Abstract

Simultaneous measurements of the photorefractive and the absorptive grating gain components in GaAs:EL2 are made and are shown to display qualitative behavior consistent with linearized solutions of a two-carrier rate equation model. These two components, together with the linear absorption coefficient, permit determination of four independent material parameters, e.g., the ionized and the nonionized EL2 densities, the hole photoionization cross section (σh), and the electro-optic coefficient (r41). Data obtained at optical wavelengths of 0.96 and 1.06 µm indicate that σh and r41 are larger than published values.

© 1996 Optical Society of America

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  1. M. H. Garrett, G. D. Fogarty, G. D. Bacher, R. N. Schwartz, and B. A. Wechsler, “The photorefractive effect in ferroelectric oxides,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Norwell, Mass., 1995), pp. 116–153.
  2. K. Walsh, T. J. Hall, and R. E. Burge, “Influence of polarization state and absorption gratings on photorefractive two-wave mixing in GaAs,” Opt. Lett. 12, 1026–1028 (1987).
    [Crossref] [PubMed]
  3. G. C. Valley, S. W. McCahon, and M. B. Klein, “Photorefractive measurement of photoionization and recombination cross sections in InP:Fe,” J. Appl. Phys. 64, 6684–6689 (1988).
    [Crossref]
  4. J. C. Fabre, J. M. C. Jonathan, and G. Roosen, “4¯3m photorefractive materials in energy transfer experiments,” Opt. Commun. 65, 257–260 (1988).
    [Crossref]
  5. G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
    [Crossref]
  6. F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
    [Crossref]
  7. P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20 and BaTiO3 with shallow traps,” J. Opt. Soc. Am. B 8, 1053–1064 (1991).
    [Crossref]
  8. R. S. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, “Absorption gratings in photorefractive crystals with multiple levels,” J. Opt. Soc. Am. B 8, 1326–1332 (1991).
    [Crossref]
  9. M. Kaminska, M. Skowronski, J. Lagowski, J. M. Parsey, and H. C. Gatos, “Intracenter transitions in the dominant deep level (EL2) in GaAs,” Appl. Phys. Lett. 43, 302–304 (1983).
    [Crossref]
  10. P. Silverberg, P. Omling, and L. Samuelson, “Hole photoionization cross sections of EL2 in GaAs,” Appl. Phys. Lett. 52, 1689–1691 (1988).
    [Crossref]
  11. M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, “High-accuracy, high-reflectivity phase conjugation at 1.06 µm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am. B 5, 2467–2472 (1988).
    [Crossref]
  12. G. Vincent, D. Bois, and A. Chantre, “Photoelectric memory effect in GaAs,” J. Appl. Phys. 53, 3643–3649 (1982).
    [Crossref]
  13. D. E. Aspnes, “Optical Functions,” in Properties of Gallium Arsenide, 2nd ed. (Institute of Electrical Engineers, London, 1990), p. 158.
  14. A. Yariv and P. Yeh, Optical Waves in Crystals, 1st ed. (Wiley, New York, 1984), Chap. 7, p. 230.
  15. D. J. Robbins, “Electro-optic properties,” in Properties of Gallium Arsenide, 2nd ed. (Institute of Electrical Engineers, London, 1990), p. 166.
  16. G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump–probe technique to measure deep-level, free-carrier, and two photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
    [Crossref]

1991 (2)

1989 (1)

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump–probe technique to measure deep-level, free-carrier, and two photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[Crossref]

1988 (4)

M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, “High-accuracy, high-reflectivity phase conjugation at 1.06 µm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am. B 5, 2467–2472 (1988).
[Crossref]

P. Silverberg, P. Omling, and L. Samuelson, “Hole photoionization cross sections of EL2 in GaAs,” Appl. Phys. Lett. 52, 1689–1691 (1988).
[Crossref]

G. C. Valley, S. W. McCahon, and M. B. Klein, “Photorefractive measurement of photoionization and recombination cross sections in InP:Fe,” J. Appl. Phys. 64, 6684–6689 (1988).
[Crossref]

J. C. Fabre, J. M. C. Jonathan, and G. Roosen, “4¯3m photorefractive materials in energy transfer experiments,” Opt. Commun. 65, 257–260 (1988).
[Crossref]

1987 (1)

1986 (2)

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
[Crossref]

G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
[Crossref]

1983 (1)

M. Kaminska, M. Skowronski, J. Lagowski, J. M. Parsey, and H. C. Gatos, “Intracenter transitions in the dominant deep level (EL2) in GaAs,” Appl. Phys. Lett. 43, 302–304 (1983).
[Crossref]

1982 (1)

G. Vincent, D. Bois, and A. Chantre, “Photoelectric memory effect in GaAs,” J. Appl. Phys. 53, 3643–3649 (1982).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, “Optical Functions,” in Properties of Gallium Arsenide, 2nd ed. (Institute of Electrical Engineers, London, 1990), p. 158.

