Abstract

We propose and demonstrate a new scheme of beam fanning reduction in photorefractive amplifiers by using incoherent erasure. This simple and effective approach employs a pump beam with a mixed polarization state or introduces a third incoherent beam for selective erasure. The approach is analyzed, and the experimental results are presented and discussed.

© 1994 Optical Society of America

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References

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  1. See, for example, P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
    [Crossref]
  2. See, for example, M. Cronin-Golomb, A. Yariv, “Optical limiters using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
    [Crossref]
  3. H. Rajenbach, A. Delboulbe, J. P. Huignard, “Noise suppression in photorefractive image amplifiers,” Opt. Lett. 14, 1275–1277(1989).
    [Crossref]
  4. J. Joseph, P. K. C. Pillari, K. Singh, “A novel way of noise reduction in image amplification by two-beam coupling in photorefractive BaTiO3 crystal,” Opt. Commun. 80, 84–88 (1990).
    [Crossref]
  5. J. Khoury, C. L. Woods, M. Cronin-Golomb, “Noise reduction using adaptive spatial filtering in photorefractive two-beam coupling,” Opt. Lett. 16, 747–749 (1991).
    [Crossref] [PubMed]
  6. W. S. Rabinovich, B. J. Feldman, G. C. Gilbreath, “Suppression of photorefractive beam fanning using achromatic gratings,” Opt. Lett. 16, 1147–1149 (1991).
    [Crossref] [PubMed]
  7. P. Brody, “Grating structure in self-pumping barium titanate by local erasure,” Appl. Phys. Lett. 53, 262–264 (1988).
    [Crossref]
  8. G. J. Dunning, D. M. Pepper, M. B. Klein, “Control of self-pumped phase-conjugate reflectivity using incoherent erasure,” Opt. Lett. 15, 100–102 (1990).
    [Crossref]
  9. S. W. James, R. W. Eason, “Extraordinary-polarized light does not always yield the highest reflectivity in self-pumped BaTiO3,” Opt. Lett. 16, 633–635 (1991).
    [Crossref] [PubMed]
  10. V. V. Voronov, I. R. Dorosh, Yu. S. Kuz'minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
    [Crossref]
  11. J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. Am. 72, 46–51 (1982).
    [Crossref]
  12. M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
    [Crossref]
  13. M. D. Ewbank, F. R. Vachss, R. A. Vazquez, “Beam fanning in coupled-wave theory of two-beam coupling,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 43–45.
  14. R. A. Vazquez, F. R. Vachss, R. R. Neurgaonkar, M. D. Ewbank, “Large photorefractive coupling coefficient in a thin cerium doped strontium barium niobate crystal,” J. Opt. Soc. Am. B 8, 1932–1940 (1991).
    [Crossref]

1991 (4)

1990 (3)

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

G. J. Dunning, D. M. Pepper, M. B. Klein, “Control of self-pumped phase-conjugate reflectivity using incoherent erasure,” Opt. Lett. 15, 100–102 (1990).
[Crossref]

J. Joseph, P. K. C. Pillari, K. Singh, “A novel way of noise reduction in image amplification by two-beam coupling in photorefractive BaTiO3 crystal,” Opt. Commun. 80, 84–88 (1990).
[Crossref]

1989 (2)

H. Rajenbach, A. Delboulbe, J. P. Huignard, “Noise suppression in photorefractive image amplifiers,” Opt. Lett. 14, 1275–1277(1989).
[Crossref]

See, for example, P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[Crossref]

1988 (1)

P. Brody, “Grating structure in self-pumping barium titanate by local erasure,” Appl. Phys. Lett. 53, 262–264 (1988).
[Crossref]

1985 (1)

See, for example, M. Cronin-Golomb, A. Yariv, “Optical limiters using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
[Crossref]

1982 (1)

1980 (1)

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz'minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Brody, P.

P. Brody, “Grating structure in self-pumping barium titanate by local erasure,” Appl. Phys. Lett. 53, 262–264 (1988).
[Crossref]

Cronin-Golomb, M.

J. Khoury, C. L. Woods, M. Cronin-Golomb, “Noise reduction using adaptive spatial filtering in photorefractive two-beam coupling,” Opt. Lett. 16, 747–749 (1991).
[Crossref] [PubMed]

See, for example, M. Cronin-Golomb, A. Yariv, “Optical limiters using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
[Crossref]

Delboulbe, A.

