Abstract

A numerical model is presented for the analysis of vectorial two-beam coupling in photorefractive materials. A powerful software tool has been developed for design purposes. For Fe,Ce-doped lithium niobate crystals, conversion efficiency and signal gain dependences on experimental parameters and beam polarization have been found. The good accuracy of the model has been demonstrated by comparisons with experimentally measured parameters.

© 2002 Optical Society of America

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References

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  1. B. Fischer, M. Cronin-Golomb, J. O. White, and A. Yariv, “Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials,” Opt. Letters 11, 239–241 (1986).
    [Crossref]
  2. J. Feinberg and K. R. MacDonald, “Phase-conjugate mirrors and resonators with photorefractive materials,” in Photorefractive Materials and their applications II, 151–203 (Springer-Verlag, Berlin, 1988).
  3. C. Yang, Y. Zhao, R. Wang, and M. Li, “Studies of photorefractive crystals of double-doped Ce,Fe:LiNbO3,” Opt. Commun. 175, 247–252 (2000).
    [Crossref]
  4. J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Wave propagation in photorefractive media,” in Photorefractive Materials and their applications II, 101–150 (Springer-Verlag, Berlin, 1988).
  5. P. Gunter and J. P. Huignard, “Photorefractive effects and materials,” in Photorefractive Materials and their applications I, 7–74 (Springer-Verlag, Berlin, 1988).
    [Crossref]

2000 (1)

C. Yang, Y. Zhao, R. Wang, and M. Li, “Studies of photorefractive crystals of double-doped Ce,Fe:LiNbO3,” Opt. Commun. 175, 247–252 (2000).
[Crossref]

1986 (1)

B. Fischer, M. Cronin-Golomb, J. O. White, and A. Yariv, “Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials,” Opt. Letters 11, 239–241 (1986).
[Crossref]

Cronin-Golomb, M.

B. Fischer, M. Cronin-Golomb, J. O. White, and A. Yariv, “Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials,” Opt. Letters 11, 239–241 (1986).
[Crossref]

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Wave propagation in photorefractive media,” in Photorefractive Materials and their applications II, 101–150 (Springer-Verlag, Berlin, 1988).

Feinberg, J.

J. Feinberg and K. R. MacDonald, “Phase-conjugate mirrors and resonators with photorefractive materials,” in Photorefractive Materials and their applications II, 151–203 (Springer-Verlag, Berlin, 1988).

Fischer, B.

B. Fischer, M. Cronin-Golomb, J. O. White, and A. Yariv, “Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials,” Opt. Letters 11, 239–241 (1986).
[Crossref]

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Wave propagation in photorefractive media,” in Photorefractive Materials and their applications II, 101–150 (Springer-Verlag, Berlin, 1988).

Gunter, P.

P. Gunter and J. P. Huignard, “Photorefractive effects and materials,” in Photorefractive Materials and their applications I, 7–74 (Springer-Verlag, Berlin, 1988).
[Crossref]

Huignard, J. P.

P. Gunter and J. P. Huignard, “Photorefractive effects and materials,” in Photorefractive Materials and their applications I, 7–74 (Springer-Verlag, Berlin, 1988).
[Crossref]

Kwong, S. K.

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Wave propagation in photorefractive media,” in Photorefractive Materials and their applications II, 101–150 (Springer-Verlag, Berlin, 1988).

Li, M.

C. Yang, Y. Zhao, R. Wang, and M. Li, “Studies of photorefractive crystals of double-doped Ce,Fe:LiNbO3,” Opt. Commun. 175, 247–252 (2000).
[Crossref]

MacDonald, K. R.

J. Feinberg and K. R. MacDonald, “Phase-conjugate mirrors and resonators with photorefractive materials,” in Photorefractive Materials and their applications II, 151–203 (Springer-Verlag, Berlin, 1988).

Wang, R.

C. Yang, Y. Zhao, R. Wang, and M. Li, “Studies of photorefractive crystals of double-doped Ce,Fe:LiNbO3,” Opt. Commun. 175, 247–252 (2000).
[Crossref]

White, J. O.