Bacher, G. D.

R. S. Cudney, R. M. Pierce, G. D. Bacher, and J. Feinberg, “Absorption gratings in photorefractive crystals with multiple levels,” J. Opt. Soc. Am. B 8, 1326–1332 (1991).
[Crossref]

M. H. Garrett, G. D. Fogarty, G. D. Bacher, R. N. Schwartz, and B. A. Wechsler, “The photorefractive effect in ferroelectric oxides,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Norwell, Mass., 1995), pp. 116–153.

Boggess, T. F.

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump–probe technique to measure deep-level, free-carrier, and two photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[Crossref]

M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, “High-accuracy, high-reflectivity phase conjugation at 1.06 µm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am. B 5, 2467–2472 (1988).
[Crossref]

Bois, D.

G. Vincent, D. Bois, and A. Chantre, “Photoelectric memory effect in GaAs,” J. Appl. Phys. 53, 3643–3649 (1982).
[Crossref]

Burge, R. E.

Chantre, A.

G. Vincent, D. Bois, and A. Chantre, “Photoelectric memory effect in GaAs,” J. Appl. Phys. 53, 3643–3649 (1982).
[Crossref]

Cudney, R. S.

Dubard, J.

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump–probe technique to measure deep-level, free-carrier, and two photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[Crossref]

Fabre, J. C.

J. C. Fabre, J. M. C. Jonathan, and G. Roosen, “4¯3m photorefractive materials in energy transfer experiments,” Opt. Commun. 65, 257–260 (1988).
[Crossref]

Feinberg, J.

Fogarty, G. D.

M. H. Garrett, G. D. Fogarty, G. D. Bacher, R. N. Schwartz, and B. A. Wechsler, “The photorefractive effect in ferroelectric oxides,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Norwell, Mass., 1995), pp. 116–153.

Garrett, M. H.

M. H. Garrett, G. D. Fogarty, G. D. Bacher, R. N. Schwartz, and B. A. Wechsler, “The photorefractive effect in ferroelectric oxides,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Norwell, Mass., 1995), pp. 116–153.

Gatos, H. C.

M. Kaminska, M. Skowronski, J. Lagowski, J. M. Parsey, and H. C. Gatos, “Intracenter transitions in the dominant deep level (EL2) in GaAs,” Appl. Phys. Lett. 43, 302–304 (1983).
[Crossref]

Hall, T. J.

Hellwarth, R. W.

Jonathan, J. M. C.

J. C. Fabre, J. M. C. Jonathan, and G. Roosen, “4¯3m photorefractive materials in energy transfer experiments,” Opt. Commun. 65, 257–260 (1988).
[Crossref]

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
[Crossref]

Kaminska, M.

M. Kaminska, M. Skowronski, J. Lagowski, J. M. Parsey, and H. C. Gatos, “Intracenter transitions in the dominant deep level (EL2) in GaAs,” Appl. Phys. Lett. 43, 302–304 (1983).
[Crossref]

Klein, M. B.

M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, “High-accuracy, high-reflectivity phase conjugation at 1.06 µm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am. B 5, 2467–2472 (1988).
[Crossref]

G. C. Valley, S. W. McCahon, and M. B. Klein, “Photorefractive measurement of photoionization and recombination cross sections in InP:Fe,” J. Appl. Phys. 64, 6684–6689 (1988).
[Crossref]

Lagowski, J.

M. Kaminska, M. Skowronski, J. Lagowski, J. M. Parsey, and H. C. Gatos, “Intracenter transitions in the dominant deep level (EL2) in GaAs,” Appl. Phys. Lett. 43, 302–304 (1983).
[Crossref]

Mahgerefteh, D.

McCahon, S. W.

G. C. Valley, S. W. McCahon, and M. B. Klein, “Photorefractive measurement of photoionization and recombination cross sections in InP:Fe,” J. Appl. Phys. 64, 6684–6689 (1988).
[Crossref]

M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, “High-accuracy, high-reflectivity phase conjugation at 1.06 µm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am. B 5, 2467–2472 (1988).
[Crossref]

Omling, P.

