Abstract

We present a new model, which incorporates both temperature and electron–hole effects, for two-beam coupling in photorefractive semiconductors under an external dc field E0. We show that the exponential gain Γ exhibits an intensity-dependent resonance. The application of this model to InP:Fe allows us to predict a value of Γ near 20 cm−1 for a thin sample at 1.06 μm with E0 = 10 kV/cm.

© 1989 Optical Society of America

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  1. B. Mainguet, Opt. Lett. 13, 657 (1988).
    [CrossRef] [PubMed]
  2. P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
    [CrossRef]
  3. P. Gravey, G. Picoli, C. Ozkul, N. Wolffer, “High two-wave mixing gain (11.4 cm−1) in photorefractive InP:Fe by using dc field,” Proc. Soc. Photo-Opt. Instrum. Eng.1127, (to be published).
  4. B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, J. P. Huignard, Opt. Lett. 13, 327 (1988).
    [CrossRef] [PubMed]
  5. J. Kumar, G. Albanese, W. H. Steier, M. Ziari, Opt. Lett. 12, 120 (1987).
    [CrossRef] [PubMed]
  6. R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
    [CrossRef]
  7. K. Walsh, T. J. Hall, Electron. Lett. 24, 477 (1988).
    [CrossRef]
  8. G. C. Valley, in Photorefractive Materials and Their ApplicationsI. P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 3.
  9. J. C. Fabre, J. M. C. Jonathan, G. Roosen, Opt. Commun. 65, 257 (1988).
    [CrossRef]
  10. F. P. Strokhendl, J. M. C. Jonathan, R. W. Hellwarth, Opt. Lett. 11, 312 (1986).
    [CrossRef]
  11. G. C. Valley, J. Appl. Phys. 59, 3363 (1986).
    [CrossRef]
  12. N. V. Kuhktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  13. G. Bremond, A. Nouilhat, G. Guillot, B. Cockayne, Electron. Lett. 17, 55 (1981).
    [CrossRef]
  14. P. S. Tapster, M. S. Skolnick, R. G. Humphreys, P. J. Dean, B. Cockayne, W. R. MacEwan, J. Phys. C 14, 5069 (1981).
    [CrossRef]
  15. K.-H. Hellwege, ed., Landolt-Börnstein New Series (Springer-Verlag, Berlin, 1982), Group III, Vol. 17.
  16. G. Bremond, G. Guillot, A. Nouilhat, Rev. Phys. Appl. 22, 873 (1987).
    [CrossRef]
  17. D. C. Look, Phys. Rev. B 20, 4160 (1979).
    [CrossRef]
  18. A. E. Iverson, D. L. Smith, N. G. Pautter, R. B. Hammond, J. Appl. Phys. 61, 234 (1987).
    [CrossRef]
  19. G. W. Iseler, Inst. Phys. Conf. Ser. 45, 144 (1979).
  20. N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
    [CrossRef]
  21. G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. (to be published).

1989 (1)

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

1988 (5)

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, J. P. Huignard, Opt. Lett. 13, 327 (1988).
[CrossRef] [PubMed]

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

K. Walsh, T. J. Hall, Electron. Lett. 24, 477 (1988).
[CrossRef]

J. C. Fabre, J. M. C. Jonathan, G. Roosen, Opt. Commun. 65, 257 (1988).
[CrossRef]

B. Mainguet, Opt. Lett. 13, 657 (1988).
[CrossRef] [PubMed]

1987 (3)

G. Bremond, G. Guillot, A. Nouilhat, Rev. Phys. Appl. 22, 873 (1987).
[CrossRef]

A. E. Iverson, D. L. Smith, N. G. Pautter, R. B. Hammond, J. Appl. Phys. 61, 234 (1987).
[CrossRef]

J. Kumar, G. Albanese, W. H. Steier, M. Ziari, Opt. Lett. 12, 120 (1987).
[CrossRef] [PubMed]

1986 (2)

1984 (1)

N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
[CrossRef]

1981 (2)

G. Bremond, A. Nouilhat, G. Guillot, B. Cockayne, Electron. Lett. 17, 55 (1981).
[CrossRef]

P. S. Tapster, M. S. Skolnick, R. G. Humphreys, P. J. Dean, B. Cockayne, W. R. MacEwan, J. Phys. C 14, 5069 (1981).
[CrossRef]

1979 (3)

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

G. W. Iseler, Inst. Phys. Conf. Ser. 45, 144 (1979).

D. C. Look, Phys. Rev. B 20, 4160 (1979).
[CrossRef]

Albanese, G.

Bremond, G.