Dorosh, I. R.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz'minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Dunning, G. J.

G. J. Dunning, D. M. Pepper, M. B. Klein, “Control of self-pumped phase-conjugate reflectivity using incoherent erasure,” Opt. Lett. 15, 100–102 (1990).
[Crossref]

Eason, R. W.

Ewbank, M. D.

R. A. Vazquez, F. R. Vachss, R. R. Neurgaonkar, M. D. Ewbank, “Large photorefractive coupling coefficient in a thin cerium doped strontium barium niobate crystal,” J. Opt. Soc. Am. B 8, 1932–1940 (1991).
[Crossref]

M. D. Ewbank, F. R. Vachss, R. A. Vazquez, “Beam fanning in coupled-wave theory of two-beam coupling,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 43–45.

Feinberg, J.

Feldman, B. J.

Fischer, B.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

Gilbreath, G. C.

Huignard, J. P.

James, S. W.

Joseph, J.

J. Joseph, P. K. C. Pillari, K. Singh, “A novel way of noise reduction in image amplification by two-beam coupling in photorefractive BaTiO3 crystal,” Opt. Commun. 80, 84–88 (1990).
[Crossref]

Khoury, J.

Klein, M. B.

G. J. Dunning, D. M. Pepper, M. B. Klein, “Control of self-pumped phase-conjugate reflectivity using incoherent erasure,” Opt. Lett. 15, 100–102 (1990).
[Crossref]

Kuz'minov, Yu. S.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz'minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Neurgaonkar, R. R.

Ophir, Y.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

Pepper, D. M.

G. J. Dunning, D. M. Pepper, M. B. Klein, “Control of self-pumped phase-conjugate reflectivity using incoherent erasure,” Opt. Lett. 15, 100–102 (1990).
[Crossref]

Pillari, P. K. C.

J. Joseph, P. K. C. Pillari, K. Singh, “A novel way of noise reduction in image amplification by two-beam coupling in photorefractive BaTiO3 crystal,” Opt. Commun. 80, 84–88 (1990).
[Crossref]

Rabinovich, W. S.

Rajenbach, H.

Segev, M.

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

Singh, K.

J. Joseph, P. K. C. Pillari, K. Singh, “A novel way of noise reduction in image amplification by two-beam coupling in photorefractive BaTiO3 crystal,” Opt. Commun. 80, 84–88 (1990).
[Crossref]

Tkachenko, N. V.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz'minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Vachss, F. R.

R. A. Vazquez, F. R. Vachss, R. R. Neurgaonkar, M. D. Ewbank, “Large photorefractive coupling coefficient in a thin cerium doped strontium barium niobate crystal,” J. Opt. Soc. Am. B 8, 1932–1940 (1991).
[Crossref]

M. D. Ewbank, F. R. Vachss, R. A. Vazquez, “Beam fanning in coupled-wave theory of two-beam coupling,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 43–45.

Vazquez, R. A.

R. A. Vazquez, F. R. Vachss, R. R. Neurgaonkar, M. D. Ewbank, “Large photorefractive coupling coefficient in a thin cerium doped strontium barium niobate crystal,” J. Opt. Soc. Am. B 8, 1932–1940 (1991).
[Crossref]

M. D. Ewbank, F. R. Vachss, R. A. Vazquez, “Beam fanning in coupled-wave theory of two-beam coupling,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 43–45.

Voronov, V. V.

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz'minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Woods, C. L.

Yariv, A.

See, for example, M. Cronin-Golomb, A. Yariv, “Optical limiters using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
[Crossref]

Yeh, P.

