Abstract

We report the results of an experimental and theoretical study of electron–hole competition in CdTe:Ge photorefractive crystal with an incoherent auxiliary illumination and alternating low-frequency field. Resonant two-wave mixing (TWM) gain enhancement is studied that has been found depending on the wavelength and intensity of the incoherent illumination. We show that a low-frequency ac field can be used for an effective TWM gain enhancement under conditions appropriate to the electron–hole resonance. A time oscillation of the photorefractive gain concerned with the ac field is studied experimentally, and self-generation of time subharmonics is reported.

© 2007 Optical Society of America

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References

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  1. D.D.Nolte, ed., Photorefractive Effects and Material (Kluwer Academic, 1995).
  2. G. Picoli, P. Gravey, and C. Ozkul, "Model for resonant intensity dependence of photorefractive two-wave mixing in InP:Fe," Opt. Lett. 14, 1362-1364 (1989).
    [CrossRef] [PubMed]
  3. G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: new mechanism of resonance," J. Appl. Phys. 66, 3798-3813 (1990).
    [CrossRef]
  4. P. Pogany, H. J. Eichler, and M. Hage Ali, "Two-wave mixing gain enhancement in photorefractive CdZnTe:V by optically stimulated electron-hole resonance," J. Opt. Soc. Am. B 15, 2716-2720 (1998).
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  5. M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, "High-accuracy, high-reflectivity phase conjugation at 1.06μm by four-wave mixing in photorefractive gallium arsenide," J. Opt. Soc. Am. B 5, 2467-2472 (1988).
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  7. K. Shcherbin, V. Danylyuk, and A. V. Khomenko, "Visualization of space-charge waves in photorefractive semiconductor using polarization technique," Ukr. J. Phys. Opt. 7, 164-170 (2006).
    [CrossRef]
  8. Y. Belaud, P. Delaye, J. C. Launay, and G. Roosen, "Photorefractive response of CdTe:V under ac electric field from 1 to 1.5μm," Opt. Commun. 105, 204-208 (1994).
    [CrossRef]
  9. J.-Y. Moisan, N. Wolffer, O. Moine, G. Martel, A. Aoudie, E. Repka, Y. Marfaing, and R. Triboulet, "Characterization of the photorefractive CdTe:V: high two-wave mixing with an optimum low-frequency periodic external electric field," J. Opt. Soc. Am. B 11, 1655-1667 (1994).
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  10. G. Martel, N. Wolffer, J. Y. Moisan, and P. Gravey, "Double-phase-conjugate mirror in CdTe:V with elimination of conical diffraction at 1.54μm," Opt. Lett. 20, 937-939 (1995).
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  11. P. M. Johansen and H. C. Pedersen, "Photorefractive space-charge field with running grating and applied sinusoidal ac electric field: solution for all time scales," J. Opt. Soc. Am. B 15, 1366-1374 (1998).
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  12. P.Günter and J.-P.Huignard, eds., Photorefractive Materials and their Applications 1. Basic Effects (Springer, 2006).
    [CrossRef]
  13. B. Briat, K. Shcherbin, B. Farid, and F. Ramaz, "Optical and magnetooptical study of photorefractive germanium-doped cadmium telluride," Opt. Commun. 156, 337-340 (1998).
    [CrossRef]
  14. B. Briat, F. Ramaz, B. Farid, K. V. Shcherbin, and H. J. von Bardeleben, "Spectroscopic characterization of photorefractive CdTe:Ge," J. Cryst. Growth 197, 724-728 (1999).
    [CrossRef]
  15. P. Delaye, L. A. de Montmorillon, I. Biaggio, J. C. Launay, and G. Roosen, "Wavelength dependent effective trap density in CdTe: evidence for the presence of two photorefractive species," Opt. Commun. 134, 580-590 (1997).
    [CrossRef]
  16. M. Johansen, H. C. Pedersen, E. V. Podivilov, and B. I. Sturman, "Ac square-wave field-induced subharmonics in photorefractive sillenite: threshold for excitation by inclusion of higher harmonics," J. Opt. Soc. Am. B 16, 103-110 (1999).
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  17. B. I. Sturman, A. I. Chernykh, E. Shamonina, V. P. Kamenov, and K. H. Ringhofer, "Rigorous three-dimensional theory of subharmonic instability in sillenites," J. Opt. Soc. Am. B 16, 1099-1103 (1999).
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2006 (1)

K. Shcherbin, V. Danylyuk, and A. V. Khomenko, "Visualization of space-charge waves in photorefractive semiconductor using polarization technique," Ukr. J. Phys. Opt. 7, 164-170 (2006).
[CrossRef]

2002 (1)

1999 (3)

1998 (3)

1997 (1)

P. Delaye, L. A. de Montmorillon, I. Biaggio, J. C. Launay, and G. Roosen, "Wavelength dependent effective trap density in CdTe: evidence for the presence of two photorefractive species," Opt. Commun. 134, 580-590 (1997).
[CrossRef]

1995 (1)

1994 (2)

1990 (1)

