Abstract

We present two-wave mixing results obtained with CdTe:V photorefractive crystals under an external dc or low-frequency square-shaped periodic electric field. The majority photorefractive carriers are holes at 1.32 and 1.54 μm, whereas electrons dominate slightly at 1.048 μm. At this wavelength an intensity-dependent resonant gain enhancement is observed in the presence of a dc field. The effective trap densities are near 1015 cm−3. The highest gains (to as high as 11 cm−1 for a field amplitude of 15 kV/cm at 1.32 μm) are obtained with a square-shaped periodic field at an optimum frequency F0. The dependence of F0 on the different experimental parameters is presented. A two-level model in which the secondary level has a thermal emission rate much larger than the principal one qualitatively describes this nonstandard frequency behavior.

© 1994 Optical Society of America

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  1. A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, and A. A. Ballman, “Four-wave mixing in semi-insulating InP and GaAs using the photorefractive effect,” Appl. Phys. Lett. 44, 948 (1984).
    [CrossRef]
  2. M. B. Klein, “Beam coupling in undoped GaAs at 1.06 μ m using the photorefractive effect,” Opt. Lett. 9, 350 (1984).
    [CrossRef] [PubMed]
  3. R. B. Bylsma, P. M. Bridenbaugh, D. H. Olson, and A. M. Glass, “Photorefractive properties of doped cadmium telluride,” Appl. Phys. Lett. 51, 889 (1987).
    [CrossRef]
  4. S. G. Odoulov, K. V. Shcherbin, A. N. Shumelyuk, P. M. Fochuk, and O. E. Panchuk, “Electron–hole competition in dynamic hologram recording in cadmium telluride,” in Technical Digest of Meeting on Photorefractive Materials, Effects, and Devices (Ukrainian Academy of Sciences, Kiev, 1993), p. 293.
  5. M. Ziari, W. H. Steier, P. M. Ranon, S. Trivedi, and M. B. Klein, “Photorefractivity in vanadium-doped ZnTe,” Appl. Phys. Lett. 60, 1052 (1992).
    [CrossRef]
  6. A. Partovi, J. Millerd, A. M. Garmire, M. Ziari, W. H. Steier, S. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μ m in CdTe:V,” Appl. Phys. Lett. 57, 846 (1990).
    [CrossRef]
  7. M. Ziari, W. H. Steier, P. M. Ranon, M. B. Klein, and S. Trivedi, “Enhancement of the photorefractive gain at 1.3–1.5μm in CdTe using alternating electric fields,” J. Opt. Soc. Am. B 9, 1461 (1992).
    [CrossRef]
  8. K. Guergouri, R. Triboulet, A. Tromson-Carli, and Y. Marfaing, “Solution hardening and dislocation density reduction in CdTe crystals by Zn addition,” J. Cryst. Growth 101, 131 (1990).
  9. D. Imhoff, A. Zozime, and R. Triboulet, “Zn influence on the plasticity of Cd0.96Zn0.04Te,” J. Phys. C 1, 1841 (1991).
  10. R. Triboulet and Y. Marfaing, “Growth of high purity CdTe single crystals by vertical zone melting,” J. Electrochem. Soc. 120, 1260 (1973).
    [CrossRef]
  11. V. I. Sokolov, “A universal trend of the variation in the 3d-impurity (0/+) and (0/−) levels in A2B6compounds,” Sov. Phys. Solid State 29, 1061 (1987).
  12. W. Giriat and J. K. Furdyna, “Crystal structure, composition and materials preparation of diluted magnetic semiconductors,” in Semiconductors and Semimetals (Academic, New York, 1988), Vol. 25, pp. 1–34.
    [CrossRef]
  13. J. Strait, J. D. Reed, and N. V. Kukhtarev, “Orientational dependence of photorefractive two-beam coupling in InP:Fe,” Opt. Lett. 15, 209 (1990).
    [CrossRef] [PubMed]
  14. G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: A new mechanism of resonance,” J. Appl. Phys. 66, 3798 (1989).
    [CrossRef]
  15. A. M. Glass, M. B. Klein, and G. C. Valley, “Photorefractive determination of the sign of photocarriers in InP and GaAs,” Electron. Lett. 21, 220 (1985).
    [CrossRef]
  16. J. C. Launay, V. Mazoyer, J. P. Zielinger, Z. Guellil, P. Delaye, and G. Roosen, “Growth, spectroscopic and photorefractive investigation of vanadium-doped cadmium telluride,” Appl. Phys. A 55, 33 (1992).
    [CrossRef]
  17. M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
    [CrossRef]
  18. K. Walsh, A. K. Powell, C. Stace, and T. J. Hall, “Techniques for the enhancement of space-charge fields in photorefractive materials,” J. Opt. Soc. Am. B 7, 288 (1990).
    [CrossRef]
  19. N. Wolffer and P. Gravey, “Two-wave mixing in photorefractive InP:Fe with an external alternative field,” Ann. Phys. (NY) 16, 143 (1991).
  20. S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292 (1985).
    [CrossRef]
  21. R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μ m by two wave mixing in InP:Fe,” Electron. Lett. 24, 360 (1988).
    [CrossRef]
  22. G. Pauliat, A. Villing, J.-C. Launay, and G. Roosen, “Optical measurements of charge-carrier mobilities in photorefractive sillenite crystals,” J. Opt. Soc. Am. B 7, 1481 (1990).
    [CrossRef]
  23. P. Mathey, G. Pauliat, J.-C. Launay, and G. Roosen, “Overcoming the trap density limitation in photorefractive two-beam coupling by applying pulsed electric fields,” Opt. Commun. 82, 101 (1991).
    [CrossRef]
  24. K. Turki, G. Picoli, and J.-E. Viallet, “Behavior of InP:Fe under high electric field,” J. Appl. Phys. 73, 8340 (1993).
    [CrossRef]
  25. P. Tayebati and D. Mahgerefteh, “Theory of the photorefractive effect for Bi12SiO20and BaTiO3with shallow traps,” J. Opt. Soc. Am. B 8, 1053 (1990).
    [CrossRef]
  26. R. S. Rana, D. D. Nolte, R. Steldt, and E. M. Monberg, “Temperature dependence of the photorefractive effect in InP:Fe: role of multiple defects,” J. Opt. Soc. Am. B 9, 1614 (1992).
    [CrossRef]
  27. P. Nouchi, J. P. Partanen, and R. W. Hellwarth, “Conduction band and trap-limited mobilities in Bi12SiO20,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 236.
  28. G. Bremond, Institut National des Sciences Appliquées de Lyon, Unité de Recherche Associée No. 358 du Centre National de la Recherche Scientifique, 69621 Villeurbanne Cedex, France (personal communication, 1993).
  29. P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

