Abstract

This paper demonstrates the frequency-varied conjugation wave generation via nondegenerate four-wave mixing in photorefractive iron-doped lithium niobate crystal. The experiment uses 4880- and 6328-Å laser beams as mixing waves. The results are different from nearly degenerate four-wave mixing. The conjugation wave intensity depends on many parameters.

© 1988 Optical Society of America

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References

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  1. D. M. Pepper, R. L. Abrams, “Narrow Optical Bandpass Filter Via Nearly Degenerate Four-Wave Mixing,” Opt. Lett. 3, 312 (1978).
    [CrossRef]
  2. J. Nilsen, A. Yariv, “Nearly Degenerate Four-Wave Mixing Applied to Optical filters,” Appl. Opt. 18, 143 (1979).
    [CrossRef] [PubMed]
  3. J. Nilsen, A. Yariv, “Nondegenerate Four-Wave Mixing in a Doppler-Broadened Resonant Medium,” J. Opt. Soc. Am. 71, 180 (1981).
    [CrossRef]
  4. J. Nilsen, A. Yariv, “Nondegenerate Four-Wave Mixing in a Homogeneously Broadened Two-Level System with Saturating Pump Waves,” IEEE J. Quantum Electron. QE-18, 1947 (1982).
    [CrossRef]
  5. N. F. Pilipetsky, V. V. Shkunov, “Narrowland Four-Wave Reflecting Filter with Frequency and Angular Tuning,” Opt. Commun. 37, 217 (1981).
    [CrossRef]
  6. J. Nilsen, A. Yariv, “A Tunable Narrowband Optical Filter via Phase Conjugation by Nondegenerate Four-Wave Mixing in a Doppler-Broadened Resonant Medium,” Opt. Commun. 39, 199 (1981).
    [CrossRef]
  7. J. Nilsen, N. S. Gluck, A. Yariv, “Narrowband Optical Filter Through Phase Conjugation by Nondegenerate Four-Wave Mixing in Sodium Vapor,” Opt. Lett. 6, 380 (1981).
    [CrossRef] [PubMed]
  8. A. M. Glass, “Photorefractive Effect,” Opt. Eng. 17, 470 (1978).
  9. W. J. Burke, D. L. Staebler, W. Phillips, G. A. Alphonse, “Volume Phase Holographic Storage in Ferroelectric Crystals,” Opt. Eng. 17, 308 (1978).

1982 (1)

J. Nilsen, A. Yariv, “Nondegenerate Four-Wave Mixing in a Homogeneously Broadened Two-Level System with Saturating Pump Waves,” IEEE J. Quantum Electron. QE-18, 1947 (1982).
[CrossRef]

1981 (4)

N. F. Pilipetsky, V. V. Shkunov, “Narrowland Four-Wave Reflecting Filter with Frequency and Angular Tuning,” Opt. Commun. 37, 217 (1981).
[CrossRef]

J. Nilsen, A. Yariv, “A Tunable Narrowband Optical Filter via Phase Conjugation by Nondegenerate Four-Wave Mixing in a Doppler-Broadened Resonant Medium,” Opt. Commun. 39, 199 (1981).
[CrossRef]

J. Nilsen, N. S. Gluck, A. Yariv, “Narrowband Optical Filter Through Phase Conjugation by Nondegenerate Four-Wave Mixing in Sodium Vapor,” Opt. Lett. 6, 380 (1981).
[CrossRef] [PubMed]

J. Nilsen, A. Yariv, “Nondegenerate Four-Wave Mixing in a Doppler-Broadened Resonant Medium,” J. Opt. Soc. Am. 71, 180 (1981).
[CrossRef]

1979 (1)

1978 (3)

D. M. Pepper, R. L. Abrams, “Narrow Optical Bandpass Filter Via Nearly Degenerate Four-Wave Mixing,” Opt. Lett. 3, 312 (1978).
[CrossRef]

A. M. Glass, “Photorefractive Effect,” Opt. Eng. 17, 470 (1978).

W. J. Burke, D. L. Staebler, W. Phillips, G. A. Alphonse, “Volume Phase Holographic Storage in Ferroelectric Crystals,” Opt. Eng. 17, 308 (1978).

