Abstract

Two-wave mixing in photorefractive InP:Fe crystals is revisited in terms of an externally applied dc field combined with the moving-grating technique. We show that the disagreement between theory and experiment that was previously observed in the literature can be reconciled by an examination of the influence of both the absorption along the propagation axis and the nonlinearities that occur at relatively large fringe modulations. A finite-difference method is used to demonstrate the dependence of these nonlinearities on the average incident intensity.

© 2000 Optical Society of America

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References

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  1. N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetski, “Holographic storage in electrooptic crystals. I. Steady state; II. Beam coupling light amplification,” Ferroelectrics 22, 949–961 (1979).
    [CrossRef]
  2. S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
    [CrossRef]
  3. J. P. Huignard and M. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
    [CrossRef]
  4. P. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [CrossRef]
  5. G. Picoli, P. Gravey, C. Özkul, and V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989); G. Picoli, P. Gravey, and C. Özkul, “Model for resonant intensity dependence of photorefractive two wave mixing in InP:Fe,” Opt. Lett. 14, 1362–1364 (1989).
    [CrossRef] [PubMed]
  6. B. Mainguet, F. Le Guiner, and G. Picoli, “Moving grating and intrinsic electron–hole resonance in two-wave mixing in photorefractive InP:Fe,” Opt. Lett. 15, 938–940 (1990).
    [CrossRef] [PubMed]
  7. R. S. Rana, D. D. Nolte, R. Steldt, and E. M. Monberg, “Temperature dependance of the photorefractive effect in InP:Fe: role of multiple defects,” J. Opt. Soc. Am. B 9, 1614–1624 (1992).
    [CrossRef]
  8. C. Özkul, S. Jamet, and V. Dupray, “Dependence on temperature of two-wave mixing in InP:Fe at three different wavelengths: an enhanced two-defect model,” J. Opt. Soc. Am. B 14, 2895–2903 (1997).
    [CrossRef]
  9. A. Abdelghani-Idrissi, C. Özkul, N. Wolffer, P. Gravey, and G. Picoli, “Resonant behaviour of temporal response of the two-wave mixing in photorefractive InP:Fe crystals under DC fields,” Opt. Commun. 86, 317–323 (1991).
    [CrossRef]
  10. N. Wolffer, P. Gravey, and R. Coquillé, “Numerical analysis of photorefractive InP:Fe at large fringe contrast,” J. Appl. Phys. 78, 6375–6383 (1995).
    [CrossRef]
  11. J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiments,” IEEE J. Quantum Electron. 24, 558–567 (1988).
    [CrossRef]
  12. D. R. Erbschloe and T. Wilson, Opt. Commun. 72, 135–140 (1989).
    [CrossRef]
  13. G. A. Brost, K. M. Magde, J. J. Larkin, and M. T. Harris, “Modulation dependence of the photorefractive response with moving grating: numerical analysis and experiments,” J. Opt. Soc. Am. B 11, 1764–1772 (1994).
    [CrossRef]
  14. F. Vachss and L. Hesselink, “Nonlinear photorefractive response at high modulation depths,” J. Opt. Soc. Am. A 5, 690–701 (1988).
    [CrossRef]
  15. L. B. Au and L. Solymar, “Space-charge field in photorefractive materials at large modulation,” Opt. Lett. 13, 660–662 (1988); “Higher harmonic grating in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554–1561 (1990).
    [CrossRef] [PubMed]
  16. G. A. Brost, “Photorefractive grating formation at large modulation with alternating electric fields,” J. Opt. Soc. Am. B 9, 1454–1460 (1992).
    [CrossRef]

1997 (1)

1995 (1)

N. Wolffer, P. Gravey, and R. Coquillé, “Numerical analysis of photorefractive InP:Fe at large fringe contrast,” J. Appl. Phys. 78, 6375–6383 (1995).
[CrossRef]

1994 (1)

1992 (2)

1991 (1)

A. Abdelghani-Idrissi, C. Özkul, N. Wolffer, P. Gravey, and G. Picoli, “Resonant behaviour of temporal response of the two-wave mixing in photorefractive InP:Fe crystals under DC fields,” Opt. Commun. 86, 317–323 (1991).
[CrossRef]

1990 (1)

1989 (1)

D. R. Erbschloe and T. Wilson, Opt. Commun. 72, 135–140 (1989).
[CrossRef]

1988 (2)

F. Vachss and L. Hesselink, “Nonlinear photorefractive response at high modulation depths,” J. Opt. Soc. Am. A 5, 690–701 (1988).
[CrossRef]

J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiments,” IEEE J. Quantum Electron. 24, 558–567 (1988).
[CrossRef]

1985 (2)

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

1981 (1)

J. P. Huignard and M. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

1979 (1)

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetski, “Holographic storage in electrooptic crystals. I. Steady state; II. Beam coupling light amplification,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Abdelghani-Idrissi, A.