See, for example, P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[Crossref]

Appl. Phys. Lett. (1)

P. Brody, “Grating structure in self-pumping barium titanate by local erasure,” Appl. Phys. Lett. 53, 262–264 (1988).
[Crossref]

IEEE J. Quantum Electron. (1)

See, for example, P. Yeh, “Two-wave mixing in nonlinear media,” IEEE J. Quantum Electron. 25, 484–519 (1989).
[Crossref]

J. Appl. Phys. (1)

See, for example, M. Cronin-Golomb, A. Yariv, “Optical limiters using photorefractive nonlinearities,” J. Appl. Phys. 57, 4906–4910 (1985).
[Crossref]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

J. Joseph, P. K. C. Pillari, K. Singh, “A novel way of noise reduction in image amplification by two-beam coupling in photorefractive BaTiO3 crystal,” Opt. Commun. 80, 84–88 (1990).
[Crossref]

M. Segev, Y. Ophir, B. Fischer, “Nonlinear multi-two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

Opt. Lett. (5)

Sov. J. Quantum Electron. (1)

V. V. Voronov, I. R. Dorosh, Yu. S. Kuz'minov, N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium niobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Other (1)

M. D. Ewbank, F. R. Vachss, R. A. Vazquez, “Beam fanning in coupled-wave theory of two-beam coupling,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), pp. 43–45.

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Figures (8)

Fig. 1
Fig. 1

Normalized transmitted intensity through a 5-mm photorefractive crystal with different fanning f and effective coupling Γ f constants.

Fig. 2
Fig. 2

Normalized transmitted intensity as a function of incoherent erasure parameter p. Circles represent experimental data, and the dashed curve is from the theoretical model with best-fitted f and Γ f , taking Fresnel reflections into account.

Fig. 3
Fig. 3

Two-wave mixing gain as a function of the coupling coefficient Γ with various fanning parameters f.

Fig. 4
Fig. 4

Calculated two-wave mixing gain as a function of the erasure parameter p, where Γ = 60 cm−1, Γ f 1 = Γ f 2 = 18.24 cm−1, f 1= f 2 = 0.376 cm−1, α = 0.2 cm−1,z = 0.5 cm, and r = 440.

Fig. 5
Fig. 5

Calculated spatial distributions of the modulation depth for various gratings, where T = 60 cm−1, Γ f 1 = Γ f 2 = 18.24 cm−1, f 1 = f 2 = 0.376 cm−1, α = 2 cm−1, z = 0.5 cm, and r = 500.

Fig. 6
Fig. 6

Calculated two-wave mixing gain as a function of the selective erasure beam positions for various sizes at peak intensity Ie = 25I 0. In the uniform erasure case the intensity Ie is 0.9I 0. All other parameters are the same as in Fig. 5.

Fig. 7
Fig. 7

Experimentally measured two-wave mixing gain as a function of erasure p.

Fig. 8
Fig. 8

Experimentally measured temporal dependence of the gain with incoherent erasure.

Equations (4)

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d I 1 d z = Γ I 1 I 2 I 0 f 1 I 1 Γ f 1 I 1 I f I 0 α I 1 , d I 2 d z = Γ I 1 I 2 I 0 f 2 I 2 Γ f 2 I 2 I f I 0 α I 2 , d I f d z = f 1 I 1 + f 2 I 2 + Γ f 1 I 1 I f I 0 + Γ f 2 I 2 I f I 0 α I f ,
d I 1 ( z ) d z = f I 1 ( z ) Γ f 1 I 1 ( z ) I f ( z ) I ( 0 ) , d I f ( z ) d z = f I 1 ( z ) + Γ f 1 I 1 ( z ) I f ( z ) I ( 0 ) .
I 1 ( z ) I ( 0 ) = f + Γ f 1 Γ f 1 + f { exp [ ( f + Γ f 1 ) z ] } , I f ( z ) I ( 0 ) = f { exp [ ( f + Γ f 1 ) z ] 1 } Γ f 1 + f { exp [ ( f + Γ f 1 ) z ] } .
I 1 ( L ) I 1 ( 0 ) = ( r + 1 ) ( f + Γ ) 2 ( f + f r + Γ + Γ r { exp [ ( f + Γ ) z ] } ) ( Γ + f { exp [ ( f + Γ ) z ] } ) , I 2 ( L ) I 2 ( 0 ) = ( r + 1 ) ( f + Γ ) Γ r + ( f + f r + Γ ) exp [ ( f + Γ ) z ] , I f ( L ) I 1 ( 0 ) = f ( r + 1 ) { exp [ ( f + Γ ) z ] 1 } ( Γ + f { exp [ ( f + Γ ) z ] } ) ,

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