Abstract

We present detailed calculations of the temporal and spatial evolution of beam fanning in photorefractive crystals that is initiated by scattering from noise. We show that fanning starts from beam coupling between the incident radiation and part of the incident radiation scattered by noise at or near the input plane. We show that scattering within the volume of the crystal has negligible effect on fanning, that absorption affects the time response but not the spatial pattern of the fanning, and that the difference between calculations including only phase-matched terms and those including non-phase-matched terms is negligible.

© 1993 Optical Society of America

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  1. V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, Kvantovaya Elektron. (Moscow) 7, 2313 (1980) [Sov. J. Quantum Electron. 10, 1346 (1980)].
  2. V. V. Obukhovskii, A. V. Stoyanov, Kvantovaya Elektron. (Moscow) 12, 563 (1985) [Sov. J. Quantum Electron. 15, 367 (1985)].
  3. R. A. Rupp, F. W. Drees, Appl. Phys. B 39, 223 (1986).
    [CrossRef]
  4. G. Zhang, Q. X. Li, P. P. Ho, S. Liu, Z. K. Wu, R. R. Alfano, Appl. Opt. 25, 2955 (1986).
    [CrossRef] [PubMed]
  5. M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
    [CrossRef]
  6. G. C. Valley, J. Opt. Soc. Am. B 4, 14 (1987); erratum, G. C. Valley, J. Opt. Soc. Am. B, 4, 934 (1987).
    [CrossRef]
  7. T. R. Moore, D. L. Walters, J. Opt. Soc. Am. B 5, 1806 (1988).
    [CrossRef]
  8. G. C. Valley, W. P. Brown, “Kinky beam paths inside photorefractive crystals,” J. Opt. Soc. Am. B (to be published).
  9. S. R. King, T. S. Hartwick, A. B. Chase, Appl. Phys. Lett. 21, 312 (1972).
    [CrossRef]
  10. J. Feinberg, J. Opt. Soc. Am. 72, 46 (1982).
    [CrossRef]
  11. P. P. Banerjee, J. J. Liu, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 100.
  12. G. C. Valley, J. Opt. Soc. Am. B 9, 1442 (1992).
    [CrossRef]
  13. M. Segev, A. Yariv, Opt. Lett. 16, 1938 (1991).
    [CrossRef] [PubMed]
  14. N. V. Kukhtarev, Kvantovaya Elektron. (Moscow) 8, 1452 (1981) [Sov. J. Quantum Electron. 11, 878 (1981)].
  15. B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
    [CrossRef]
  16. P. Günter, E. Voit, M. Z. Zha, J. Albers, Opt. Commun. 55, 210 (1985).
    [CrossRef]

1993 (1)

1992 (1)

G. C. Valley, J. Opt. Soc. Am. B 9, 1442 (1992).
[CrossRef]

1991 (1)

1990 (1)

M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
[CrossRef]

1988 (1)

1987 (1)

1986 (2)

1985 (2)

P. Günter, E. Voit, M. Z. Zha, J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

V. V. Obukhovskii, A. V. Stoyanov, Kvantovaya Elektron. (Moscow) 12, 563 (1985) [Sov. J. Quantum Electron. 15, 367 (1985)].

1982 (1)

1981 (1)

N. V. Kukhtarev, Kvantovaya Elektron. (Moscow) 8, 1452 (1981) [Sov. J. Quantum Electron. 11, 878 (1981)].

1980 (1)

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, Kvantovaya Elektron. (Moscow) 7, 2313 (1980) [Sov. J. Quantum Electron. 10, 1346 (1980)].

1972 (1)

S. R. King, T. S. Hartwick, A. B. Chase, Appl. Phys. Lett. 21, 312 (1972).
[CrossRef]

Albers, J.

P. Günter, E. Voit, M. Z. Zha, J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

Alfano, R. R.

Banerjee, P. P.

P. P. Banerjee, J. J. Liu, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 100.

Brown, W. P.

G. C. Valley, W. P. Brown, “Kinky beam paths inside photorefractive crystals,” J. Opt. Soc. Am. B (to be published).

Chase, A. B.

S. R. King, T. S. Hartwick, A. B. Chase, Appl. Phys. Lett. 21, 312 (1972).
[CrossRef]

Crosignani, B.

DiPorto, P.

Dorosh, I. R.

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, Kvantovaya Elektron. (Moscow) 7, 2313 (1980) [Sov. J. Quantum Electron. 10, 1346 (1980)].

Drees, F. W.

R. A. Rupp, F. W. Drees, Appl. Phys. B 39, 223 (1986).
[CrossRef]

Engin, D.

Feinberg, J.

Fischer, B.

M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
[CrossRef]

Günter, P.

P. Günter, E. Voit, M. Z. Zha, J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

Hartwick, T. S.

S. R. King, T. S. Hartwick, A. B. Chase, Appl. Phys. Lett. 21, 312 (1972).
[CrossRef]

Ho, P. P.

King, S. R.

S. R. King, T. S. Hartwick, A. B. Chase, Appl. Phys. Lett. 21, 312 (1972).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, Kvantovaya Elektron. (Moscow) 8, 1452 (1981) [Sov. J. Quantum Electron. 11, 878 (1981)].

Kuz’minov, Y. S.

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, Kvantovaya Elektron. (Moscow) 7, 2313 (1980) [Sov. J. Quantum Electron. 10, 1346 (1980)].