Abrams, R. L.

D. M. Pepper, R. L. Abrams, “Narrow Optical Bandpass Filter Via Nearly Degenerate Four-Wave Mixing,” Opt. Lett. 3, 312 (1978).
[CrossRef]

Alphonse, G. A.

W. J. Burke, D. L. Staebler, W. Phillips, G. A. Alphonse, “Volume Phase Holographic Storage in Ferroelectric Crystals,” Opt. Eng. 17, 308 (1978).

Burke, W. J.

W. J. Burke, D. L. Staebler, W. Phillips, G. A. Alphonse, “Volume Phase Holographic Storage in Ferroelectric Crystals,” Opt. Eng. 17, 308 (1978).

Glass, A. M.

A. M. Glass, “Photorefractive Effect,” Opt. Eng. 17, 470 (1978).

Gluck, N. S.

Nilsen, J.

J. Nilsen, A. Yariv, “Nondegenerate Four-Wave Mixing in a Homogeneously Broadened Two-Level System with Saturating Pump Waves,” IEEE J. Quantum Electron. QE-18, 1947 (1982).
[CrossRef]

J. Nilsen, A. Yariv, “Nondegenerate Four-Wave Mixing in a Doppler-Broadened Resonant Medium,” J. Opt. Soc. Am. 71, 180 (1981).
[CrossRef]

J. Nilsen, A. Yariv, “A Tunable Narrowband Optical Filter via Phase Conjugation by Nondegenerate Four-Wave Mixing in a Doppler-Broadened Resonant Medium,” Opt. Commun. 39, 199 (1981).
[CrossRef]

J. Nilsen, N. S. Gluck, A. Yariv, “Narrowband Optical Filter Through Phase Conjugation by Nondegenerate Four-Wave Mixing in Sodium Vapor,” Opt. Lett. 6, 380 (1981).
[CrossRef] [PubMed]

J. Nilsen, A. Yariv, “Nearly Degenerate Four-Wave Mixing Applied to Optical filters,” Appl. Opt. 18, 143 (1979).
[CrossRef] [PubMed]

Pepper, D. M.

D. M. Pepper, R. L. Abrams, “Narrow Optical Bandpass Filter Via Nearly Degenerate Four-Wave Mixing,” Opt. Lett. 3, 312 (1978).
[CrossRef]

Phillips, W.

W. J. Burke, D. L. Staebler, W. Phillips, G. A. Alphonse, “Volume Phase Holographic Storage in Ferroelectric Crystals,” Opt. Eng. 17, 308 (1978).

Pilipetsky, N. F.

N. F. Pilipetsky, V. V. Shkunov, “Narrowland Four-Wave Reflecting Filter with Frequency and Angular Tuning,” Opt. Commun. 37, 217 (1981).
[CrossRef]

Shkunov, V. V.

N. F. Pilipetsky, V. V. Shkunov, “Narrowland Four-Wave Reflecting Filter with Frequency and Angular Tuning,” Opt. Commun. 37, 217 (1981).
[CrossRef]

Staebler, D. L.

W. J. Burke, D. L. Staebler, W. Phillips, G. A. Alphonse, “Volume Phase Holographic Storage in Ferroelectric Crystals,” Opt. Eng. 17, 308 (1978).

Yariv, A.

J. Nilsen, A. Yariv, “Nondegenerate Four-Wave Mixing in a Homogeneously Broadened Two-Level System with Saturating Pump Waves,” IEEE J. Quantum Electron. QE-18, 1947 (1982).
[CrossRef]

J. Nilsen, A. Yariv, “Nondegenerate Four-Wave Mixing in a Doppler-Broadened Resonant Medium,” J. Opt. Soc. Am. 71, 180 (1981).
[CrossRef]

J. Nilsen, N. S. Gluck, A. Yariv, “Narrowband Optical Filter Through Phase Conjugation by Nondegenerate Four-Wave Mixing in Sodium Vapor,” Opt. Lett. 6, 380 (1981).
[CrossRef] [PubMed]

