Abstract

We present measurements of the two-wave mixing gain as a function of frequency detuning in photorefractive crystals. In many cases, this function is asymmetric, indicating that the phase shift of the photorefractive index grating with respect to the light interference pattern is not exactly 90°, as is often assumed. In four-wave mixing, the phase of the phase-conjugate wave contains the phase of the pumping and probe waves and a phase shift determined by the interaction taking place in the nonlinear medium. This second term, the phase shift of the phase conjugator, is a function of the type of grating and the phase shift of this grating. The phase shift of the grating obtained from the two-wave mixing measurements compares well with that obtained from four-wave mixing measurements of the phase of the phase conjugator.

© 1987 Optical Society of America

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  1. D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
    [CrossRef]
  2. V. Vinetskii, N. Kukhtarev, S. Odolov, M. Soskin, Sov. Phys. Usp. 22, 742 (1979).
    [CrossRef]
  3. N. Kukhtarev, V. Markov, S. Odolov, M. Soskin, V. Vinetskii, Ferroelectrics 22, 961 (1979).
    [CrossRef]
  4. M. Gower, Opt. Lett. 11, 458 (1986).
    [CrossRef] [PubMed]
  5. A. Glass, D. von der Linde, T. Negran, Appl. Phys. Lett. 25, 233 (1974).
    [CrossRef]
  6. J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
    [CrossRef]
  7. I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 32 (1986).
  8. S. Kwong, A. Yariv, M. Cronin-Golomb, B. Fischer, J. Opt. Soc. Am. A 3, 157 (1986).
    [CrossRef]
  9. M. Klein, G. Valley, J. Appl. Phys. 57, 4901 (1985).
    [CrossRef]
  10. K. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
    [CrossRef] [PubMed]
  11. J. Feinberg, D. Heiman, A. Tanguay, R. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [CrossRef]

1986 (3)

1985 (2)

M. Klein, G. Valley, J. Appl. Phys. 57, 4901 (1985).
[CrossRef]

K. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

1981 (1)

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

1980 (1)

J. Feinberg, D. Heiman, A. Tanguay, R. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

1979 (2)

V. Vinetskii, N. Kukhtarev, S. Odolov, M. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

N. Kukhtarev, V. Markov, S. Odolov, M. Soskin, V. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

1974 (1)

A. Glass, D. von der Linde, T. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

1972 (1)

D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Amodei, J.

D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Cronin-Golomb, M.

Feinberg, J.

K. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

J. Feinberg, D. Heiman, A. Tanguay, R. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Fischer, B.

Glass, A.

A. Glass, D. von der Linde, T. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

Gower, M.

Heiman, D.

J. Feinberg, D. Heiman, A. Tanguay, R. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Hellwarth, R.

J. Feinberg, D. Heiman, A. Tanguay, R. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Huignard, J. P.

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Khoshnevisan, M.

I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 32 (1986).

Klein, M.

M. Klein, G. Valley, J. Appl. Phys. 57, 4901 (1985).
[CrossRef]

Kukhtarev, N.

V. Vinetskii, N. Kukhtarev, S. Odolov, M. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

N. Kukhtarev, V. Markov, S. Odolov, M. Soskin, V. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

Kwong, S.

MacDonald, K.

K. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

Markov, V.

N. Kukhtarev, V. Markov, S. Odolov, M. Soskin, V. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

Marrakchi, A.

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

McMichael, I.

I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 32 (1986).

Negran, T.

A. Glass, D. von der Linde, T. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

Odolov, S.

N. Kukhtarev, V. Markov, S. Odolov, M. Soskin, V. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

V. Vinetskii, N. Kukhtarev, S. Odolov, M. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

Soskin, M.

V. Vinetskii, N. Kukhtarev, S. Odolov, M. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

N. Kukhtarev, V. Markov, S. Odolov, M. Soskin, V. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

Staebler, D.

D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

Tanguay, A.