G. Bremond, G. Guillot, A. Nouilhat, Rev. Phys. Appl. 22, 873 (1987).
[CrossRef]

G. Bremond, A. Nouilhat, G. Guillot, B. Cockayne, Electron. Lett. 17, 55 (1981).
[CrossRef]

Bylsma, R. B.

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

Cockayne, B.

P. S. Tapster, M. S. Skolnick, R. G. Humphreys, P. J. Dean, B. Cockayne, W. R. MacEwan, J. Phys. C 14, 5069 (1981).
[CrossRef]

G. Bremond, A. Nouilhat, G. Guillot, B. Cockayne, Electron. Lett. 17, 55 (1981).
[CrossRef]

Dean, P. J.

P. S. Tapster, M. S. Skolnick, R. G. Humphreys, P. J. Dean, B. Cockayne, W. R. MacEwan, J. Phys. C 14, 5069 (1981).
[CrossRef]

Fabre, J. C.

J. C. Fabre, J. M. C. Jonathan, G. Roosen, Opt. Commun. 65, 257 (1988).
[CrossRef]

Glass, A. M.

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

Gravey, P.

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

P. Gravey, G. Picoli, C. Ozkul, N. Wolffer, “High two-wave mixing gain (11.4 cm−1) in photorefractive InP:Fe by using dc field,” Proc. Soc. Photo-Opt. Instrum. Eng.1127, (to be published).

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. (to be published).

Guillot, G.

G. Bremond, G. Guillot, A. Nouilhat, Rev. Phys. Appl. 22, 873 (1987).
[CrossRef]

G. Bremond, A. Nouilhat, G. Guillot, B. Cockayne, Electron. Lett. 17, 55 (1981).
[CrossRef]

Hall, T. J.

K. Walsh, T. J. Hall, Electron. Lett. 24, 477 (1988).
[CrossRef]

Hammond, R. B.

A. E. Iverson, D. L. Smith, N. G. Pautter, R. B. Hammond, J. Appl. Phys. 61, 234 (1987).
[CrossRef]

Hellwarth, R. W.

Herriau, J. P.

Huignard, J. P.

Humphreys, R. G.

P. S. Tapster, M. S. Skolnick, R. G. Humphreys, P. J. Dean, B. Cockayne, W. R. MacEwan, J. Phys. C 14, 5069 (1981).
[CrossRef]

Imbert, B.

Iseler, G. W.

G. W. Iseler, Inst. Phys. Conf. Ser. 45, 144 (1979).

Iverson, A. E.

A. E. Iverson, D. L. Smith, N. G. Pautter, R. B. Hammond, J. Appl. Phys. 61, 234 (1987).
[CrossRef]

Jonathan, J. M. C.

J. C. Fabre, J. M. C. Jonathan, G. Roosen, Opt. Commun. 65, 257 (1988).
[CrossRef]

F. P. Strokhendl, J. M. C. Jonathan, R. W. Hellwarth, Opt. Lett. 11, 312 (1986).
[CrossRef]

Kuhktarev, N. V.

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

Kumar, J.

Labandibar, J. Y.

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

Look, D. C.

D. C. Look, Phys. Rev. B 20, 4160 (1979).
[CrossRef]

MacEwan, W. R.

P. S. Tapster, M. S. Skolnick, R. G. Humphreys, P. J. Dean, B. Cockayne, W. R. MacEwan, J. Phys. C 14, 5069 (1981).
[CrossRef]

Mainguet, B.

Mallick, S.

Markov, V. B.

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

Nouilhat, A.

G. Bremond, G. Guillot, A. Nouilhat, Rev. Phys. Appl. 22, 873 (1987).
[CrossRef]

G. Bremond, A. Nouilhat, G. Guillot, B. Cockayne, Electron. Lett. 17, 55 (1981).
[CrossRef]

Odulov, S. G.

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

Olson, D. H.

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

Ozkul, C.

P. Gravey, G. Picoli, C. Ozkul, N. Wolffer, “High two-wave mixing gain (11.4 cm−1) in photorefractive InP:Fe by using dc field,” Proc. Soc. Photo-Opt. Instrum. Eng.1127, (to be published).

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. (to be published).

Pautter, N. G.

A. E. Iverson, D. L. Smith, N. G. Pautter, R. B. Hammond, J. Appl. Phys. 61, 234 (1987).
[CrossRef]

Picoli, G.

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

P. Gravey, G. Picoli, C. Ozkul, N. Wolffer, “High two-wave mixing gain (11.4 cm−1) in photorefractive InP:Fe by using dc field,” Proc. Soc. Photo-Opt. Instrum. Eng.1127, (to be published).

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. (to be published).

Rajbenbach, H.

Roosen, G.