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: new mechanism of resonance," J. Appl. Phys. 66, 3798-3813 (1990).
[CrossRef]

1989 (1)

1988 (1)

Appl. Opt. (1)

J. Appl. Phys. (1)

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: new mechanism of resonance," J. Appl. Phys. 66, 3798-3813 (1990).
[CrossRef]

J. Cryst. Growth (1)

B. Briat, F. Ramaz, B. Farid, K. V. Shcherbin, and H. J. von Bardeleben, "Spectroscopic characterization of photorefractive CdTe:Ge," J. Cryst. Growth 197, 724-728 (1999).
[CrossRef]

J. Opt. Soc. Am. B (6)

Opt. Commun. (3)

Y. Belaud, P. Delaye, J. C. Launay, and G. Roosen, "Photorefractive response of CdTe:V under ac electric field from 1 to 1.5μm," Opt. Commun. 105, 204-208 (1994).
[CrossRef]

B. Briat, K. Shcherbin, B. Farid, and F. Ramaz, "Optical and magnetooptical study of photorefractive germanium-doped cadmium telluride," Opt. Commun. 156, 337-340 (1998).
[CrossRef]

P. Delaye, L. A. de Montmorillon, I. Biaggio, J. C. Launay, and G. Roosen, "Wavelength dependent effective trap density in CdTe: evidence for the presence of two photorefractive species," Opt. Commun. 134, 580-590 (1997).
[CrossRef]

Opt. Lett. (2)

Ukr. J. Phys. Opt. (1)

K. Shcherbin, V. Danylyuk, and A. V. Khomenko, "Visualization of space-charge waves in photorefractive semiconductor using polarization technique," Ukr. J. Phys. Opt. 7, 164-170 (2006).
[CrossRef]

Other (2)

D.D.Nolte, ed., Photorefractive Effects and Material (Kluwer Academic, 1995).

P.Günter and J.-P.Huignard, eds., Photorefractive Materials and their Applications 1. Basic Effects (Springer, 2006).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Gain dependence on auxiliary light wavelength for different intensities of auxiliary illumination.

Fig. 3
Fig. 3

Spectral dependence of the total absorption α ( λ ) . Light absorption in the bands α n ( λ ) and α p ( λ ) results in electrons and holes generation, respectively.

Fig. 4
Fig. 4

Calculated gain dependences on auxiliary light wavelength for different intensities of auxiliary illumination.

Fig. 5
Fig. 5

Theoretical dependencies of the photorefractive grating phase on the wavelength of auxiliary illumination. 1 and 1 , I ( A ) = 4 mW cm 2 ; 2 and 2 , I ( A ) = 5.5 ; 3 and 3 , I ( A ) = 6.5 ; 4 and 4 , I ( A ) = 9.0 . Curves 1, 2, 3, and 4 are calculated for positive applied dc field E 0 = 5.6 kV cm ; curves 1 , 2 , 3 , and 4 are calculated for negative field E 0 = 5.6 kV cm .

Fig. 6
Fig. 6

Intensity ratio between the auxiliary and recording light intensities that yields the electron–hole resonance as a function of auxiliary light wavelength. Curve 1 is calculated without taking into account the thermal generation of free carriers using Eq. (6), while curve 2 is calculated assuming the thermal generation of electrons with a rate of 2 × 10 16 cm 3 s 1 .

Fig. 7
Fig. 7

Time dependences of the applied voltage and temporal modulation of the amplified beam intensity recorded with different intensities of the auxiliary light. (a) Applied voltage; (b) modulation of intensity, I A = 2.6 mW cm 2 ; (c) I A = 3.2 mW cm 2 ; (d) I A = 4.0 mW cm 2 .

Fig. 8
Fig. 8

Time-frequency spectra of the TWM gain modulation for different intensities of the auxiliary light I A .

Fig. 9
Fig. 9

Temporal average gain g 0 and modulation coefficients of the first and second harmonics as a function of auxiliary light wavelength.

Equations (10)

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E S C = i m G R n G R p G n ( 1 E q + 1 E D n i E 0 ) + G p ( 1 E q + 1 E D p + i E 0 ) ,
E q = e ε K N n N p N n + N p , E D n = E M n + E D , E D p = E M p + E D ,
E D = K k B T e , E M n = γ n N p μ n K , E M p = γ p N n μ p K .
α n ( λ ) = α n 0 exp [ ( λ λ n ) 2 Δ λ n 2 ] ,
α p ( λ ) = α p 0 exp [ ( λ λ p ) 2 Δ λ p 2 ] ,
G n , p = 1 2 π c [ α n , p ( λ A ) λ A I A + α n , p ( λ R ) λ R I R 0 ] ,
g = 1 + β 1 + β exp ( Γ L ) ,
Γ = 4 π n 3 r 41 Im ( E S C ) 3 λ R m ,
R = I A I R = α n ( λ R ) α p ( λ R ) α p ( λ A ) α n ( λ A ) λ A λ R .
g = g 0 [ 1 + k = 1 8 c k 2 sin ( 2 π k f 0 t 2 + φ k 2 ) ] ,

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