1993 (1)

K. Turki, G. Picoli, and J.-E. Viallet, “Behavior of InP:Fe under high electric field,” J. Appl. Phys. 73, 8340 (1993).
[CrossRef]

1992 (4)

R. S. Rana, D. D. Nolte, R. Steldt, and E. M. Monberg, “Temperature dependence of the photorefractive effect in InP:Fe: role of multiple defects,” J. Opt. Soc. Am. B 9, 1614 (1992).
[CrossRef]

M. Ziari, W. H. Steier, P. M. Ranon, S. Trivedi, and M. B. Klein, “Photorefractivity in vanadium-doped ZnTe,” Appl. Phys. Lett. 60, 1052 (1992).
[CrossRef]

M. Ziari, W. H. Steier, P. M. Ranon, M. B. Klein, and S. Trivedi, “Enhancement of the photorefractive gain at 1.3–1.5μm in CdTe using alternating electric fields,” J. Opt. Soc. Am. B 9, 1461 (1992).
[CrossRef]

J. C. Launay, V. Mazoyer, J. P. Zielinger, Z. Guellil, P. Delaye, and G. Roosen, “Growth, spectroscopic and photorefractive investigation of vanadium-doped cadmium telluride,” Appl. Phys. A 55, 33 (1992).
[CrossRef]

1991 (3)

N. Wolffer and P. Gravey, “Two-wave mixing in photorefractive InP:Fe with an external alternative field,” Ann. Phys. (NY) 16, 143 (1991).

D. Imhoff, A. Zozime, and R. Triboulet, “Zn influence on the plasticity of Cd0.96Zn0.04Te,” J. Phys. C 1, 1841 (1991).

P. Mathey, G. Pauliat, J.-C. Launay, and G. Roosen, “Overcoming the trap density limitation in photorefractive two-beam coupling by applying pulsed electric fields,” Opt. Commun. 82, 101 (1991).
[CrossRef]

1990 (6)

1989 (1)

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: A new mechanism of resonance,” J. Appl. Phys. 66, 3798 (1989).
[CrossRef]

1988 (1)

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μ m by two wave mixing in InP:Fe,” Electron. Lett. 24, 360 (1988).
[CrossRef]

1987 (2)

R. B. Bylsma, P. M. Bridenbaugh, D. H. Olson, and A. M. Glass, “Photorefractive properties of doped cadmium telluride,” Appl. Phys. Lett. 51, 889 (1987).
[CrossRef]

V. I. Sokolov, “A universal trend of the variation in the 3d-impurity (0/+) and (0/−) levels in A2B6compounds,” Sov. Phys. Solid State 29, 1061 (1987).

1985 (3)

A. M. Glass, M. B. Klein, and G. C. Valley, “Photorefractive determination of the sign of photocarriers in InP and GaAs,” Electron. Lett. 21, 220 (1985).
[CrossRef]

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

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
[CrossRef]

1984 (2)

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, and A. A. Ballman, “Four-wave mixing in semi-insulating InP and GaAs using the photorefractive effect,” Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

M. B. Klein, “Beam coupling in undoped GaAs at 1.06 μ m using the photorefractive effect,” Opt. Lett. 9, 350 (1984).
[CrossRef] [PubMed]

1973 (1)

R. Triboulet and Y. Marfaing, “Growth of high purity CdTe single crystals by vertical zone melting,” J. Electrochem. Soc. 120, 1260 (1973).
[CrossRef]

Aoudia, A.

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Ballman, A. A.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, and A. A. Ballman, “Four-wave mixing in semi-insulating InP and GaAs using the photorefractive effect,” Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

Bremond, G.

G. Bremond, Institut National des Sciences Appliquées de Lyon, Unité de Recherche Associée No. 358 du Centre National de la Recherche Scientifique, 69621 Villeurbanne Cedex, France (personal communication, 1993).

Bridenbaugh, P. M.

R. B. Bylsma, P. M. Bridenbaugh, D. H. Olson, and A. M. Glass, “Photorefractive properties of doped cadmium telluride,” Appl. Phys. Lett. 51, 889 (1987).
[CrossRef]

Busch, M. C.

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Bylsma, R. B.

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μ m by two wave mixing in InP:Fe,” Electron. Lett. 24, 360 (1988).
[CrossRef]

R. B. Bylsma, P. M. Bridenbaugh, D. H. Olson, and A. M. Glass, “Photorefractive properties of doped cadmium telluride,” Appl. Phys. Lett. 51, 889 (1987).
[CrossRef]

Delaye, P.

