Abstract

We report measurements of the photorefractive phase shift and coupling constant of several photorefractive materials. We solve the problem of beam coupling and diffraction in a material with a dynamically written grating for arbitrary input beams. These solutions are used to determine the beam coupling as a function of the photorefractive phase ϕ and coupling constant g when one beam is either sinusoidally phase modulated or ramped in phase. Experimental results are obtained for LiNbO3, BaTiO3, and for paraelectric potassium lithium tantalate niobate as a function of applied electric field.

© 1993 Optical Society of America

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  1. R. S. Cudney, G. D. Bacher, R. M. Pierce, J. Feinberg, Opt. Lett. 17, 67 (1992).
    [Crossref] [PubMed]
  2. P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
    [Crossref]
  3. M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
    [Crossref]
  4. W. B. Lawler, C. J. Sherman, M. G. Moharam, J. Opt. Soc. Am. B 8, 2190 (1991).
    [Crossref]
  5. D. Vahey, J. Appl. Phys. 46, 3510 (1975).
    [Crossref]
  6. J. O. White, S. Z. Kwong, M. Cronin-Golomb, B. Fischer, A. Yariv, in Photorefractive Materials and Their Applications II, P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.
  7. R. Hofmeister, A. Yariv, Appl. Phys. Lett. 61, 2395 (1992).
    [Crossref]
  8. R. Hofmeister, A. Yariv, S. Yagi, A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
    [Crossref] [PubMed]
  9. A. Agranat, R. Hofmeister, A. Yariv, Opt. Lett. 17, 713 (1992).
    [Crossref] [PubMed]

1992 (4)

R. S. Cudney, G. D. Bacher, R. M. Pierce, J. Feinberg, Opt. Lett. 17, 67 (1992).
[Crossref] [PubMed]

R. Hofmeister, A. Yariv, Appl. Phys. Lett. 61, 2395 (1992).
[Crossref]

R. Hofmeister, A. Yariv, S. Yagi, A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

A. Agranat, R. Hofmeister, A. Yariv, Opt. Lett. 17, 713 (1992).
[Crossref] [PubMed]

1991 (1)

1990 (1)

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[Crossref]

1989 (1)

P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[Crossref]

1975 (1)

D. Vahey, J. Appl. Phys. 46, 3510 (1975).
[Crossref]

Agranat, A.

R. Hofmeister, A. Yariv, S. Yagi, A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

A. Agranat, R. Hofmeister, A. Yariv, Opt. Lett. 17, 713 (1992).
[Crossref] [PubMed]

Amrhein, P.

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[Crossref]

Bacher, G. D.

Cescato, L.

P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[Crossref]

Cronin-Golomb, M.

J. O. White, S. Z. Kwong, M. Cronin-Golomb, B. Fischer, A. Yariv, in Photorefractive Materials and Their Applications II, P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Cudney, R. S.

Feinberg, J.

Fischer, B.

J. O. White, S. Z. Kwong, M. Cronin-Golomb, B. Fischer, A. Yariv, in Photorefractive Materials and Their Applications II, P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Frejlich, J.

P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[Crossref]

Garcia, P. M.

P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[Crossref]

Günter, P.

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[Crossref]

Hofmeister, R.

A. Agranat, R. Hofmeister, A. Yariv, Opt. Lett. 17, 713 (1992).
[Crossref] [PubMed]

R. Hofmeister, A. Yariv, Appl. Phys. Lett. 61, 2395 (1992).
[Crossref]

R. Hofmeister, A. Yariv, S. Yagi, A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

Kwong, S. Z.

J. O. White, S. Z. Kwong, M. Cronin-Golomb, B. Fischer, A. Yariv, in Photorefractive Materials and Their Applications II, P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Lawler, W. B.

Moharam, M. G.

Pierce, R. M.

Sherman, C. J.

Vahey, D.

D. Vahey, J. Appl. Phys. 46, 3510 (1975).
[Crossref]

White, J. O.

J. O. White, S. Z. Kwong, M. Cronin-Golomb, B. Fischer, A. Yariv, in Photorefractive Materials and Their Applications II, P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Yagi, S.

R. Hofmeister, A. Yariv, S. Yagi, A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

Yariv, A.

R. Hofmeister, A. Yariv, S. Yagi, A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

R. Hofmeister, A. Yariv, Appl. Phys. Lett. 61, 2395 (1992).
[Crossref]

A. Agranat, R. Hofmeister, A. Yariv, Opt. Lett. 17, 713 (1992).
[Crossref] [PubMed]

J. O. White, S. Z. Kwong, M. Cronin-Golomb, B. Fischer, A. Yariv, in Photorefractive Materials and Their Applications II, P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

Zha, M. Z.