Li, Q. X.

Liu, J. J.

P. P. Banerjee, J. J. Liu, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 100.

Liu, S.

Moore, T. R.

Obukhovskii, V. V.

V. V. Obukhovskii, A. V. Stoyanov, Kvantovaya Elektron. (Moscow) 12, 563 (1985) [Sov. J. Quantum Electron. 15, 367 (1985)].

Ophir, Y.

M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
[CrossRef]

Rupp, R. A.

R. A. Rupp, F. W. Drees, Appl. Phys. B 39, 223 (1986).
[CrossRef]

Salamo, G.

Segev, M.

Stoyanov, A. V.

V. V. Obukhovskii, A. V. Stoyanov, Kvantovaya Elektron. (Moscow) 12, 563 (1985) [Sov. J. Quantum Electron. 15, 367 (1985)].

Tkachenko, N. V.

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, Kvantovaya Elektron. (Moscow) 7, 2313 (1980) [Sov. J. Quantum Electron. 10, 1346 (1980)].

Valley, G. C.

G. C. Valley, J. Opt. Soc. Am. B 9, 1442 (1992).
[CrossRef]

G. C. Valley, J. Opt. Soc. Am. B 4, 14 (1987); erratum, G. C. Valley, J. Opt. Soc. Am. B, 4, 934 (1987).
[CrossRef]

G. C. Valley, W. P. Brown, “Kinky beam paths inside photorefractive crystals,” J. Opt. Soc. Am. B (to be published).

Voit, E.

P. Günter, E. Voit, M. Z. Zha, J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

Voronov, V. V.

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, Kvantovaya Elektron. (Moscow) 7, 2313 (1980) [Sov. J. Quantum Electron. 10, 1346 (1980)].

Walters, D. L.

Wu, Z. K.

Yariv, A.

Zha, M. Z.

P. Günter, E. Voit, M. Z. Zha, J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

Zhang, G.

Appl. Opt. (1)

Appl. Phys. B (1)

R. A. Rupp, F. W. Drees, Appl. Phys. B 39, 223 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

S. R. King, T. S. Hartwick, A. B. Chase, Appl. Phys. Lett. 21, 312 (1972).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (4)

Kvantovaya Elektron. (3)

N. V. Kukhtarev, Kvantovaya Elektron. (Moscow) 8, 1452 (1981) [Sov. J. Quantum Electron. 11, 878 (1981)].

V. V. Voronov, I. R. Dorosh, Y. S. Kuz’minov, N. V. Tkachenko, Kvantovaya Elektron. (Moscow) 7, 2313 (1980) [Sov. J. Quantum Electron. 10, 1346 (1980)].

V. V. Obukhovskii, A. V. Stoyanov, Kvantovaya Elektron. (Moscow) 12, 563 (1985) [Sov. J. Quantum Electron. 15, 367 (1985)].

Opt. Commun. (2)

M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
[CrossRef]

P. Günter, E. Voit, M. Z. Zha, J. Albers, Opt. Commun. 55, 210 (1985).
[CrossRef]

Opt. Lett. (1)

Other (2)

P. P. Banerjee, J. J. Liu, in Nonlinear Optics: Materials, Fundamentals, and Applications, Vol. 18 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 100.

G. C. Valley, W. P. Brown, “Kinky beam paths inside photorefractive crystals,” J. Opt. Soc. Am. B (to be published).

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Figures (3)

Fig. 1
Fig. 1

Temporal evolution of fanning at the output of a photorefractive crystal characterized by parameters that are typical of BaTiO3, with no absorption and an inhomogeneous input surface. We plot amplitude versus angle (degrees) with normalized time (as defined in the text). The spike corresponds to the far field of the incident plane wave.

Fig. 2
Fig. 2

Steady-state fanning at the output of a photorefractive crystal characterized by parameters that are typical of BaTiO3 with zero absorption and seeded by varying noise conditions. The dashed curve is the baseline case with the crystal seeded by surface scattering, the curve next to it is with the crystal seeded by an inhomogeneous input surface and by scattering distributed throughout the volume, and the solid curve is with the crystal seeded by twice as much surface scattering.

Fig. 3
Fig. 3

Comparison of the plane-wave amplitudes after propagation of 50 μm (upper curves), 100 μm (middle curves), and 200 μm (lower curves) with (dashed curves) and without (solid curves) non-phase-matched terms in the wave equation.

Equations (8)

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E ( x , z , t ) = 1 2 [ exp ( i k z - i ω t ) A ( x , z , t ) + c . c . ] ,
A ( x , z , t ) = m a m ( z , t ) exp [ - i k m ( x + m z / 2 ) ] ,
A z - i 2 k 2 A x 2 + α A 2 = i k n b δ n ( x , z , t ) A ,
δ n t + ( 1 + A 2 ) δ n = i m , n γ m n a m a n * × exp [ - i k ( m - n ) x - i k 2 ( m 2 - n 2 ) z / 2 ] ,
δ n ( x , z , t ) = m , n n m , n ( z , t ) × exp [ i k ( m - n ) x - i k 2 ( m 2 - n 2 ) z / 2 ] .
a p z + α a p 2 = i k n b m , n n m n a p + n - m exp ( - i k 2 Δ z / 2 ) ,
n m n t + I 0 n m n = γ m n a m a n * ,
a p z + α a p 2 = i k n b n n p n a n .

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