Abstract

Photorefractive two-beam coupling with reduced spatiotemporal coherence is investigated both theoretically and experimentally. Limited spatiotemporal coherence results in spatially limited grating regions. Theoretical predictions of the beam-coupling behavior in two symmetries are supported by experimental results.

© 1991 Optical Society of America

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References

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  1. B. Fischer, S. Sternklar, S. Weiss, IEEE J. Quantum Electron. 25, 550 (1989).
    [Crossref]
  2. M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
    [Crossref]
  3. M. Cronin-Golomb, Opt. Lett. 14, 1297 (1989).
    [Crossref] [PubMed]
  4. B. Fisher, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [Crossref]
  5. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).
  6. N. V. Kukhtarev, B. V Markov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [Crossref]

1989 (2)

B. Fischer, S. Sternklar, S. Weiss, IEEE J. Quantum Electron. 25, 550 (1989).
[Crossref]

M. Cronin-Golomb, Opt. Lett. 14, 1297 (1989).
[Crossref] [PubMed]

1985 (1)

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[Crossref]

1981 (1)

1979 (1)

N. V. Kukhtarev, B. V Markov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

Cronin-Golomb, M.

Fischer, B.

B. Fischer, S. Sternklar, S. Weiss, IEEE J. Quantum Electron. 25, 550 (1989).
[Crossref]

Fisher, B.

Kukhtarev, N. V.

N. V. Kukhtarev, B. V Markov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

Markov, B. V

N. V. Kukhtarev, B. V Markov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

Soskin, M. S.

N. V. Kukhtarev, B. V Markov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

Sternklar, S.

B. Fischer, S. Sternklar, S. Weiss, IEEE J. Quantum Electron. 25, 550 (1989).
[Crossref]

Vinetskii, V. L.

N. V. Kukhtarev, B. V Markov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

Weiss, S.

B. Fischer, S. Sternklar, S. Weiss, IEEE J. Quantum Electron. 25, 550 (1989).
[Crossref]

White, J. O.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

Yariv, A.

Ferroelectrics (1)

N. V. Kukhtarev, B. V Markov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[Crossref]

IEEE J. Quantum Electron. (1)

B. Fischer, S. Sternklar, S. Weiss, IEEE J. Quantum Electron. 25, 550 (1989).
[Crossref]

J. Appl. Phys. (1)

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[Crossref]

Opt. Lett. (2)

Other (1)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the two-beam coupling with reduced spatiotemporal coherence: (a) configuration 1, (b) configuration 2. S, extended incoherent light source with circular symmetry; L, lens; M’s, mirrors; BS, beam splitter.

Fig. 2
Fig. 2

Actual grating regions in the crystal for a given coherence width d, crystal length L, beam diameter W, and beam intersection angle θ. (a) For configuration 1, the interference fringes exist only within approximately −Leff1/2 < z < Leff1/2. (b) For configuration 2, the grating region is enclosed by |z| = Leff2/2 and |x| = L/2.

Fig. 3
Fig. 3

Theoretical plot and experimental data for the intensity profile of the depleted output beam with configuration 2 and θ = 4°, d/W = 0.7.

Fig. 4
Fig. 4

Theoretical plot and experimental data for the output beam intensities I1 and I2 as a function of the normalized beam coherent width d/W for configuration 1.

Equations (10)

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k 1 k 1 A 1 ( r ) = γ 3 D I 0 ( r ) [ A 1 ( r ) A 2 * ( r ) μ 12 ( r ) ] A 2 ( r ) ,
k 2 k 2 A 2 * ( r ) = γ 3 D I 0 ( r ) [ A 1 ( r ) A 2 * ( r ) μ 12 ( r ) ] A 1 * ( r ) ,
μ 12 ( r 1 , r 2 ) = μ 12 ( | r 1 r 2 | ) = μ 12 ( r ) = 2 J 1 ( 3 . 83 r / d ) ( 3 . 83 r / d ) ,
μ 12 ( z ) = 2 J 1 [ 3 . 83 z / ( L eff 1 / 2 ) ] 3 . 83 z / ( L eff 1 / 2 ) configuration 1 ,
μ 12 ( x ) = 2 J 1 [ 3 . 83 x / ( L eff 2 / 2 ) ] 3 . 83 x / ( L eff 2 / 2 ) configuration 2 ,
ξ = z sin θ + x cos θ , η = z sin θ x cos θ ,
A 1 ( ξ , η ) ξ = g I 0 ( ξ , η ) A 1 ( ξ , η ) A 2 * ( ξ , η ) μ 12 ( ξ , η ) A 2 ( ξ , η ) ,
A 2 * ( ξ , η ) η = g I 0 ( ξ , η ) A 1 ( ξ , η ) A 2 * ( ξ , η ) μ 12 ( ξ , η ) A 1 * ( ξ , η ) ,
μ 12 [ x ( ξ , η ) ] cos [ π L eff 2 x ( ξ , η ) ] = cos ( ξ η b ) , L eff 2 / 2 < x < L eff 2 / 2 , μ 12 [ x ( ξ , η ) ] = 0 , | x | > L eff 2 / 2 ,
A 2 * ( ξ ) = A 0 ( ξ ) exp { g b [ 1 sin ( 2 ξ L sin θ b ) ] } for ξ B ξ ξ A if ξ A > ξ D , for ξ B ξ ξ D if ξ A > ξ D , A 2 * ( ξ ) = A 0 ( ξ ) exp [ g b cos ( 2 ξ b ) sin ( L sin θ b ) ] for ξ A ξ ξ D if ξ A > ξ D , A 2 * ( ξ ) = A 0 ( ξ ) exp ( 2 g b ) for ξ D ξ ξ A if ξ A < ξ D , A 2 * ( ξ ) = A 0 ( ξ ) exp { g b [ 1 + sin ( 2 ξ L sin θ b ) ] } for ξ D ξ ξ C if ξ A > ξ D , for ξ A ξ ξ C if ξ A > ξ D , A 2 * ( ξ ) = A 0 ( ξ ) for ξ > | ξ B | ,

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