P. Silverberg, P. Omling, and L. Samuelson, “Hole photoionization cross sections of EL2 in GaAs,” Appl. Phys. Lett. 52, 1689–1691 (1988).
[Crossref]

Parsey, J. M.

M. Kaminska, M. Skowronski, J. Lagowski, J. M. Parsey, and H. C. Gatos, “Intracenter transitions in the dominant deep level (EL2) in GaAs,” Appl. Phys. Lett. 43, 302–304 (1983).
[Crossref]

Pierce, R. M.

Robbins, D. J.

D. J. Robbins, “Electro-optic properties,” in Properties of Gallium Arsenide, 2nd ed. (Institute of Electrical Engineers, London, 1990), p. 166.

Roosen, G.

J. C. Fabre, J. M. C. Jonathan, and G. Roosen, “4¯3m photorefractive materials in energy transfer experiments,” Opt. Commun. 65, 257–260 (1988).
[Crossref]

Samuelson, L.

P. Silverberg, P. Omling, and L. Samuelson, “Hole photoionization cross sections of EL2 in GaAs,” Appl. Phys. Lett. 52, 1689–1691 (1988).
[Crossref]

Schwartz, R. N.

M. H. Garrett, G. D. Fogarty, G. D. Bacher, R. N. Schwartz, and B. A. Wechsler, “The photorefractive effect in ferroelectric oxides,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Norwell, Mass., 1995), pp. 116–153.

Silverberg, P.

P. Silverberg, P. Omling, and L. Samuelson, “Hole photoionization cross sections of EL2 in GaAs,” Appl. Phys. Lett. 52, 1689–1691 (1988).
[Crossref]

Skowronski, M.

M. Kaminska, M. Skowronski, J. Lagowski, J. M. Parsey, and H. C. Gatos, “Intracenter transitions in the dominant deep level (EL2) in GaAs,” Appl. Phys. Lett. 43, 302–304 (1983).
[Crossref]

Smirl, A. L.

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump–probe technique to measure deep-level, free-carrier, and two photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[Crossref]

Strohkendl, F. P.

Tayebati, P.

Valley, G. C.

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump–probe technique to measure deep-level, free-carrier, and two photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[Crossref]

M. B. Klein, S. W. McCahon, T. F. Boggess, and G. C. Valley, “High-accuracy, high-reflectivity phase conjugation at 1.06 µm by four-wave mixing in photorefractive gallium arsenide,” J. Opt. Soc. Am. B 5, 2467–2472 (1988).
[Crossref]

G. C. Valley, S. W. McCahon, and M. B. Klein, “Photorefractive measurement of photoionization and recombination cross sections in InP:Fe,” J. Appl. Phys. 64, 6684–6689 (1988).
[Crossref]

G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
[Crossref]

Vincent, G.

G. Vincent, D. Bois, and A. Chantre, “Photoelectric memory effect in GaAs,” J. Appl. Phys. 53, 3643–3649 (1982).
[Crossref]

Walsh, K.

Wechsler, B. A.

M. H. Garrett, G. D. Fogarty, G. D. Bacher, R. N. Schwartz, and B. A. Wechsler, “The photorefractive effect in ferroelectric oxides,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Norwell, Mass., 1995), pp. 116–153.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals, 1st ed. (Wiley, New York, 1984), Chap. 7, p. 230.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals, 1st ed. (Wiley, New York, 1984), Chap. 7, p. 230.

Appl. Phys. Lett. (2)

M. Kaminska, M. Skowronski, J. Lagowski, J. M. Parsey, and H. C. Gatos, “Intracenter transitions in the dominant deep level (EL2) in GaAs,” Appl. Phys. Lett. 43, 302–304 (1983).
[Crossref]

P. Silverberg, P. Omling, and L. Samuelson, “Hole photoionization cross sections of EL2 in GaAs,” Appl. Phys. Lett. 52, 1689–1691 (1988).
[Crossref]

J. Appl. Phys. (4)

G. C. Valley, T. F. Boggess, J. Dubard, and A. L. Smirl, “Picosecond pump–probe technique to measure deep-level, free-carrier, and two photon cross sections in GaAs,” J. Appl. Phys. 66, 2407–2413 (1989).
[Crossref]

G. Vincent, D. Bois, and A. Chantre, “Photoelectric memory effect in GaAs,” J. Appl. Phys. 53, 3643–3649 (1982).
[Crossref]