J. C. Fabre, J. M. C. Jonathan, G. Roosen, Opt. Commun. 65, 257 (1988).
[CrossRef]

Skolnick, M. S.

P. S. Tapster, M. S. Skolnick, R. G. Humphreys, P. J. Dean, B. Cockayne, W. R. MacEwan, J. Phys. C 14, 5069 (1981).
[CrossRef]

Smith, D. L.

A. E. Iverson, D. L. Smith, N. G. Pautter, R. B. Hammond, J. Appl. Phys. 61, 234 (1987).
[CrossRef]

Soskin, M. S.

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

Steier, W. H.

Strokhendl, F. P.

Suzuki, N.

N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
[CrossRef]

Tada, K.

N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
[CrossRef]

Tapster, P. S.

P. S. Tapster, M. S. Skolnick, R. G. Humphreys, P. J. Dean, B. Cockayne, W. R. MacEwan, J. Phys. C 14, 5069 (1981).
[CrossRef]

Valley, G. C.

G. C. Valley, J. Appl. Phys. 59, 3363 (1986).
[CrossRef]

G. C. Valley, in Photorefractive Materials and Their ApplicationsI. P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 3.

Vieux, V.

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. (to be published).

Vinetskii, V. L.

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

Walsh, K.

K. Walsh, T. J. Hall, Electron. Lett. 24, 477 (1988).
[CrossRef]

Wolffer, N.

P. Gravey, G. Picoli, C. Ozkul, N. Wolffer, “High two-wave mixing gain (11.4 cm−1) in photorefractive InP:Fe by using dc field,” Proc. Soc. Photo-Opt. Instrum. Eng.1127, (to be published).

Ziari, M.

Electron. Lett. (3)

R. B. Bylsma, A. M. Glass, D. H. Olson, Electron. Lett. 24, 360 (1988).
[CrossRef]

K. Walsh, T. J. Hall, Electron. Lett. 24, 477 (1988).
[CrossRef]

G. Bremond, A. Nouilhat, G. Guillot, B. Cockayne, Electron. Lett. 17, 55 (1981).
[CrossRef]

Ferroelectrics (1)

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

Inst. Phys. Conf. Ser. (1)

G. W. Iseler, Inst. Phys. Conf. Ser. 45, 144 (1979).

J. Appl. Phys. (2)

A. E. Iverson, D. L. Smith, N. G. Pautter, R. B. Hammond, J. Appl. Phys. 61, 234 (1987).
[CrossRef]

G. C. Valley, J. Appl. Phys. 59, 3363 (1986).
[CrossRef]

J. Phys. C (1)

P. S. Tapster, M. S. Skolnick, R. G. Humphreys, P. J. Dean, B. Cockayne, W. R. MacEwan, J. Phys. C 14, 5069 (1981).
[CrossRef]

Jpn. J. Appl. Phys. (1)

N. Suzuki, K. Tada, Jpn. J. Appl. Phys. 23, 291 (1984).
[CrossRef]

Opt. Commun. (2)

J. C. Fabre, J. M. C. Jonathan, G. Roosen, Opt. Commun. 65, 257 (1988).
[CrossRef]

P. Gravey, G. Picoli, J. Y. Labandibar, Opt. Commun. 70, 190 (1989).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. B (1)

D. C. Look, Phys. Rev. B 20, 4160 (1979).
[CrossRef]

Rev. Phys. Appl. (1)

G. Bremond, G. Guillot, A. Nouilhat, Rev. Phys. Appl. 22, 873 (1987).
[CrossRef]

Other (4)

K.-H. Hellwege, ed., Landolt-Börnstein New Series (Springer-Verlag, Berlin, 1982), Group III, Vol. 17.

G. C. Valley, in Photorefractive Materials and Their ApplicationsI. P. Günter, J. P. Huignard, eds. (Springer-Verlag, Berlin, 1988), Chap. 3.

P. Gravey, G. Picoli, C. Ozkul, N. Wolffer, “High two-wave mixing gain (11.4 cm−1) in photorefractive InP:Fe by using dc field,” Proc. Soc. Photo-Opt. Instrum. Eng.1127, (to be published).

G. Picoli, P. Gravey, C. Ozkul, V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: a new mechanism of resonance,” J. Appl. Phys. (to be published).

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Figures (3)

Fig. 1
Fig. 1

Theoretical 2WM gain in InP:Fe versus the pump intensity at 1.06 μm for T = 290, 300, and 305 K. Λ = 10 μm, E0 = 10 kV/cm, and the [Fe2+] and [Fe3+] concentrations are 2 × 1016 and 5 × 1016 cm−3, respectively. The material parameters are summarized in Table 1.