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[Crossref]

Appl. Phys. Lett. (1)

R. Hofmeister, A. Yariv, Appl. Phys. Lett. 61, 2395 (1992).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Z. Zha, P. Amrhein, P. Günter, IEEE J. Quantum Electron. 26, 788 (1990).
[Crossref]

J. Appl. Phys. (2)

P. M. Garcia, L. Cescato, J. Frejlich, J. Appl. Phys. 66, 47 (1989).
[Crossref]

D. Vahey, J. Appl. Phys. 46, 3510 (1975).
[Crossref]

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

Opt. Lett. (2)

Phys. Rev. Lett. (1)

R. Hofmeister, A. Yariv, S. Yagi, A. Agranat, Phys. Rev. Lett. 69, 1459 (1992).
[Crossref] [PubMed]

Other (1)

J. O. White, S. Z. Kwong, M. Cronin-Golomb, B. Fischer, A. Yariv, in Photorefractive Materials and Their Applications II, P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1989), Chap. 4.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for determining the photorefractive coupling constant and phase of dynamic gratings. The piezoelectric mirror PM modulates the phase of one beam either sinusoidally or as a ramp.

Fig. 2
Fig. 2

Intensity I1(L) of Fig. 1 at ω and 2ω relative to the dc power (=0 dB) when one of two interfering beams is phase modulated at ω as a function of the photorefractive phase ϕ. The results are plotted for coupling constants gL = 3, 5, 10.

Fig. 3
Fig. 3

(a) Photorefractive phase ϕ of gratings written in KLTN versus applied electric field. Solid curve describes the theoretical interaction between a ZEFPR grating and an electro-optic grating. (b) Coupling constant g of KLTN versus applied field. Again, the data are in accord with the theory.

Tables (1)

Tables Icon

Table 1 Values of the Coupling Constant g and the Photorefractive Phase ϕ for the Crystal Samples Testeda

Equations (18)

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T ( z ) cos β = i g I 1 I 2 exp [ + i ( ϕ + θ ) ] [ I 1 exp ( - Γ z / 2 ) + I 2 exp ( + Γ z / 2 ) ] + i cot ϕ - 1 V ( z ) - α 2 T ( z ) ,
V ( z ) cos β = i g I 1 I 2 exp [ - i ( ϕ + θ ) ] [ I 1 exp ( - Γ z / 2 ) + I 2 exp ( + Γ z / 2 ) ] - i cot ϕ - 1 T ( z ) - α 2 V ( z ) ,
T ( z ) exp ( α L / 2 ) = C 1 [ I 2 + I 1 exp ( - Γ z ) + i η - 1 / 2 + C 2 [ I 2 exp ( + Γ z ) + I 1 ] + i η - 1 / 2 ,
V ( z ) exp ( α L / 2 ) = C 3 [ I 2 + I 1 exp ( - Γ z ) - i η - 1 / 2 + C 4 [ I 2 exp ( + Γ z ) + I 1 ] - i η - 1 / 2 ,
C 1 = I 1 / ( I 1 + I 2 ) I 2 [ 1 - exp ( i θ ) ] ,
C 2 = I 1 / ( I 1 + I 2 ) [ I 1 + I 2 exp ( i θ ) ] ,
C 3 = I 2 / ( I 1 + I 2 ) [ I 2 + exp ( i θ ) I 1 ] ,
C 4 = I 2 / ( I 1 + I 2 ) I 1 [ 1 - exp ( i θ ) ] .
P 1 ( z ) / I 1 = 1 - tanh ( Γ z / 2 ) cos θ - sin ( g cos ϕ z ) cosh ( Γ z / 2 ) sin θ ,
P 1 ( z ) / I 1 = 1 + tanh ( Γ z / 2 ) cos θ + sin ( g cos ϕ z ) cosh ( Γ z / 2 ) sin θ .
C 1 = I 1 / ( I 1 + I 2 ) I 2 ,
C 2 = I 1 / ( I 1 + I 2 ) I 1 ,
C 3 = I 2 / ( I 1 + I 2 ) I 1 ,
C 3 = - C 4 .
P 1 ( z ) = I 1 2 [ 1 + cos ( g cos ϕ z ) / cosh ( g sin ϕ z ) ] ,
P 2 ( z ) = I 1 2 [ 1 - cos ( g cos ϕ z ) / cosh ( g sin ϕ z ) ] .
| P dc P 2 ω | = 4 θ 0 2 [ coth ( g sin θ z ) ± 1 ] ,
| P ω P 2 ω | = 4 θ 0 sin ( g cos θ z ) sinh ( g sin ϕ z ) ,

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