A. Abdelghani-Idrissi, C. Özkul, N. Wolffer, P. Gravey, and G. Picoli, “Resonant behaviour of temporal response of the two-wave mixing in photorefractive InP:Fe crystals under DC fields,” Opt. Commun. 86, 317–323 (1991).
[CrossRef]

Brost, G. A.

Coquillé, R.

N. Wolffer, P. Gravey, and R. Coquillé, “Numerical analysis of photorefractive InP:Fe at large fringe contrast,” J. Appl. Phys. 78, 6375–6383 (1995).
[CrossRef]

Dupray, V.

Erbschloe, D. R.

D. R. Erbschloe and T. Wilson, Opt. Commun. 72, 135–140 (1989).
[CrossRef]

Gravey, P.

N. Wolffer, P. Gravey, and R. Coquillé, “Numerical analysis of photorefractive InP:Fe at large fringe contrast,” J. Appl. Phys. 78, 6375–6383 (1995).
[CrossRef]

A. Abdelghani-Idrissi, C. Özkul, N. Wolffer, P. Gravey, and G. Picoli, “Resonant behaviour of temporal response of the two-wave mixing in photorefractive InP:Fe crystals under DC fields,” Opt. Commun. 86, 317–323 (1991).
[CrossRef]

Harris, M. T.

Heaton, J. M.

J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiments,” IEEE J. Quantum Electron. 24, 558–567 (1988).
[CrossRef]

Hesselink, L.

Huignard, J. P.

P. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J. P. Huignard and M. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Jamet, S.

Kukhtarev, N.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetski, “Holographic storage in electrooptic crystals. I. Steady state; II. Beam coupling light amplification,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Larkin, J. J.

Le Guiner, F.

Magde, K. M.

Mainguet, B.

Markov, V.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetski, “Holographic storage in electrooptic crystals. I. Steady state; II. Beam coupling light amplification,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Marrakchi, M.

J. P. Huignard and M. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Monberg, E. M.

Nolte, D. D.

Odulov, S.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetski, “Holographic storage in electrooptic crystals. I. Steady state; II. Beam coupling light amplification,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Özkul, C.

C. Özkul, S. Jamet, and V. Dupray, “Dependence on temperature of two-wave mixing in InP:Fe at three different wavelengths: an enhanced two-defect model,” J. Opt. Soc. Am. B 14, 2895–2903 (1997).
[CrossRef]

A. Abdelghani-Idrissi, C. Özkul, N. Wolffer, P. Gravey, and G. Picoli, “Resonant behaviour of temporal response of the two-wave mixing in photorefractive InP:Fe crystals under DC fields,” Opt. Commun. 86, 317–323 (1991).
[CrossRef]

Petrov, M. P.

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

Picoli, G.

A. Abdelghani-Idrissi, C. Özkul, N. Wolffer, P. Gravey, and G. Picoli, “Resonant behaviour of temporal response of the two-wave mixing in photorefractive InP:Fe crystals under DC fields,” Opt. Commun. 86, 317–323 (1991).
[CrossRef]

B. Mainguet, F. Le Guiner, and G. Picoli, “Moving grating and intrinsic electron–hole resonance in two-wave mixing in photorefractive InP:Fe,” Opt. Lett. 15, 938–940 (1990).
[CrossRef] [PubMed]

Rajbenbach, H.

P. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Rana, R. S.

Réfrégier, P.

P. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Solymar, L.

J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiments,” IEEE J. Quantum Electron. 24, 558–567 (1988).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Soskin, M.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetski, “Holographic storage in electrooptic crystals. I. Steady state; II. Beam coupling light amplification,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Steldt, R.

Stepanov, S. I.

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

Vachss, F.

Vinetski, V.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetski, “Holographic storage in electrooptic crystals. I. Steady state; II. Beam coupling light amplification,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Wilson, T.