G. C. Valley, S. W. McCahon, and M. B. Klein, “Photorefractive measurement of photoionization and recombination cross sections in InP:Fe,” J. Appl. Phys. 64, 6684–6689 (1988).
[Crossref]

G. C. Valley, “Simultaneous electron/hole transport in photorefractive materials,” J. Appl. Phys. 59, 3363–3366 (1986).
[Crossref]

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

J. C. Fabre, J. M. C. Jonathan, and G. Roosen, “4¯3m photorefractive materials in energy transfer experiments,” Opt. Commun. 65, 257–260 (1988).
[Crossref]

Opt. Lett. (2)

Other (4)

M. H. Garrett, G. D. Fogarty, G. D. Bacher, R. N. Schwartz, and B. A. Wechsler, “The photorefractive effect in ferroelectric oxides,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Norwell, Mass., 1995), pp. 116–153.

D. E. Aspnes, “Optical Functions,” in Properties of Gallium Arsenide, 2nd ed. (Institute of Electrical Engineers, London, 1990), p. 158.

A. Yariv and P. Yeh, Optical Waves in Crystals, 1st ed. (Wiley, New York, 1984), Chap. 7, p. 230.

D. J. Robbins, “Electro-optic properties,” in Properties of Gallium Arsenide, 2nd ed. (Institute of Electrical Engineers, London, 1990), p. 166.

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Figures (5)

Fig. 1
Fig. 1

Crystal configuration used in the two-beam coupling experiment. The angle ϕ indicates the clockwise rotation of the polarizations from the vertical.

Fig. 2
Fig. 2

Two-beam coupling gain as a function of polarization angle, ϕ, measured at a grating spacing of 1.64 µm. The curve is a best fit to the gain expression described in the text.

Fig. 3
Fig. 3

Induced transparency (circles) measured with cross-polarized beams and the sum of absorptive and photorefractive gain (squares) measured with copolarized beams set at ϕ = 90°. The line is a linear least-squares fit to the induced transparency data.

Fig. 4
Fig. 4

(a) Measured absorptive grating gain (squares) along with the best fit (curve), obtained as described in the text. (b) Illustration of the linear dependence of 1/Λ2Γa versus 1/Λ2 as anticipated from theory. The linearity at small values of 1/Λ2 indicates that the assumptions made regarding the electron–hole competition factor are valid for this sample.

Fig. 5
Fig. 5

(a) Measured photorefractive grating gain (squares) along with the best fit (curve), obtained as described in text. (b) Illustration of the linear dependence of 1/ΛΓp versus 1/Λ2 as anticipated from theory. Consistent with the absorptive case, the linearity at small values of 1/Λ2 indicates that the assumptions made regarding the electron–hole competition factor are valid for this sample.

Tables (2)

Tables Icon

Table 1 Comparison of Best-Fit Values from These Measurements (λ0=0.96 µm) with Those Obtained by Other Techniques

Tables Icon

Table 2 Comparison of Best-Fit Values from These Measurements (λ 0=1.06 µm) with Those Obtained by Other Techniquesa

Equations (14)

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

Γ = Γ i + f ( θ , ϕ ) [ Γ a + Γ p g ( θ , ϕ ) ] .
g ( θ , ϕ ) = ( cos 2   ϕ + sin 2   ϕ   sin 2   θ ) .
f ( θ , ϕ ) = ( cos 2   ϕ + sin 2   ϕ   cos   2 θ ) .
Γ p = b r 41 N e Λ 1 + a N e Λ 2 ξ ,
ξ = η e σ e N d η h σ h N a η e σ e N d + η h σ h N a ,
Γ a = ( σ e σ h ) N e 1 + a N e Λ 2 ξ .
Γ i = ( σ e σ h ) η e σ e N d γ e N a η h σ h N a γ h N d I p ћ ω ,
Γ = cos   θ l ln I s   ( with pump ) I s ( without pump ) ,
1 Λ Γ p = x 1 + x 2 1 Λ 2 ,
1 Λ 2 Γ a = x 3 + x 4 1 Λ 2 ,
r 41 3 + 2 σ e x 4 b x 2 α a x 4 2 b x 1 a b x 1 r 41 2 + α a 3 x 4 2 b 3 x 1 3 = 0 ,
1 N d = x 2 2 a x 1 1 + a b r 41 x 1 2 b r 41 a x 4 ,
1 N a = x 2 2 a x 1 1 a b r 41 x 1 + 2 b r 41 a x 4 ,
σ h = x 2 4 1 + a b r 41 x 1 α a x 1 1 a b r 41 x 1 + 2 b r 41 x 4 ,

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