B. Fischer, M. Cronin-Golomb, J. O. White, and A. Yariv, “Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials,” Opt. Letters 11, 239–241 (1986).
[Crossref]

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Wave propagation in photorefractive media,” in Photorefractive Materials and their applications II, 101–150 (Springer-Verlag, Berlin, 1988).

Yang, C.

C. Yang, Y. Zhao, R. Wang, and M. Li, “Studies of photorefractive crystals of double-doped Ce,Fe:LiNbO3,” Opt. Commun. 175, 247–252 (2000).
[Crossref]

Yariv, A.

B. Fischer, M. Cronin-Golomb, J. O. White, and A. Yariv, “Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials,” Opt. Letters 11, 239–241 (1986).
[Crossref]

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Wave propagation in photorefractive media,” in Photorefractive Materials and their applications II, 101–150 (Springer-Verlag, Berlin, 1988).

Zhao, Y.

C. Yang, Y. Zhao, R. Wang, and M. Li, “Studies of photorefractive crystals of double-doped Ce,Fe:LiNbO3,” Opt. Commun. 175, 247–252 (2000).
[Crossref]

Opt. Commun. (1)

C. Yang, Y. Zhao, R. Wang, and M. Li, “Studies of photorefractive crystals of double-doped Ce,Fe:LiNbO3,” Opt. Commun. 175, 247–252 (2000).
[Crossref]

Opt. Letters (1)

B. Fischer, M. Cronin-Golomb, J. O. White, and A. Yariv, “Nonlinear vectorial two-beam coupling and forward four-wave mixing in photorefractive materials,” Opt. Letters 11, 239–241 (1986).
[Crossref]

Other (3)

J. Feinberg and K. R. MacDonald, “Phase-conjugate mirrors and resonators with photorefractive materials,” in Photorefractive Materials and their applications II, 151–203 (Springer-Verlag, Berlin, 1988).

J. O. White, S. K. Kwong, M. Cronin-Golomb, B. Fischer, and A. Yariv, “Wave propagation in photorefractive media,” in Photorefractive Materials and their applications II, 101–150 (Springer-Verlag, Berlin, 1988).

P. Gunter and J. P. Huignard, “Photorefractive effects and materials,” in Photorefractive Materials and their applications I, 7–74 (Springer-Verlag, Berlin, 1988).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1.

Vectorial two-beam coupling geometry.

Fig. 2.
Fig. 2.

Conversion efficiency dependence on crossing angle.

Fig. 3.
Fig. 3.

Conversion efficiency dependence on crossing angle.

Fig. 4.
Fig. 4.

Signal gain dependence on crossing angle.

Fig. 5.
Fig. 5.

Signal gain dependence on crossing angle.

Tables (1)

Tables Icon

Table 1. Comparisons among experimental [3] and numerical values of two-beam coupling gain coefficient Γ.

Equations (9)

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{ d A 1 dz = γ I g A 4 γ II g A 3 α A 1 d A 2 dz = γ I g A 3 γ II g A 4 α A 2 d A 3 * dz = γ I g A 2 * γ II g A 1 * α A 3 * d A 4 * dz = γ I g A 1 * γ II g A 2 * α A 4 *
A i = Re { A i } + j Im { A i } i = 1,2,3,4
g = Re { g } + j Im { g } =
= ( Re { A 1 } Re { A 4 } + Im { A 1 } Im { A 4 } + Re { A 2 } Re { A 3 } + Im { A 2 } Im { A 3 } ) +
+ j ( Re { A 4 } Im { A 1 } Re { A 1 } Im { A 4 } + Re { A 3 } Im { A 2 } Re { A 2 } Im { A 3 } )
γ p = 4 π λ k B T q r eff n cos [ ϑ 1 + ϑ 2 2 ] · K ¯ 1 + ( K ¯ k o ) 2 e 1 g e 2 * p = I , II
k 0 = 4 π N eff q 2 ε 0 ε rK k B T
r eff = 1 n 4 e 1 * · { ε 0 0 [ r 0 0 ( K ¯ K ¯ ) ] · ε 0 0 } · e 2
Λ = λ 2 n sin ( ϑ C 2 )

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