partovi, A.

L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[CrossRef]

Petrov, M. P.

S. I. Stepanov, M. P. Petrov, in Photorefractive Materials and Their Applications I, Fundamental Phenomena, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 9, pp. 284–285.

Pettit, G. D.

G. D. Pettit, J. J. Turner, J. Appl. Phys. 36, 2081 (1965).
[CrossRef]

Picoli, G.

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

Rajbenbach, H.

Roosen, G.

Rouède, D.

G. Khitrova, D. Rouède, N. V. Kukhtarev, H. M. Gibbs, Phys. Rev. Lett. 62, 1110 (1989);N. V. Kukhtarev, D. Rouède, G. Khitrova, H. M. Gibbs, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), postdeadline paper PB-2.
[CrossRef] [PubMed]

Steier, W. H.

Stepanov, S. I.

S. I. Stepanov, M. P. Petrov, in Photorefractive Materials and Their Applications I, Fundamental Phenomena, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 9, pp. 284–285.

Suzuki, N.

N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
[CrossRef]

Tada, K.

N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
[CrossRef]

Takanohashi, T.

T. Takanohashi, K. Nakajima, J. Appl. Phys. 65, 3933 (1989).
[CrossRef]

Turner, J. J.

G. D. Pettit, J. J. Turner, J. Appl. Phys. 36, 2081 (1965).
[CrossRef]

Valley, G. C.

G. C. Valley, S. W. McCahon, M. B. Klein, J. Appl. Phys. 64, 6684 (1988).
[CrossRef]

G. C. Valley, J. Appl. Phys. 59, 3363 (1986);F. P. Strohkendl, J. M. C. Jonathan, R. W. Hellwarth, Opt. Lett. 11, 312 (1986).
[CrossRef] [PubMed]

A. M. Glass, M. B. Klein, G. C. Valley, Electron. Lett. 21, 220 (1985).
[CrossRef]

Walsh, K.

Yeh, P.

Appl. Phys. Lett. (1)

L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[CrossRef]

Electron. Lett. (2)

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

A. M. Glass, M. B. Klein, G. C. Valley, Electron. Lett. 21, 220 (1985).
[CrossRef]

J. Appl. Phys. (4)

T. Takanohashi, K. Nakajima, J. Appl. Phys. 65, 3933 (1989).
[CrossRef]

G. C. Valley, S. W. McCahon, M. B. Klein, J. Appl. Phys. 64, 6684 (1988).
[CrossRef]

G. C. Valley, J. Appl. Phys. 59, 3363 (1986);F. P. Strohkendl, J. M. C. Jonathan, R. W. Hellwarth, Opt. Lett. 11, 312 (1986).
[CrossRef] [PubMed]

G. D. Pettit, J. J. Turner, J. Appl. Phys. 36, 2081 (1965).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
[CrossRef]

Opt. Commun. (1)

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. Lett. (1)

G. Khitrova, D. Rouède, N. V. Kukhtarev, H. M. Gibbs, Phys. Rev. Lett. 62, 1110 (1989);N. V. Kukhtarev, D. Rouède, G. Khitrova, H. M. Gibbs, in Digest of Optical Society of America Annual Meeting (Optical Society of America, Washington, D.C., 1988), postdeadline paper PB-2.
[CrossRef] [PubMed]

Other (3)

N. V. Kukhtarev, in Photorefractive Materials and Their Applications I, Fundamental Phenomena, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 4, pp. 99–129.
[CrossRef]

S. I. Stepanov, M. P. Petrov, in Photorefractive Materials and Their Applications I, Fundamental Phenomena, P. Günter, J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 9, pp. 284–285.

We determined the effective trap density NE by measuring Γ versus the grating spacing Λ.

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Figures (3)

Fig. 1
Fig. 1

Two-beam coupling geometry. The crystal is aligned along the (x′, y, z′) coordinate system. The grating wave vector q is aligned along the x axis of the (x, y, z) coordinate system. ϕ is the angle of rotation between the two coordinate systems about their common y axis (the [110] crystal axis); a and b represent the optical electric fields of the signal beam and the reference beam, respectively.

Fig. 2
Fig. 2

Experimental arrangement. The InP:Fe crystal is mounted in a rotational state such that it can be rotated around its [110] axis.

Fig. 3
Fig. 3

Gain coefficient Γ as a function of the rotation angle ϕ for both beams s polarized and for both beams p polarized. The dots are data, and the solid curves are the fit to the theory. Vertical error bars would be approximately the same size as the dots.

Equations (11)

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d d y [ a x a z ] = i π n 3 r 41 λ cos θ in [ E z E x E x 0 ] [ b x b z ] ,
E x , z = i ξ E D x , z a b * ( 1 + E D / E q ) ( I a + I b )
d d y [ a x a z ] = i π n 3 r 41 λ cos θ in E x × [ 3 c ϕ 2 s ϕ c ϕ ( 3 c ϕ 2 2 ) c ϕ ( 3 c ϕ 2 2 ) s ϕ ( 3 s ϕ 2 2 ) ] [ b x b z ] .
( Δ I a ) x , z = | a x , z + y 0 d a x , z d y | 2 | a x , z | 2 = 2 π n 3 ξ r 41 y 0 λ cos θ in E D ( 1 + E D / E q ) I a I b ( I a + I b ) × F x , z ( α , β , ϕ ) ,
F x ( α , β , ϕ ) c α β c α c ϕ [ ( 3 c ϕ 2 2 ) s β + 3 c ϕ s ϕ c β ] ,
F z ( α , β , ϕ ) c α β s α [ c ϕ ( 3 c ϕ 2 2 ) c β + s ϕ ( 3 s ϕ 2 2 ) s β ] .
F x ( 90 ° , 90 ° , ϕ ) = 0 , F z ( 90 ° , 90 ° , ϕ ) = ¼ [ sin ϕ 3 sin ( 3 ϕ ) ] .
F x ( 0 , 0 , ϕ ) = ¾ [ sin ϕ + sin ( 3 ϕ ) ] , F z ( 0 , 0 , ϕ ) = 0.
Γ x , z = 2 π n 3 r 41 λ E D ( 1 + E D / E q ) ξ F x , z ( α , β , ϕ ) .
s polarization Γ = ( 0.109 cm 1 ) F z ( 90 ° , 90 ° , ϕ ) + ( 0.006 cm 1 ) ,
p polarization Γ = ( 0.109 cm 1 ) F x ( 0 , 0 , ϕ ) + ( 0.006 cm 1 ) .

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