Abstract

A transient model of degenerate four-wave mixing in saturable amplifiers is developed for calculation of the phase-conjugate reflectivity in the weak-probe-beam limit. Our model takes into account the laser amplification of all the interacting beams together with the wave-mixing process between the two counterpropagating pump waves. Experimental investigations are made in a flash-lamp-pumped Nd:YAG amplifier with nanosecond pulses at 1.06 μm. A reflectivity of 22% is achieved when all the waves interfere within the laser medium.

© 1994 Optical Society of America

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References

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  1. D. A. Rockwell, IEEE J. Quantum Electron. 24, 1124 (1988).
    [CrossRef]
  2. N. F. Andreev, E. Khazanov, G. A. Pasmanik, IEEE J. Quantum Electron. 28, 330 (1992).
    [CrossRef]
  3. F. Dizier, J.-L. Ayral, J. Montel, J.-P. Huignard, Int. J. Nonlinear Opt. Phys. 2, 229 (1993).
    [CrossRef]
  4. A. Tomita, Appl. Phys. Lett. 34, 463 (1979).
    [CrossRef]
  5. G. J. Crofts, R. P. M. Green, M. J. Damzen, Opt. Lett. 17, 920 (1992).
    [CrossRef] [PubMed]
  6. A. Brignon, J.-P. Huignard, Opt. Lett. 18, 1639 (1993).
    [CrossRef] [PubMed]
  7. A. Brignon, J.-P. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonal pump beams in a saturable Nd:YAG amplifier,”IEEE J. Quantum Electron. (to be published).
  8. W. P. Brown, J. Opt. Soc. Am. 73, 629 (1983).
    [CrossRef]
  9. R. L. Abrams, R. C. Lind, Opt. Lett. 2, 94 (1978); R. L. Abrams, R. C. Lind, Opt. Lett. 3, 205 (1978).
    [CrossRef] [PubMed]
  10. J. Reintjes, L. J. Palumbo, IEEE J. Quantum Electron. QE-18, 1934 (1982).
    [CrossRef]
  11. J. C. Diels, I. McMichael, H. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).
    [CrossRef]
  12. Y. Silberberg, I. Bar-Joseph, IEEE J. Quantum Electron. QE-17, 1967 (1981).
    [CrossRef]
  13. R. P. M. Green, G. J. Crofts, M. J. Damzen, Opt. Commun. 102, 288 (1993).
    [CrossRef]

1993 (3)

F. Dizier, J.-L. Ayral, J. Montel, J.-P. Huignard, Int. J. Nonlinear Opt. Phys. 2, 229 (1993).
[CrossRef]

R. P. M. Green, G. J. Crofts, M. J. Damzen, Opt. Commun. 102, 288 (1993).
[CrossRef]

A. Brignon, J.-P. Huignard, Opt. Lett. 18, 1639 (1993).
[CrossRef] [PubMed]

1992 (2)

G. J. Crofts, R. P. M. Green, M. J. Damzen, Opt. Lett. 17, 920 (1992).
[CrossRef] [PubMed]

N. F. Andreev, E. Khazanov, G. A. Pasmanik, IEEE J. Quantum Electron. 28, 330 (1992).
[CrossRef]

1988 (1)

D. A. Rockwell, IEEE J. Quantum Electron. 24, 1124 (1988).
[CrossRef]

1984 (1)

J. C. Diels, I. McMichael, H. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).
[CrossRef]

1983 (1)

1982 (1)

J. Reintjes, L. J. Palumbo, IEEE J. Quantum Electron. QE-18, 1934 (1982).
[CrossRef]

1981 (1)

Y. Silberberg, I. Bar-Joseph, IEEE J. Quantum Electron. QE-17, 1967 (1981).
[CrossRef]

1979 (1)

A. Tomita, Appl. Phys. Lett. 34, 463 (1979).
[CrossRef]

1978 (1)

Abrams, R. L.

Andreev, N. F.

N. F. Andreev, E. Khazanov, G. A. Pasmanik, IEEE J. Quantum Electron. 28, 330 (1992).
[CrossRef]

Ayral, J.-L.

F. Dizier, J.-L. Ayral, J. Montel, J.-P. Huignard, Int. J. Nonlinear Opt. Phys. 2, 229 (1993).
[CrossRef]

Bar-Joseph, I.

Y. Silberberg, I. Bar-Joseph, IEEE J. Quantum Electron. QE-17, 1967 (1981).
[CrossRef]

Brignon, A.

A. Brignon, J.-P. Huignard, Opt. Lett. 18, 1639 (1993).
[CrossRef] [PubMed]

A. Brignon, J.-P. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonal pump beams in a saturable Nd:YAG amplifier,”IEEE J. Quantum Electron. (to be published).

Brown, W. P.

Crofts, G. J.

R. P. M. Green, G. J. Crofts, M. J. Damzen, Opt. Commun. 102, 288 (1993).
[CrossRef]

G. J. Crofts, R. P. M. Green, M. J. Damzen, Opt. Lett. 17, 920 (1992).
[CrossRef] [PubMed]

Damzen, M. J.

R. P. M. Green, G. J. Crofts, M. J. Damzen, Opt. Commun. 102, 288 (1993).
[CrossRef]

G. J. Crofts, R. P. M. Green, M. J. Damzen, Opt. Lett. 17, 920 (1992).
[CrossRef] [PubMed]

Diels, J. C.

J. C. Diels, I. McMichael, H. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).
[CrossRef]

Dizier, F.

F. Dizier, J.-L. Ayral, J. Montel, J.-P. Huignard, Int. J. Nonlinear Opt. Phys. 2, 229 (1993).
[CrossRef]

Green, R. P. M.

