Abstract

An exact solution to the slowly varying envelope wave equations for two-wave mixing with both photorefractive and photochromic gratings present and with an arbitrary dependence of the gain and absorption on the fringe modulation is obtained.

© 1996 Optical Society of America

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References

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  1. R. B. Bylsma, D. H. Olson, A. M. Glass, Opt. Lett. 13, 853 (1988).
    [CrossRef] [PubMed]
  2. S. L. Clapham, R. W. Eason, N. A. Vainos, Opt. Commun. 74, 290 (1990).
    [CrossRef]
  3. C. H. Kwak, S. Y. Park, H. K. Lee, E.-H. Lee, Opt. Comun. 79, 349 (1990).
    [CrossRef]
  4. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  5. P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, J. Appl. Phys. 58, 45 (1985).
    [CrossRef]
  6. C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, E.-H. Lee, Opt. Commun. 105, 353 (1994).
    [CrossRef]
  7. M. Belić, D. Timotijević, M. Petrović, M. Jarić, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. (to be published).
  8. M. Belić, Opt. Quantum Electron. 16, 551 (1984).
    [CrossRef]

1994 (1)

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, E.-H. Lee, Opt. Commun. 105, 353 (1994).
[CrossRef]

1990 (2)

S. L. Clapham, R. W. Eason, N. A. Vainos, Opt. Commun. 74, 290 (1990).
[CrossRef]

C. H. Kwak, S. Y. Park, H. K. Lee, E.-H. Lee, Opt. Comun. 79, 349 (1990).
[CrossRef]

1988 (1)

1985 (1)

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

1984 (1)

M. Belić, Opt. Quantum Electron. 16, 551 (1984).
[CrossRef]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
[CrossRef]

Belic, M.

M. Belić, Opt. Quantum Electron. 16, 551 (1984).
[CrossRef]

M. Belić, D. Timotijević, M. Petrović, M. Jarić, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. (to be published).

Bylsma, R. B.

Clapham, S. L.

S. L. Clapham, R. W. Eason, N. A. Vainos, Opt. Commun. 74, 290 (1990).
[CrossRef]

Eason, R. W.

S. L. Clapham, R. W. Eason, N. A. Vainos, Opt. Commun. 74, 290 (1990).
[CrossRef]

Glass, A. M.

Huignard, J.-P.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Jaric, M.

M. Belić, D. Timotijević, M. Petrović, M. Jarić, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. (to be published).

Jeong, J. S.

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, E.-H. Lee, Opt. Commun. 105, 353 (1994).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
[CrossRef]

Kwak, C. H.

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, E.-H. Lee, Opt. Commun. 105, 353 (1994).
[CrossRef]

C. H. Kwak, S. Y. Park, H. K. Lee, E.-H. Lee, Opt. Comun. 79, 349 (1990).
[CrossRef]

Lee, E.-H.

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, E.-H. Lee, Opt. Commun. 105, 353 (1994).
[CrossRef]

C. H. Kwak, S. Y. Park, H. K. Lee, E.-H. Lee, Opt. Comun. 79, 349 (1990).
[CrossRef]

Lee, H. K.

C. H. Kwak, S. Y. Park, H. K. Lee, E.-H. Lee, Opt. Comun. 79, 349 (1990).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
[CrossRef]

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
[CrossRef]

Olson, D. H.

Park, S. Y.

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, E.-H. Lee, Opt. Commun. 105, 353 (1994).
[CrossRef]

C. H. Kwak, S. Y. Park, H. K. Lee, E.-H. Lee, Opt. Comun. 79, 349 (1990).
[CrossRef]

Petrovic, M.

M. Belić, D. Timotijević, M. Petrović, M. Jarić, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. (to be published).

Rajbenbach, H.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Refregier, P.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Solymar, L.

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
[CrossRef]

Suh, H. H.

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, E.-H. Lee, Opt. Commun. 105, 353 (1994).
[CrossRef]

Timotijevic, D.

M. Belić, D. Timotijević, M. Petrović, M. Jarić, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. (to be published).

Vainos, N. A.