J. C. Launay, V. Mazoyer, J. P. Zielinger, Z. Guellil, P. Delaye, and G. Roosen, “Growth, spectroscopic and photorefractive investigation of vanadium-doped cadmium telluride,” Appl. Phys. A 55, 33 (1992).
[CrossRef]

Fochuk, P. M.

S. G. Odoulov, K. V. Shcherbin, A. N. Shumelyuk, P. M. Fochuk, and O. E. Panchuk, “Electron–hole competition in dynamic hologram recording in cadmium telluride,” in Technical Digest of Meeting on Photorefractive Materials, Effects, and Devices (Ukrainian Academy of Sciences, Kiev, 1993), p. 293.

Furdyna, J. K.

W. Giriat and J. K. Furdyna, “Crystal structure, composition and materials preparation of diluted magnetic semiconductors,” in Semiconductors and Semimetals (Academic, New York, 1988), Vol. 25, pp. 1–34.
[CrossRef]

Garmire, A. M.

A. Partovi, J. Millerd, A. M. Garmire, M. Ziari, W. H. Steier, S. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μ m in CdTe:V,” Appl. Phys. Lett. 57, 846 (1990).
[CrossRef]

Giriat, W.

W. Giriat and J. K. Furdyna, “Crystal structure, composition and materials preparation of diluted magnetic semiconductors,” in Semiconductors and Semimetals (Academic, New York, 1988), Vol. 25, pp. 1–34.
[CrossRef]

Glass, A. M.

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μ m by two wave mixing in InP:Fe,” Electron. Lett. 24, 360 (1988).
[CrossRef]

R. B. Bylsma, P. M. Bridenbaugh, D. H. Olson, and A. M. Glass, “Photorefractive properties of doped cadmium telluride,” Appl. Phys. Lett. 51, 889 (1987).
[CrossRef]

A. M. Glass, M. B. Klein, and G. C. Valley, “Photorefractive determination of the sign of photocarriers in InP and GaAs,” Electron. Lett. 21, 220 (1985).
[CrossRef]

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, and A. A. Ballman, “Four-wave mixing in semi-insulating InP and GaAs using the photorefractive effect,” Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

Gravey, P.

N. Wolffer and P. Gravey, “Two-wave mixing in photorefractive InP:Fe with an external alternative field,” Ann. Phys. (NY) 16, 143 (1991).

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: A new mechanism of resonance,” J. Appl. Phys. 66, 3798 (1989).
[CrossRef]

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Guellil, Z.

J. C. Launay, V. Mazoyer, J. P. Zielinger, Z. Guellil, P. Delaye, and G. Roosen, “Growth, spectroscopic and photorefractive investigation of vanadium-doped cadmium telluride,” Appl. Phys. A 55, 33 (1992).
[CrossRef]

Guergouri, K.

K. Guergouri, R. Triboulet, A. Tromson-Carli, and Y. Marfaing, “Solution hardening and dislocation density reduction in CdTe crystals by Zn addition,” J. Cryst. Growth 101, 131 (1990).

Hage-Ali, M.

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Hall, T. J.

Hellwarth, R. W.

P. Nouchi, J. P. Partanen, and R. W. Hellwarth, “Conduction band and trap-limited mobilities in Bi12SiO20,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 236.

Imhoff, D.

D. Imhoff, A. Zozime, and R. Triboulet, “Zn influence on the plasticity of Cd0.96Zn0.04Te,” J. Phys. C 1, 1841 (1991).

Johnson, A. M.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, and A. A. Ballman, “Four-wave mixing in semi-insulating InP and GaAs using the photorefractive effect,” Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

Klein, M. B.

M. Ziari, W. H. Steier, P. M. Ranon, M. B. Klein, and S. Trivedi, “Enhancement of the photorefractive gain at 1.3–1.5μm in CdTe using alternating electric fields,” J. Opt. Soc. Am. B 9, 1461 (1992).
[CrossRef]

M. Ziari, W. H. Steier, P. M. Ranon, S. Trivedi, and M. B. Klein, “Photorefractivity in vanadium-doped ZnTe,” Appl. Phys. Lett. 60, 1052 (1992).
[CrossRef]

A. Partovi, J. Millerd, A. M. Garmire, M. Ziari, W. H. Steier, S. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μ m in CdTe:V,” Appl. Phys. Lett. 57, 846 (1990).
[CrossRef]

A. M. Glass, M. B. Klein, and G. C. Valley, “Photorefractive determination of the sign of photocarriers in InP and GaAs,” Electron. Lett. 21, 220 (1985).
[CrossRef]

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
[CrossRef]

M. B. Klein, “Beam coupling in undoped GaAs at 1.06 μ m using the photorefractive effect,” Opt. Lett. 9, 350 (1984).
[CrossRef] [PubMed]

Koebel, J. M.

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Kukhtarev, N. V.

Launay, J. C.

J. C. Launay, V. Mazoyer, J. P. Zielinger, Z. Guellil, P. Delaye, and G. Roosen, “Growth, spectroscopic and photorefractive investigation of vanadium-doped cadmium telluride,” Appl. Phys. A 55, 33 (1992).
[CrossRef]

Launay, J.-C.

P. Mathey, G. Pauliat, J.-C. Launay, and G. Roosen, “Overcoming the trap density limitation in photorefractive two-beam coupling by applying pulsed electric fields,” Opt. Commun. 82, 101 (1991).
[CrossRef]

G. Pauliat, A. Villing, J.-C. Launay, and G. Roosen, “Optical measurements of charge-carrier mobilities in photorefractive sillenite crystals,” J. Opt. Soc. Am. B 7, 1481 (1990).
[CrossRef]

Mahgerefteh, D.

Marfaing, Y.