R. P. M. Green, G. J. Crofts, M. J. Damzen, Opt. Commun. 102, 288 (1993).
[CrossRef]

G. J. Crofts, R. P. M. Green, M. J. Damzen, Opt. Lett. 17, 920 (1992).
[CrossRef] [PubMed]

Huignard, J.-P.

A. Brignon, J.-P. Huignard, Opt. Lett. 18, 1639 (1993).
[CrossRef] [PubMed]

F. Dizier, J.-L. Ayral, J. Montel, J.-P. Huignard, Int. J. Nonlinear Opt. Phys. 2, 229 (1993).
[CrossRef]

A. Brignon, J.-P. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonal pump beams in a saturable Nd:YAG amplifier,”IEEE J. Quantum Electron. (to be published).

Khazanov, E.

N. F. Andreev, E. Khazanov, G. A. Pasmanik, IEEE J. Quantum Electron. 28, 330 (1992).
[CrossRef]

Lind, R. C.

McMichael, I.

J. C. Diels, I. McMichael, H. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).
[CrossRef]

Montel, J.

F. Dizier, J.-L. Ayral, J. Montel, J.-P. Huignard, Int. J. Nonlinear Opt. Phys. 2, 229 (1993).
[CrossRef]

Palumbo, L. J.

J. Reintjes, L. J. Palumbo, IEEE J. Quantum Electron. QE-18, 1934 (1982).
[CrossRef]

Pasmanik, G. A.

N. F. Andreev, E. Khazanov, G. A. Pasmanik, IEEE J. Quantum Electron. 28, 330 (1992).
[CrossRef]

Reintjes, J.

J. Reintjes, L. J. Palumbo, IEEE J. Quantum Electron. QE-18, 1934 (1982).
[CrossRef]

Rockwell, D. A.

D. A. Rockwell, IEEE J. Quantum Electron. 24, 1124 (1988).
[CrossRef]

Silberberg, Y.

Y. Silberberg, I. Bar-Joseph, IEEE J. Quantum Electron. QE-17, 1967 (1981).
[CrossRef]

Tomita, A.

A. Tomita, Appl. Phys. Lett. 34, 463 (1979).
[CrossRef]

Vanherzeele, H.

J. C. Diels, I. McMichael, H. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).
[CrossRef]

Appl. Phys. Lett. (1)

A. Tomita, Appl. Phys. Lett. 34, 463 (1979).
[CrossRef]

IEEE J. Quantum Electron. (5)

J. Reintjes, L. J. Palumbo, IEEE J. Quantum Electron. QE-18, 1934 (1982).
[CrossRef]

J. C. Diels, I. McMichael, H. Vanherzeele, IEEE J. Quantum Electron. QE-20, 630 (1984).
[CrossRef]

Y. Silberberg, I. Bar-Joseph, IEEE J. Quantum Electron. QE-17, 1967 (1981).
[CrossRef]

D. A. Rockwell, IEEE J. Quantum Electron. 24, 1124 (1988).
[CrossRef]

N. F. Andreev, E. Khazanov, G. A. Pasmanik, IEEE J. Quantum Electron. 28, 330 (1992).
[CrossRef]

Int. J. Nonlinear Opt. Phys. (1)

F. Dizier, J.-L. Ayral, J. Montel, J.-P. Huignard, Int. J. Nonlinear Opt. Phys. 2, 229 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

R. P. M. Green, G. J. Crofts, M. J. Damzen, Opt. Commun. 102, 288 (1993).
[CrossRef]

Opt. Lett. (3)

Other (1)

A. Brignon, J.-P. Huignard, “Transient analysis of degenerate four-wave mixing with orthogonal pump beams in a saturable Nd:YAG amplifier,”IEEE J. Quantum Electron. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the DFWM interaction.

Fig. 2
Fig. 2

Theoretical plots obtained from Eqs. (8) showing the transient phase-conjugate reflectivity as a function of the normalized forward pump-beam fluence for various small-intensity gain–length products α0L. Equal-input pump-beam fluences [Uf(0) = Ub(L)].

Fig. 3
Fig. 3

Comparisons of the DFWM reflectivities obtained from different models: Curves a, steady-state regime including the pump-beam effects.10 Curves b, transient regime with constant pump beams.11 Curves c, transient regime including the pump-beam effects [Eqs. (8)]. All the curves have been plotted with equal-input pump beams.

Fig. 4
Fig. 4

Experimental behavior of the reflectivities as a functions of the normalized forward pump-beam fluence. The theoretical curve for the copolarized beam case has been obtained from Eqs. (8). The theoretical curves for the transmission and reflection gratings have been calculated with the model developed in Ref. 7.

Equations (14)

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E ( r , t ) = E 0 ( r , t ) + Δ E ( r , t ) ,
E 0 ( z 0 , t ) = A f exp ( i k z 0 ) + A b exp ( + i k z 0 ) ,
Δ E ( z , t ) = A p exp ( i k z ) + A c exp ( + i k z ) .
χ ( r , t ) = i α 0 k exp [ 0 t | E ( r , t ) | 2 d t / U sat ] ,
χ ( E ) = 2 i k [ 1 0 t ( E 0 Δ E * + E 0 * Δ E ) d t U sat ] ,
= α 0 2 exp ( 0 t | E 0 | 2 d t / U sat ) .
= n = + ( 1 ) | n | γ | n | exp ( 2 i k n z 0 ) ,
γ n = α 0 2 exp ( U S ) I n ( U M ) .
d A f d ξ = γ 0 A f γ 1 A b ,
d A b d ξ = γ 0 A b + γ 1 A f ,
d A p d ξ = α A p κ A c ,
d A c d ξ = α A c + κ A p ,
α = ( 1 U S ) γ 0 + U M γ 1 ,
κ = U M γ 0 U S γ 1 .

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