Abstract

Multigrating operation of degenerate four-wave mixing in photorefractive media is considered in the strong pump regime. Closed-form expressions for the reflectivity are obtained for the cases of absorption and no absorption. An arbitrary phase mismatch between the intensity interference fringes and the refractive-index gratings is allowed.

© 1988 Optical Society of America

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References

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  1. M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  2. R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983); Y. H. Ja, Opt. Commun. 41, 159 (1982).
    [CrossRef]
  3. P. Günter, Phys. Rep. 93, 199 (1982); P. Hariharan, Optical Holography (Cambridge U. Press, Cambridge, 1984).
    [CrossRef]
  4. M. R. Belić, Opt. Quantum Electron. 16, 551 (1984).
    [CrossRef]
  5. M. R. Belić, Opt. Lett. 12, 105 (1987).
    [CrossRef]
  6. M. Abramowitz, J. Stegun, Handbook of Mathematical Functions (Dover, New York, 1953); P. M. Morse, H. Feshbach, Mathematical Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
  7. D. J. Gauthier, P. Narum, R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
    [CrossRef] [PubMed]

1987 (2)

D. J. Gauthier, P. Narum, R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

M. R. Belić, Opt. Lett. 12, 105 (1987).
[CrossRef]

1984 (2)

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

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

1982 (1)

P. Günter, Phys. Rep. 93, 199 (1982); P. Hariharan, Optical Holography (Cambridge U. Press, Cambridge, 1984).
[CrossRef]

Abramowitz, M.

M. Abramowitz, J. Stegun, Handbook of Mathematical Functions (Dover, New York, 1953); P. M. Morse, H. Feshbach, Mathematical Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

Belic, M. R.

M. R. Belić, Opt. Lett. 12, 105 (1987).
[CrossRef]

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

Boyd, R. W.

D. J. Gauthier, P. Narum, R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Fisher, B.

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Gauthier, D. J.

D. J. Gauthier, P. Narum, R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

Günter, P.

P. Günter, Phys. Rep. 93, 199 (1982); P. Hariharan, Optical Holography (Cambridge U. Press, Cambridge, 1984).
[CrossRef]

Narum, P.

D. J. Gauthier, P. Narum, R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

Stegun, J.

M. Abramowitz, J. Stegun, Handbook of Mathematical Functions (Dover, New York, 1953); P. M. Morse, H. Feshbach, Mathematical Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

White, J. O.

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fisher, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

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

Phys. Rep. (1)

P. Günter, Phys. Rep. 93, 199 (1982); P. Hariharan, Optical Holography (Cambridge U. Press, Cambridge, 1984).
[CrossRef]

Phys. Rev. Lett. (1)

D. J. Gauthier, P. Narum, R. W. Boyd, Phys. Rev. Lett. 58, 1640 (1987).
[CrossRef] [PubMed]

Other (2)

M. Abramowitz, J. Stegun, Handbook of Mathematical Functions (Dover, New York, 1953); P. M. Morse, H. Feshbach, Mathematical Methods of Theoretical Physics (McGraw-Hill, New York, 1953).

R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1983); Y. H. Ja, Opt. Commun. 41, 159 (1982).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Intensity reflectivity |ρ0|2 as a function of the pump ratio I2d/I10 and for different absorptions (given in reciprocal centimeters). Transmission and reflection couplings are γT = γR = 10 cm−1, and the pump coupling varies from −5 cm−1 (solid lines) to +5 cm−1 (dashed lines). The thickness of the crystal is set to d = 0.3 cm.

Equations (21)

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I A 1 = γ A 1 A 2 * A 2 α 2 I A 1 ,
I A 2 * = γ A 1 A 2 * A 1 * + α 2 I A 2 * ,
I A 3 = γ T ( A 1 A 4 * + A 2 * A 3 ) A 2 + γ R ( A 1 * A 3 + A 2 A 4 * ) A 1 + α 2 I A 3 ,
I A 4 * = γ T ( A 1 A 4 * + A 2 * A 3 ) A 1 * + γ R ( A 1 * A 3 + A 2 A 4 * ) A 2 α 2 I A 4 * ,
I 1 = 1 2 exp ( f 0 γ r z + F ) , I 2 = 1 2 exp ( f 0 γ r z F ) ,
F = γ r tanh F α
ψ = γ i I 2 I 1 I 1 + I 2 ,
ρ = ( I 1 I 2 ) 1 / 2 I ( γ R + γ T ) [ 1 exp ( 2 i ψ ) ρ 2 ] exp ( i ψ ) + I 2 I 1 I ( γ T γ R ) ρ + α ρ .
R = κ 1 I ( I 1 I 2 ) 1 / 2 ( 1 R 2 ) + κ 2 I ( I 2 I 1 ) R + α R ,
( γ r tanh F α ) R = κ 1 2 1 R 2 cosh F κ 2 tanh F R + α R ,
υ + ( γ r α tanh F α γ r tanh F α + κ 2 γ r α coth F ) υ κ 1 2 4 ( γ r tanh F α ) 2 cosh 2 F υ = 0 .
υ + ( coth F + κ 2 γ r ) υ κ 1 2 4 γ r 2 cosech 2 F υ = 0 ,
ξ ( ξ 1 ) υ + ( ξ c ) υ κ 1 2 4 γ r 2 υ = 0 ,
ρ 0 = 2 γ r sinh F 0 exp ( i ψ 0 ) κ 1 υ 1 d υ 20 υ 2 d υ 10 υ 1 d υ 20 υ 2 d υ 10 ,
ξ ( ξ 1 ) υ ( 1 2 ξ + ξ κ 2 α 2 γ r + γ r + κ 2 4 γ r ξ γ r + α 2 γ r ) υ + κ 1 2 16 γ r 2 ( ξ γ r + α 2 γ r ) 2 υ = 0 ,
η = ξ γ r α 2 γ r ξ γ r + α 2 γ r ,
η ( 1 η ) υ + [ c η ( a + b + 1 ) υ a b υ = 0 ,
c = 2 α + γ r κ 2 2 ( γ r + α ) ,
a + b = α ( γ r κ 2 ) 2 γ r κ 2 γ r 2 α 2 , a b = κ 1 2 4 ( γ r 2 α 2 ) .
υ 1 d υ 20 υ 2 d υ 10 = 0 ,
υ + [ ( 1 κ 2 α ) tanh F + 1 ] υ κ 1 2 4 α 2 sech 2 F υ = 0 ,

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