K. Guergouri, R. Triboulet, A. Tromson-Carli, and Y. Marfaing, “Solution hardening and dislocation density reduction in CdTe crystals by Zn addition,” J. Cryst. Growth 101, 131 (1990).

R. Triboulet and Y. Marfaing, “Growth of high purity CdTe single crystals by vertical zone melting,” J. Electrochem. Soc. 120, 1260 (1973).
[CrossRef]

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Martel, G.

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Mathey, P.

P. Mathey, G. Pauliat, J.-C. Launay, and G. Roosen, “Overcoming the trap density limitation in photorefractive two-beam coupling by applying pulsed electric fields,” Opt. Commun. 82, 101 (1991).
[CrossRef]

Mazoyer, V.

J. C. Launay, V. Mazoyer, J. P. Zielinger, Z. Guellil, P. Delaye, and G. Roosen, “Growth, spectroscopic and photorefractive investigation of vanadium-doped cadmium telluride,” Appl. Phys. A 55, 33 (1992).
[CrossRef]

Millerd, J.

A. Partovi, J. Millerd, A. M. Garmire, M. Ziari, W. H. Steier, S. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μ m in CdTe:V,” Appl. Phys. Lett. 57, 846 (1990).
[CrossRef]

Moisan, J.-Y.

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Monberg, E. M.

Nolte, D. D.

Nouchi, P.

P. Nouchi, J. P. Partanen, and R. W. Hellwarth, “Conduction band and trap-limited mobilities in Bi12SiO20,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 236.

Odoulov, S. G.

S. G. Odoulov, K. V. Shcherbin, A. N. Shumelyuk, P. M. Fochuk, and O. E. Panchuk, “Electron–hole competition in dynamic hologram recording in cadmium telluride,” in Technical Digest of Meeting on Photorefractive Materials, Effects, and Devices (Ukrainian Academy of Sciences, Kiev, 1993), p. 293.

Olson, D. H.

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μ m by two wave mixing in InP:Fe,” Electron. Lett. 24, 360 (1988).
[CrossRef]

R. B. Bylsma, P. M. Bridenbaugh, D. H. Olson, and A. M. Glass, “Photorefractive properties of doped cadmium telluride,” Appl. Phys. Lett. 51, 889 (1987).
[CrossRef]

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, and A. A. Ballman, “Four-wave mixing in semi-insulating InP and GaAs using the photorefractive effect,” Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

Ozkul, C.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: A new mechanism of resonance,” J. Appl. Phys. 66, 3798 (1989).
[CrossRef]

Panchuk, O. E.

S. G. Odoulov, K. V. Shcherbin, A. N. Shumelyuk, P. M. Fochuk, and O. E. Panchuk, “Electron–hole competition in dynamic hologram recording in cadmium telluride,” in Technical Digest of Meeting on Photorefractive Materials, Effects, and Devices (Ukrainian Academy of Sciences, Kiev, 1993), p. 293.

Partanen, J. P.

P. Nouchi, J. P. Partanen, and R. W. Hellwarth, “Conduction band and trap-limited mobilities in Bi12SiO20,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 236.

Partovi, A.

A. Partovi, J. Millerd, A. M. Garmire, M. Ziari, W. H. Steier, S. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μ m in CdTe:V,” Appl. Phys. Lett. 57, 846 (1990).
[CrossRef]

Pauliat, G.

P. Mathey, G. Pauliat, J.-C. Launay, and G. Roosen, “Overcoming the trap density limitation in photorefractive two-beam coupling by applying pulsed electric fields,” Opt. Commun. 82, 101 (1991).
[CrossRef]

G. Pauliat, A. Villing, J.-C. Launay, and G. Roosen, “Optical measurements of charge-carrier mobilities in photorefractive sillenite crystals,” J. Opt. Soc. Am. B 7, 1481 (1990).
[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 (1985).
[CrossRef]

Picoli, G.

K. Turki, G. Picoli, and J.-E. Viallet, “Behavior of InP:Fe under high electric field,” J. Appl. Phys. 73, 8340 (1993).
[CrossRef]

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: A new mechanism of resonance,” J. Appl. Phys. 66, 3798 (1989).
[CrossRef]

Powell, A. K.

Rana, R. S.

Ranon, P. M.

M. Ziari, W. H. Steier, P. M. Ranon, M. B. Klein, and S. Trivedi, “Enhancement of the photorefractive gain at 1.3–1.5μm in CdTe using alternating electric fields,” J. Opt. Soc. Am. B 9, 1461 (1992).
[CrossRef]

M. Ziari, W. H. Steier, P. M. Ranon, S. Trivedi, and M. B. Klein, “Photorefractivity in vanadium-doped ZnTe,” Appl. Phys. Lett. 60, 1052 (1992).
[CrossRef]

Reed, J. D.

Roosen, G.

J. C. Launay, V. Mazoyer, J. P. Zielinger, Z. Guellil, P. Delaye, and G. Roosen, “Growth, spectroscopic and photorefractive investigation of vanadium-doped cadmium telluride,” Appl. Phys. A 55, 33 (1992).
[CrossRef]

P. Mathey, G. Pauliat, J.-C. Launay, and G. Roosen, “Overcoming the trap density limitation in photorefractive two-beam coupling by applying pulsed electric fields,” Opt. Commun. 82, 101 (1991).
[CrossRef]

G. Pauliat, A. Villing, J.-C. Launay, and G. Roosen, “Optical measurements of charge-carrier mobilities in photorefractive sillenite crystals,” J. Opt. Soc. Am. B 7, 1481 (1990).
[CrossRef]

Shcherbin, K. V.