J. Nilsen, A. Yariv, “A Tunable Narrowband Optical Filter via Phase Conjugation by Nondegenerate Four-Wave Mixing in a Doppler-Broadened Resonant Medium,” Opt. Commun. 39, 199 (1981).
[CrossRef]

J. Nilsen, A. Yariv, “Nearly Degenerate Four-Wave Mixing Applied to Optical filters,” Appl. Opt. 18, 143 (1979).
[CrossRef] [PubMed]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

J. Nilsen, A. Yariv, “Nondegenerate Four-Wave Mixing in a Homogeneously Broadened Two-Level System with Saturating Pump Waves,” IEEE J. Quantum Electron. QE-18, 1947 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

N. F. Pilipetsky, V. V. Shkunov, “Narrowland Four-Wave Reflecting Filter with Frequency and Angular Tuning,” Opt. Commun. 37, 217 (1981).
[CrossRef]

J. Nilsen, A. Yariv, “A Tunable Narrowband Optical Filter via Phase Conjugation by Nondegenerate Four-Wave Mixing in a Doppler-Broadened Resonant Medium,” Opt. Commun. 39, 199 (1981).
[CrossRef]

Opt. Eng. (2)

A. M. Glass, “Photorefractive Effect,” Opt. Eng. 17, 470 (1978).

W. J. Burke, D. L. Staebler, W. Phillips, G. A. Alphonse, “Volume Phase Holographic Storage in Ferroelectric Crystals,” Opt. Eng. 17, 308 (1978).

Opt. Lett. (2)

J. Nilsen, N. S. Gluck, A. Yariv, “Narrowband Optical Filter Through Phase Conjugation by Nondegenerate Four-Wave Mixing in Sodium Vapor,” Opt. Lett. 6, 380 (1981).
[CrossRef] [PubMed]

D. M. Pepper, R. L. Abrams, “Narrow Optical Bandpass Filter Via Nearly Degenerate Four-Wave Mixing,” Opt. Lett. 3, 312 (1978).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Experimental setup of nondegenerate four-wave mixing.

Fig. 2
Fig. 2

Nondegenerate four-wave mixing experimental demonstration: (a) probe wave; (b) pump beam 2; (c) phase conjugation wave.

Fig. 3
Fig. 3

Dependence of the phase conjugation wave intensity on the amount of doping iron.

Fig. 4
Fig. 4

Dependence of the conjugation wave intensity on angle θ.

Fig. 5
Fig. 5

Dependence of the conjugation wave intensity on angle Φ.

Fig. 6
Fig. 6

Dependence of the conjugation wave intensity on pump beam powers: (a) pump beam 1; (b) pump beam 2.

Equations (10)

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α = θ 2 sin 1 ( 2 λ 2 λ 1 λ 1 sin θ 2 ) ,
Δ k = K c + K p K 1 K 2 ,
Δ k = n c [ ω 1 2 + ω 2 2 + Δ ω 2 + 2 ω 1 Δ ω cos θ 2 ω 2 Δ ω cos ( θ α ) 2 ω 1 ω 2 cos α ] 1 / 2 .
Δ ϕ = Δ k · l ,
d ε c d z = α c ε c i χ * c ε * p exp ( i Δ k z ) ,
d ε * p d z = α * p ε * p + i χ p ε c exp ( i Δ k z ) ,
χ * j = ω j 2 n c χ ( 3 ) ε 1 ε 2
α j = i ω j 2 n c χ ( 1 )
ε c ( 0 ) = i χ * c D [ exp ( r 2 l ) exp ( r 1 l ) ] ε * p ( 0 ) ,
r 1 , 2 = 1 2 { ( α c + α * p i Δ k ) ± [ 4 χ p χ * c + ( α c α p + i Δ k ) 2 ] 1 / 2 } , D = ( r 2 + α 2 ) exp ( r 1 l ) ( r 1 + α c ) exp ( r 2 l ) .

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