Fig. 2
Fig. 2

Modulus [curve (a)] and phase [curve (b)] of the normalized space-charge field E1/m versus the pump intensity. T = 290 K, Λ = 10 μm, and E0 = 10 kV/cm.

Fig. 3
Fig. 3

Calculated gain and intensity profiles at 1.06 μm with α = 2 cm−1 across a 5-mm-long sample. T = 290 K, Λ = 10 μm, and E0 = 10 kV/cm.

Tables (1)

Tables Icon

Table 1 InP:Fe Parameters Relevant to the Photorefractive Effect

Equations (39)

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Γ = ( 2 π n 3 r 41 / λ cos θ ) [ Im ( E 1 ) / m ] ,
d E / d x = ( e / ) ( N D N A + p n n T ) ,
J n = n e μ n E + μ n k B T ( d n / d x ) ,
J p = p e μ p E μ p k B T ( d p / d x ) ,
d n / d t = e n n T c n n p T + ( 1 / e ) ( d J n / d x ) ,
d p / d t = e p p T c p p n T ( 1 / e ) ( d J p / d x ) ,
d n T / d t = e n n T + c n n p T + e p p T c p p n T ,
n T + p T = N T ,
e n ( x ) = e n 0 + Re [ m σ n 0 ( I 0 e iKx ) ] ,
e p ( x ) = e p 0 + Re [ m σ n 0 ( I 0 e iKx ) ] ,
e n 0 = e n th + σ n 0 I 0 , e p 0 = e p th + σ p 0 I 0 .
n 0 = e n 0 ( N D N A ) / c n ( N T N D + N A ) ,
p 0 = e p 0 ( N T N D + N A ) / c p ( N D N A ) .
i K E 1 = ( e / ) ( p 1 n 1 n T 1 ) ,
J n 1 = e μ n [ n 0 E 1 + n 1 ( E 0 + i E D ) ] ,
J p 1 = e μ p [ p 0 E 1 + p 1 ( E 0 i E D ) ] ,
0 = e n 0 n T 1 + σ n 0 n T 0 m I 0 c n ( n 0 p T 1 + n 1 p T 0 ) + i K J n 1 / e ,
0 = e p 0 p T 1 + σ p 0 p T 0 m I 0 c p ( p 0 n T 1 + p 1 n T 0 ) i K J p 1 / e ,
0 = J n 1 + J p 1 ,
0 = n T 1 + p T 1 ,
E 1 = i m I 0 σ p 0 p T 0 ( 1 + i E M p E 0 i E D p ) σ n 0 n T 0 ( 1 i E M n E 0 + i E D n ) e n 0 n T 0 ( 1 E q + i 1 E M n / E q E D n i E 0 ) + e p 0 p T 0 ( 1 E q + 1 E M p / E q E D p + i E 0 ) ,
E q = ( e / K ) ( n T 0 p T 0 n T 0 + p T 0 ) , E M p = c p n T 0 / μ p K , E M n = c n p T 0 / μ n K ;
E D = K ( k B T / e ) , E D p = E M p + E D , E D n = E M n + E D .
E 1 = i m I 0 × ( σ p 0 p T 0 σ n 0 n T 0 ) e n 0 n T 0 ( 1 E q + 1 E D i E 0 ) + e p 0 p T 0 ( 1 E q + 1 E D + i E 0 ) .
Im ( E 1 ) = m ξ R ( I 0 ) × A ( E 0 , K ) A 2 ( E 0 , K ) + ( e n 0 n T 0 e p 0 p T 0 e n 0 n T 0 + e p 0 p T 0 ) 2 B 2 ( E 0 , K ) ,
ξ R ( I 0 , T ) = ( σ p 0 p T 0 σ n 0 n T 0 ) I 0 e n 0 n T 0 + e p 0 p T 0 ,
A ( E 0 , K ) = 1 E q + E D E 0 2 + E D 2 , B ( E 0 , K ) = E 0 E 0 2 + E D 2 .
e n th ( T ) n T 0 e p th ( T ) p T 0 = ( σ p 0 p T 0 σ n 0 n T 0 ) I 0 .
n n th = 3.25 T 2 × 10 25 ( m e * / m ) σ n exp ( n a / k B T )
e p th e n th
m e * / m = 0.078
m h * / m = 0.056
σ n = 3.5 × 10 14 cm 2
σ n 0 = 4 × 10 18 cm 2
σ p 0 = 5 × 10 17 cm 2
c n = σ n υ n th
c p = σ p υ p th
υ n th = 4.1 × 10 7 cm / sec
υ p t h = 1.6 × 10 7 cm / sec

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