S. G. Odoulov, K. V. Shcherbin, A. N. Shumelyuk, P. M. Fochuk, and O. E. Panchuk, “Electron–hole competition in dynamic hologram recording in cadmium telluride,” in Technical Digest of Meeting on Photorefractive Materials, Effects, and Devices (Ukrainian Academy of Sciences, Kiev, 1993), p. 293.

Shumelyuk, A. N.

S. G. Odoulov, K. V. Shcherbin, A. N. Shumelyuk, P. M. Fochuk, and O. E. Panchuk, “Electron–hole competition in dynamic hologram recording in cadmium telluride,” in Technical Digest of Meeting on Photorefractive Materials, Effects, and Devices (Ukrainian Academy of Sciences, Kiev, 1993), p. 293.

Siffert, P.

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Simpson, W.

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, and A. A. Ballman, “Four-wave mixing in semi-insulating InP and GaAs using the photorefractive effect,” Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

Sokolov, V. I.

V. I. Sokolov, “A universal trend of the variation in the 3d-impurity (0/+) and (0/−) levels in A2B6compounds,” Sov. Phys. Solid State 29, 1061 (1987).

Stace, C.

Steier, W. H.

M. Ziari, W. H. Steier, P. M. Ranon, M. B. Klein, and S. Trivedi, “Enhancement of the photorefractive gain at 1.3–1.5μm in CdTe using alternating electric fields,” J. Opt. Soc. Am. B 9, 1461 (1992).
[CrossRef]

M. Ziari, W. H. Steier, P. M. Ranon, S. Trivedi, and M. B. Klein, “Photorefractivity in vanadium-doped ZnTe,” Appl. Phys. Lett. 60, 1052 (1992).
[CrossRef]

A. Partovi, J. Millerd, A. M. Garmire, M. Ziari, W. H. Steier, S. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μ m in CdTe:V,” Appl. Phys. Lett. 57, 846 (1990).
[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 (1985).
[CrossRef]

Strait, J.

Tayebati, P.

Triboulet, R.

D. Imhoff, A. Zozime, and R. Triboulet, “Zn influence on the plasticity of Cd0.96Zn0.04Te,” J. Phys. C 1, 1841 (1991).

K. Guergouri, R. Triboulet, A. Tromson-Carli, and Y. Marfaing, “Solution hardening and dislocation density reduction in CdTe crystals by Zn addition,” J. Cryst. Growth 101, 131 (1990).

R. Triboulet and Y. Marfaing, “Growth of high purity CdTe single crystals by vertical zone melting,” J. Electrochem. Soc. 120, 1260 (1973).
[CrossRef]

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Trivedi, S.

M. Ziari, W. H. Steier, P. M. Ranon, S. Trivedi, and M. B. Klein, “Photorefractivity in vanadium-doped ZnTe,” Appl. Phys. Lett. 60, 1052 (1992).
[CrossRef]

M. Ziari, W. H. Steier, P. M. Ranon, M. B. Klein, and S. Trivedi, “Enhancement of the photorefractive gain at 1.3–1.5μm in CdTe using alternating electric fields,” J. Opt. Soc. Am. B 9, 1461 (1992).
[CrossRef]

A. Partovi, J. Millerd, A. M. Garmire, M. Ziari, W. H. Steier, S. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μ m in CdTe:V,” Appl. Phys. Lett. 57, 846 (1990).
[CrossRef]

Tromson-Carli, A.

K. Guergouri, R. Triboulet, A. Tromson-Carli, and Y. Marfaing, “Solution hardening and dislocation density reduction in CdTe crystals by Zn addition,” J. Cryst. Growth 101, 131 (1990).

Turki, K.

K. Turki, G. Picoli, and J.-E. Viallet, “Behavior of InP:Fe under high electric field,” J. Appl. Phys. 73, 8340 (1993).
[CrossRef]

Valley, G. C.

A. M. Glass, M. B. Klein, and G. C. Valley, “Photorefractive determination of the sign of photocarriers in InP and GaAs,” Electron. Lett. 21, 220 (1985).
[CrossRef]

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
[CrossRef]

Viallet, J.-E.

K. Turki, G. Picoli, and J.-E. Viallet, “Behavior of InP:Fe under high electric field,” J. Appl. Phys. 73, 8340 (1993).
[CrossRef]

Vieux, V.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: A new mechanism of resonance,” J. Appl. Phys. 66, 3798 (1989).
[CrossRef]

Villing, A.

Walsh, K.

Wolffer, N.

N. Wolffer and P. Gravey, “Two-wave mixing in photorefractive InP:Fe with an external alternative field,” Ann. Phys. (NY) 16, 143 (1991).

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

Ziari, M.

M. Ziari, W. H. Steier, P. M. Ranon, S. Trivedi, and M. B. Klein, “Photorefractivity in vanadium-doped ZnTe,” Appl. Phys. Lett. 60, 1052 (1992).
[CrossRef]

M. Ziari, W. H. Steier, P. M. Ranon, M. B. Klein, and S. Trivedi, “Enhancement of the photorefractive gain at 1.3–1.5μm in CdTe using alternating electric fields,” J. Opt. Soc. Am. B 9, 1461 (1992).
[CrossRef]

A. Partovi, J. Millerd, A. M. Garmire, M. Ziari, W. H. Steier, S. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μ m in CdTe:V,” Appl. Phys. Lett. 57, 846 (1990).
[CrossRef]

Zielinger, J. P.

J. C. Launay, V. Mazoyer, J. P. Zielinger, Z. Guellil, P. Delaye, and G. Roosen, “Growth, spectroscopic and photorefractive investigation of vanadium-doped cadmium telluride,” Appl. Phys. A 55, 33 (1992).
[CrossRef]

Zozime, A.