S. L. Clapham, R. W. Eason, N. A. Vainos, Opt. Commun. 74, 290 (1990).
[CrossRef]

Vinetski, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
[CrossRef]

J. Appl. Phys. (1)

P. Refregier, L. Solymar, H. Rajbenbach, J.-P. Huignard, J. Appl. Phys. 58, 45 (1985).
[CrossRef]

Opt. Commun. (2)

C. H. Kwak, S. Y. Park, J. S. Jeong, H. H. Suh, E.-H. Lee, Opt. Commun. 105, 353 (1994).
[CrossRef]

S. L. Clapham, R. W. Eason, N. A. Vainos, Opt. Commun. 74, 290 (1990).
[CrossRef]

Opt. Comun. (1)

C. H. Kwak, S. Y. Park, H. K. Lee, E.-H. Lee, Opt. Comun. 79, 349 (1990).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

M. Belić, Opt. Quantum Electron. 16, 551 (1984).
[CrossRef]

Other (1)

M. Belić, D. Timotijević, M. Petrović, M. Jarić, “Exact solution to photorefractive two-wave mixing with arbitrary modulation depth,” Opt. Commun. (to be published).

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Figures (3)

Fig. 1
Fig. 1

Functions F (solid curve), f (dashed curve), and m (dashed–dotted curve) as functions of z in the TG.

Fig. 2
Fig. 2

Functions F (solid curves), f (dashed curves), and m (dashed–dotted curves) as functions of z in the RG. Two branches are shown for each function; however, only the lower branches should be taken into account.

Fig. 3
Fig. 3

Intensities I1 and I2 as functions of z, for both the TG and the RG, corresponding to the functions F and f presented in Figs. 1 and 2. The solid and dashed–dotted curves are I1 for TG and RG, and the dashed and the dotted curves are I2 for TG and RG.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

I 1 = α 0 I 1 Γ + α I I 1 I 2 , σ I 2 = α 0 I 2 + Γ α I I 1 I 2 .
Γ ( m ) = Γ s f x ( m ) m , α ( m ) = α s f x ( m ) m ,
f = 2 ( I 1 I 2 ) 1 / 2 , F = 1 2 ln ( I 1 I 2 ) .
2 F = α tanh ( F ) Γ , 2 f f = Γ tanh ( F ) β ,
z = F 0 F 2 d F α ( m ) tanh ( F ) Γ ( m )
z = 2 α s 2 Γ s 2 { Γ s ( F F 0 ) + α s ln [ cosh ( F F c ) cosh ( F 0 F c ) ] } ,
f = f 0 exp [ Γ s α s ( F F 0 ) + ( Γ s 2 α s 2 2 α s α 0 ) z ] .
I 1 = f 2 exp ( F ) , I 2 = f 2 exp ( F ) .
2 F = Γ tanh ( F ) β , 2 f f = α tanh ( F ) Γ .
z ( F , F 0 ) = F 0 F 2 d F Γ ( m ) tanh ( F ) β ( m ) ,
z = 2 Γ s 2 β s 2 [ β s ( F F 0 ) + Γ s ln | sinh ( F F c ) sinh ( F 0 F c ) | ] ,
f = f 0 exp [ α s Γ s ( F F 0 + α 0 z ) + ( α s 2 Γ s 2 2 Γ s ) z ] ,
β s ( F 0 F d ) + Γ s 2 β s 2 2 d = Γ s ln | sinh ( F d F c ) sinh ( F 0 F c ) | ,
F d = ( δ + 1 ) F 0 ( δ α 0 + δ 2 1 2 Γ s ) d + ln ( C 2 C 1 ) δ 1 ,
T 1 = I 1 d C 1 = C exp [ 1 + δ δ ( F d F 0 ) ] , T 2 = I 2 d C 2 = C exp [ 1 δ δ ( F d F 0 ) ] ,
T 1 = I 1 d C 1 = C exp [ ( 1 + δ ) ( F d F 0 ) ] , T 2 = I 20 C 2 = C 1 exp [ ( 1 δ ) ( F d F 0 ) ] ,

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