J. Feinberg, D. Heiman, A. Tanguay, R. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Valley, G.

M. Klein, G. Valley, J. Appl. Phys. 57, 4901 (1985).
[CrossRef]

Vinetskii, V.

N. Kukhtarev, V. Markov, S. Odolov, M. Soskin, V. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

V. Vinetskii, N. Kukhtarev, S. Odolov, M. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

von der Linde, D.

A. Glass, D. von der Linde, T. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

Yariv, A.

Yeh, P.

I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 32 (1986).

Appl. Phys. Lett. (1)

A. Glass, D. von der Linde, T. Negran, Appl. Phys. Lett. 25, 233 (1974).
[CrossRef]

Ferroelectrics (1)

N. Kukhtarev, V. Markov, S. Odolov, M. Soskin, V. Vinetskii, Ferroelectrics 22, 961 (1979).
[CrossRef]

J. Appl. Phys. (3)

D. Staebler, J. Amodei, J. Appl. Phys. 43, 1042 (1972).
[CrossRef]

M. Klein, G. Valley, J. Appl. Phys. 57, 4901 (1985).
[CrossRef]

J. Feinberg, D. Heiman, A. Tanguay, R. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

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

Opt. Commun. (1)

J. P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

K. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

I. McMichael, P. Yeh, M. Khoshnevisan, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 32 (1986).

Sov. Phys. Usp. (1)

V. Vinetskii, N. Kukhtarev, S. Odolov, M. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Measurements of the TWM gain Γ(δ)/Γ(0) as a function of frequency detuning δ for SBN and BaTiO3. For BaTiO3, Γ is asymmetric, indicating that the phase shift of the grating is not 90°.

Fig. 2
Fig. 2

Measured difference between the phase shift of the grating ϕg and 90° (Δϕ = ϕg − 90°) as a function of the TWM pump power for BaTiO3 #1. The lines are to aid the viewer; they are not theoretical fits.

Fig. 3
Fig. 3

Measured difference between the phase shift of the grating ϕg and 90° (Δϕ = ϕg − 90°) as a function of the angle θ between the perpendicular to the bisector to the two waves and the crystal axis for BaTiO3 #1. The dependence of Δϕ on θ indicates the existence of a field oriented along the crystal axis. The line is to aid the viewer; it is not a theoretical fit.

Fig. 4
Fig. 4

Interferometer used to measure the phase shift of the phase conjugator. The light transmitted by the beam splitter, BS, and the light reflected from the self-pumped crystal of BaTiO3 provide the pump waves for FWM in the crystal XTL. The light reflected by the beam splitter provides the probe wave. The conjugate wave and the reflection from the self-pumper interfere at the detector D with a relative phase shift ϕ0, the phase shift of the phase conjugator.

Tables (1)

Tables Icon

Table 1 Phase of Phase Conjugators

Equations (9)

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Γ sin  ( ϕ g + tan - 1 δ ) / 1 + δ 2 ,
ϕ g = tan - 1 [ ( E D / E 0 ) + ( E D 2 / E 0 E S ) + ( E 0 / E S ) ] ,
E n = A n exp [ i ( k n · r - ω t + ϕ n ) e n ] ,
I = A 1 2 + A 4 2 + A 1 A 4 ( e 1 · e 4 ) × ( exp { i [ ( k 1 - k 4 ) · r + ( ϕ 1 - ϕ 4 ) ] } + c . c . ) .
k = k 0 + Δ k ( exp { i [ ( k 1 - k 4 ) · r + ( ϕ 1 - ϕ 4 ) + ϕ g ] } + c . c . ) .
ϕ 3 = ϕ 1 + ϕ 2 - ϕ 4 + ϕ 0 ,
ϕ 0 = π / 2 + ϕ Δ k + ϕ g ,
I 1 + I 2 - 2 I 1 I 2 cos ϕ 0 ,
ϕ 0 tan - 1 ( R ϕ m / 4 ) ,

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