D. Imhoff, A. Zozime, and R. Triboulet, “Zn influence on the plasticity of Cd0.96Zn0.04Te,” J. Phys. C 1, 1841 (1991).

Ann. Phys. (NY) (1)

N. Wolffer and P. Gravey, “Two-wave mixing in photorefractive InP:Fe with an external alternative field,” Ann. Phys. (NY) 16, 143 (1991).

Appl. Phys. A (1)

J. C. Launay, V. Mazoyer, J. P. Zielinger, Z. Guellil, P. Delaye, and G. Roosen, “Growth, spectroscopic and photorefractive investigation of vanadium-doped cadmium telluride,” Appl. Phys. A 55, 33 (1992).
[CrossRef]

Appl. Phys. Lett. (4)

A. M. Glass, A. M. Johnson, D. H. Olson, W. Simpson, and A. A. Ballman, “Four-wave mixing in semi-insulating InP and GaAs using the photorefractive effect,” Appl. Phys. Lett. 44, 948 (1984).
[CrossRef]

R. B. Bylsma, P. M. Bridenbaugh, D. H. Olson, and A. M. Glass, “Photorefractive properties of doped cadmium telluride,” Appl. Phys. Lett. 51, 889 (1987).
[CrossRef]

M. Ziari, W. H. Steier, P. M. Ranon, S. Trivedi, and M. B. Klein, “Photorefractivity in vanadium-doped ZnTe,” Appl. Phys. Lett. 60, 1052 (1992).
[CrossRef]

A. Partovi, J. Millerd, A. M. Garmire, M. Ziari, W. H. Steier, S. Trivedi, and M. B. Klein, “Photorefractivity at 1.5 μ m in CdTe:V,” Appl. Phys. Lett. 57, 846 (1990).
[CrossRef]

Electron. Lett. (2)

R. B. Bylsma, A. M. Glass, and D. H. Olson, “Optical signal amplification at 1.3 μ m by two wave mixing in InP:Fe,” Electron. Lett. 24, 360 (1988).
[CrossRef]

A. M. Glass, M. B. Klein, and G. C. Valley, “Photorefractive determination of the sign of photocarriers in InP and GaAs,” Electron. Lett. 21, 220 (1985).
[CrossRef]

J. Appl. Phys. (3)

K. Turki, G. Picoli, and J.-E. Viallet, “Behavior of InP:Fe under high electric field,” J. Appl. Phys. 73, 8340 (1993).
[CrossRef]

M. B. Klein and G. C. Valley, “Beam coupling in BaTiO3at 442 nm,” J. Appl. Phys. 57, 4901 (1985).
[CrossRef]

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP:Fe: A new mechanism of resonance,” J. Appl. Phys. 66, 3798 (1989).
[CrossRef]

J. Cryst. Growth (1)

K. Guergouri, R. Triboulet, A. Tromson-Carli, and Y. Marfaing, “Solution hardening and dislocation density reduction in CdTe crystals by Zn addition,” J. Cryst. Growth 101, 131 (1990).

J. Electrochem. Soc. (1)

R. Triboulet and Y. Marfaing, “Growth of high purity CdTe single crystals by vertical zone melting,” J. Electrochem. Soc. 120, 1260 (1973).
[CrossRef]

J. Opt. Soc. Am. B (5)

J. Phys. C (1)

D. Imhoff, A. Zozime, and R. Triboulet, “Zn influence on the plasticity of Cd0.96Zn0.04Te,” J. Phys. C 1, 1841 (1991).

Opt. Commun. (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 (1985).
[CrossRef]

P. Mathey, G. Pauliat, J.-C. Launay, and G. Roosen, “Overcoming the trap density limitation in photorefractive two-beam coupling by applying pulsed electric fields,” Opt. Commun. 82, 101 (1991).
[CrossRef]

Opt. Lett. (2)

Sov. Phys. Solid State (1)

V. I. Sokolov, “A universal trend of the variation in the 3d-impurity (0/+) and (0/−) levels in A2B6compounds,” Sov. Phys. Solid State 29, 1061 (1987).

Other (5)

W. Giriat and J. K. Furdyna, “Crystal structure, composition and materials preparation of diluted magnetic semiconductors,” in Semiconductors and Semimetals (Academic, New York, 1988), Vol. 25, pp. 1–34.
[CrossRef]

S. G. Odoulov, K. V. Shcherbin, A. N. Shumelyuk, P. M. Fochuk, and O. E. Panchuk, “Electron–hole competition in dynamic hologram recording in cadmium telluride,” in Technical Digest of Meeting on Photorefractive Materials, Effects, and Devices (Ukrainian Academy of Sciences, Kiev, 1993), p. 293.

P. Nouchi, J. P. Partanen, and R. W. Hellwarth, “Conduction band and trap-limited mobilities in Bi12SiO20,” in Photorefractive Materials, Effects, and Devices, Vol. 14 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), p. 236.

G. Bremond, Institut National des Sciences Appliquées de Lyon, Unité de Recherche Associée No. 358 du Centre National de la Recherche Scientifique, 69621 Villeurbanne Cedex, France (personal communication, 1993).

P. Gravey, G. Martel, J.-Y. Moisan, N. Wolffer, A. Aoudia, Y. Marfaing, R. Triboulet, M. C. Busch, M. Hage-Ali, J. M. Koebel, and P. Siffert, “Behavior of hole and electron dominated photorefractive CdTe:V crystals under external continuous or periodic electric field,” in Proceedings of 1994 European Material Research Society Spring Meeting on Photorefractive Materials (Elsevier, Amsterdam, to be published).

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Figures (16)

Fig. 1
Fig. 1

Photoconductive spectrum of DAV 30. The applied electric field is 1 kV/cm, and the incident intensity is 1015 photons/cm2 s.