D. R. Erbschloe and T. Wilson, Opt. Commun. 72, 135–140 (1989).
[CrossRef]

Wolffer, N.

N. Wolffer, P. Gravey, and R. Coquillé, “Numerical analysis of photorefractive InP:Fe at large fringe contrast,” J. Appl. Phys. 78, 6375–6383 (1995).
[CrossRef]

A. Abdelghani-Idrissi, C. Özkul, N. Wolffer, P. Gravey, and G. Picoli, “Resonant behaviour of temporal response of the two-wave mixing in photorefractive InP:Fe crystals under DC fields,” Opt. Commun. 86, 317–323 (1991).
[CrossRef]

Ferroelectrics (1)

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetski, “Holographic storage in electrooptic crystals. I. Steady state; II. Beam coupling light amplification,” Ferroelectrics 22, 949–961 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. M. Heaton and L. Solymar, “Transient effects during dynamic hologram formation in BSO crystals: theory and experiments,” IEEE J. Quantum Electron. 24, 558–567 (1988).
[CrossRef]

J. Appl. Phys. (2)

N. Wolffer, P. Gravey, and R. Coquillé, “Numerical analysis of photorefractive InP:Fe at large fringe contrast,” J. Appl. Phys. 78, 6375–6383 (1995).
[CrossRef]

P. Réfrégier, L. Solymar, H. Rajbenbach, and J. P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (4)

Opt. Commun. (4)

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[CrossRef]

J. P. Huignard and M. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

A. Abdelghani-Idrissi, C. Özkul, N. Wolffer, P. Gravey, and G. Picoli, “Resonant behaviour of temporal response of the two-wave mixing in photorefractive InP:Fe crystals under DC fields,” Opt. Commun. 86, 317–323 (1991).
[CrossRef]

D. R. Erbschloe and T. Wilson, Opt. Commun. 72, 135–140 (1989).
[CrossRef]

Opt. Lett. (1)

Other (2)

L. B. Au and L. Solymar, “Space-charge field in photorefractive materials at large modulation,” Opt. Lett. 13, 660–662 (1988); “Higher harmonic grating in photorefractive materials at large modulation with moving fringes,” J. Opt. Soc. Am. A 7, 1554–1561 (1990).
[CrossRef] [PubMed]

G. Picoli, P. Gravey, C. Özkul, and V. Vieux, “Theory of two wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989); G. Picoli, P. Gravey, and C. Özkul, “Model for resonant intensity dependence of photorefractive two wave mixing in InP:Fe,” Opt. Lett. 14, 1362–1364 (1989).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Experimental setup. Abbreviations are defined in text.

Fig. 2
Fig. 2

Representation of experimental and theoretical TWM gain versus fringe velocity for two incident intensities I0.

Fig. 3
Fig. 3

Theoretical evolution of empirical parameter R and values of a used to fit the experimental data versus incident intensity.

Fig. 4
Fig. 4

Exponential gain as a function of incident intensity for m1=0.06 (curve a) and m2=0.2 (curve b) and experimental correction function defined by fm2(I)=m2[Γ(I, m2)/Γ(I, m1)] (curve c).

Fig. 5
Fig. 5

Space-charge field across the fringe at incident intensity I0=6.5 mW cm-2 and at fringe velocity v=vopt.

Fig. 6
Fig. 6

Theoretical evolution of fm=0.2 versus incident intensity for three fringe velocities v.

Equations (15)

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

nT+pT=nT0+pT0,
dEdx=-e(nT-nT0)-e(n-p)=ρe,
Jn=eμnnE+μnkbT dndx,
Jp=eμppE-μpkbT dpdx,
dndt=(σn0I+enth)nT-cnnpT+1edJndx,
dpdt=(σp0I+epth)pT-cppnT-1edJpdx,
dnTdt=-dpTdt=-(σn0I+enth)nT+cnnpT+(σp0I+epth)pT-cppnT,
I=I0 {1+m cos[Kr(x-vt)]},
A(x)=A0+Re{A1 exp[iKr(x-vt)]}.
fm=[1-exp(-am)]/a,
R=Im(E1)V=VoptIm(E1)V=0,
0ΛE(x)dx=E0Λ,
Γ(I, m)=fm(I)mΓ0,
fm2(I)=fm1(I)m1m2 Γ(I, m2)Γ(I, m1).
fm2(I)=m2 Γ(I, m2)Γ(I, m1).

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