Fig. 2
Fig. 2

TWM gain as a function of the incident intensity: The crystal is the DAV 30 sample, and the experimental conditions are indicated in the figure. The points denote the experimental results, and the curves represent the fits according to Γ = Γ0/(1 + Id/I0), with Γ0 = 0.240 cm−1, Id = 75 μW/cm2 at the 1.32-μm wavelength and Γ0 = 0.260 cm−1, Id = 155 μW/cm2 at the 1.535-μm wavelength, respectively.

Fig. 3
Fig. 3

Experimental plot of K/Γ versus K2. K is the grating wave vector, and Γ is the TWM gain. The deduced ξ value is 0.72 ± 0.01, and the Neff value is 9.0 ± 0.03 × 1014 cm2.

Fig. 4
Fig. 4

TWM gain in the DAV 31 crystal versus a continuous electric field for different grating periods.

Fig. 5
Fig. 5

Gain as a function of the incident intensity with the DAV 30 crystal. The curve represents the best fit with Γ0 = 0.180 cm−1, Id = 20 μW/cm2, as used in Fig. 2.

Fig. 6
Fig. 6

Gain as a function of the incident intensity with the DAV 31 crystal.

Fig. 7
Fig. 7

Gain versus frequency of the square-shaped alternative electric field (in kilovolts per centimeter), as indicated, with the DAV 31 crystal.

Fig. 8
Fig. 8

Gain versus frequency of the square-shaped alternative electric field, with the DAV 31 crystal. The conditions are the same as in Fig. 7, except for the wavelength of incident light.

Fig. 9
Fig. 9

TWM gain versus frequency, with the DAV 30 crystal, with two high-voltage amplifiers with different slew rates (105 and 25 V/μs).

Fig. 10
Fig. 10

Gain versus frequency of the 10-kV/cm square-shaped alternative electric field, with the DAV 31 crystal. The light intensity is indicated for each curve. The decrease of the gain, for 10 and 20 mW/cm2, is probably due to a nonhomogeneous pump-beam intensity.

Fig. 11
Fig. 11

Gain versus frequency of the 10-kV/cm square-shaped alternative electric field. The grating period is indicated for each curve.

Fig. 12
Fig. 12

Gain versus frequency of the 10-kV/cm square-shaped alternative electric field, with the DAV 31 crystal, for different beam ratios β. A plot of the gain value at each optimum frequency versus β is shown in the inset.

Fig. 13
Fig. 13

Gain versus the square-shaped electric-field amplitude E0 obtained with the DAV 31 crystal at the 1.32 μm wavelength.

Fig. 14
Fig. 14

Energy diagram for the two-level model with the different parameters used for the calculation.

Fig. 15
Fig. 15

TWM gain as a function of the square-shaped field frequency for different values of the second-level concentration NT′ (in inverse cubic centimeters): λ0 = 1.32 μm, Λ = 10 μm, I0 = 1 mW/cm2, E0 = 10 kV/cm.

Fig. 16
Fig. 16

Plot of the trajectory of the complex gain Γc (in inverse centimeters) in the complex plane for three different values of the second-level concentration (where NT′ is 0, 3 × 1013 cm3, and 1014 cm3). In each figure, curves a, b, and c correspond to cases in which F is 0, 40, and 100 Hz, respectively, with curves c being close to the imaginary axis. The conditions are the same as in Fig. 14.

Tables (3)

Tables Icon

Table 1 Crystal Growth Parameters for DAV 30 and DAV 31 Crystals

Tables Icon

Table 2 Electrical and Photorefractive Parameters of DAV 30 and DAV 31 Crystalsa

Tables Icon

Table 3 Theoretical DAV 31 Characteristics Deduced From the Two-Level Model Parameters, as Used in Fig. 14, Compared with Experimental Values, as Given in Table 2

Equations (68)

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

C s = k C 0 ( 1 - g ) k - 1 ,
Γ = 2 π λ 0 cos ( θ ) 2 3 ξ n 0 3 r 41 E d E q E d + E q ,
Γ = A ξ E d E q E d + E q ,
E d = k B T e K ,             E q = e ɛ K N eff ,             N eff = n T 0 p T 0 n T 0 + p T 0 .
ξ = σ p p T 0 - σ n n T 0 ( σ n o n T 0 + σ p o p T 0 ) ( 1 + I d / I 0 ) ,
I d = e n th n T 0 + e p th p T 0 σ n o n T 0 + σ p o p T 0 ,
ξ = e Or k B T A .
N eff = ɛ P A ξ e .
τ g d E 1 d t + E 1 = m E sc ,
τ R T τ g .
n T + p T = n T 0 + p T 0 = N T ,
n T + p T = n T 0 + p T 0 = N T ,
ɛ d E d x = - e ( n T - n T 0 ) - e ( n T - n T 0 ) ,
J n = e μ n n E + μ n k B T d n d x ,
J p = e μ p p E - μ p k B T d p d x ,
d p d t = ( σ n 0 I + e n th ) n T - c n n p T + 1 e d J n d x ,
d n d t = ( σ p o I + e p th ) p T - c p p n T - 1 e d J p d x + e p p t - c p p n T ,
d n T d t = - [ ( σ n o I + e n th ) n T - c n n p T ] + [ ( σ p o I + e p th ) p T - c p p n T ]
d p T d t = - e p p t + c p p n T .
I = I 0 [ 1 + m exp ( i K x ) ] .
A = A 0 + A 1 exp ( i K x ) .
n 0 = ( σ n o I + e n th ) n T 0 c n p T 0 ,
p 0 = ( σ p o I + e p th ) p T 0 c p n T 0 = e p c p p T n T 0 ,
p T 0 = n T c p p 0 e p + c p p 0 ,
n T 0 = N T - p T 0 .
n T 1 = - p T 1 ,
n T 1 = - p T 1 ,
ɛ i K E 1 = - e ( n T 1 + n T 1 ) ,
i K J n 1 e = i K μ n [ n 0 E 1 + n 1 ( E 0 + i E d ) ] ,
i K J p 1 e = i K μ p [ p 0 E 1 + p 1 ( E 0 - i E d ) ] .
d n 1 d t = - n 1 ( c n p T 0 + K μ n E d - i K μ n E 0 ) + n T 1 [ c n n 0 + ( σ n o I 0 + e n th ) ] + i K μ n n 0 E 1 + m σ n o I 0 n T 0 ,
d p 1 d t = - p 1 ( c p n T 0 + c p n T 0 + K μ p E d + i K μ p E 0 ) - n T 1 [ c p p 0 + ( σ p o I 0 + e p th ) ] - i K μ p p 0 E 1 - n T 1 ( c p p 0 + e p ) + m σ p o I 0 p T 0 ,
d n T 1 d t = - n T 1 [ ( σ p o I 0 + e p th ) + ( σ n o I 0 + e n th ) + c n n 0 + c p p 0 ] + c n n 1 p T 0 - c p p 1 n T 0 - m σ n o I 0 n T 0 + m σ p o I 0 p T 0 ,
d n T 1 d t = - n T 1 ( c p p 0 + e p ) - c p p 1 n T 0 .
τ n 1 = 1 / ( c n p T 0 + K μ n E d ) = 10 - 9 s ,
τ p 1 = 1 / ( c p n T 0 + c p n T 0 + K μ p E d ) = 4 × 10 - 11 s ,
τ n T 1 = 1 [ ( σ p o I 0 + e p th ) + ( σ n o I 0 + e n th ) + c n n 0 + c p p 0 ] = 0.4 s ,
τ n T 1 = 1 ( c p p 0 + e p ) = 0.25 ms .
n 1 = m σ n o I 0 n T 0 c n p T 0 + n 0 [ - e ( n T 1 + n T 1 ) ɛ K E m n + n T 1 N eff ] 1 + E d E m n - i E 0 E m n ,
p 1 = m σ p o I 0 p T 0 c p n T 0 - p 0 [ - e ( n T 1 + n T 1 ) ɛ K E m p + n T 1 N eff ] - n T 1 e p + c p p 0 c p n T 0 1 + ω + E d E m p + i E 0 E m p ,
E m n = c n p T 0 μ n K ,             E m p = c p n T 0 μ p K ,             ω = c p n T 0 c p n T 0 .
d n T 1 d t = - n T 1 N eff [ ( σ n o I 0 + e n th ) n T 0 E d + E q - i E 0 E d + E m n - i E 0 + ( σ n o I 0 + e p th ) p T 0 ω E m p + E d + E q + i E 0 E d + E m p ( 1 + ω ) + i E 0 ] - n T 1 N eff [ E q ( σ n o I 0 + e n th ) n T 0 E d + E m n - i E 0 + E q ( σ p o I 0 + e p th ) p T 0 - E m p ( e p + c p p 0 ) N eff E d + E m p ( 1 + ω ) + i E 0 ] - m σ n o I 0 n T 0 E d - i E 0 E d + E m n - i E 0 + m σ p o I 0 p T 0 E d + ω E m p + i E 0 E d + E m p ( 1 + ω ) + i E 0 ,
d n T 1 d t = - n T 1 N eff [ N eff ( e p + c p p 0 ) - ω E m p N eff ( e p + c p p 0 ) - E q ( σ p o I 0 + e p th ) p T 0 E d + E m p ( 1 + ω ) + i E 0 ] + n T 1 N eff [ ω ( σ p o I 0 + e p th ) p T 0 E m p - E q E d + E m p ( 1 + ω ) + i E 0 ] - ω m σ p o I 0 p T 0 E m p E d + E m p ( 1 + ω ) + i E 0 .
τ z d n T 1 d t + n T 1 = m n T 1 sat + α n T 1
τ y d n T 1 d t + n T 1 = m n T 1 sat + β n T 1 .
Γ = Im [ 2 π λ 0 cos ( θ ) i e ɛ K n 3 r 41 2 3 ( n T 1 + n T 1 ) ] × 1 m = Re Θ m ( n T 1 + n T 1 ) ] = Re ( Γ c ) ,
z = Θ m n T 1 , z s = Θ n T 1 sat , y = Θ m n T 1 , y s = Θ n T 1 sat .
τ z d z d t + z = z s + α y ,
τ z d y d t + y = y s + β z ,
Γ c = y + z .
τ y τ z d 2 z d t 2 + ( τ y + τ z ) d z d t + z ( 1 - α β ) = z s + α y s ,
τ y τ z d 2 y d t 2 + ( τ y + τ z ) d y d t + y ( 1 - α β ) = y s + α z s .
z = a 0 + a 1 exp ( γ 1 t ) + a 2 exp ( γ 2 t ) ,
y = b 0 + b 1 exp ( γ 1 t ) + b 2 exp ( γ 2 t ) ,
γ 2 ( τ y τ z ) + γ ( τ y + τ z ) + ( 1 - α β ) = 0.
τ z [ a 1 γ 1 exp ( γ 1 t ) + a 2 γ 2 exp ( γ 2 t ) ] = z s - [ a 0 + a 1 exp ( γ 1 t ) + a 2 exp ( γ 2 t ) ] + α [ b 0 + b 1 exp ( γ 1 t ) + b 2 exp ( γ 2 t ) ] ,
τ y [ b 1 γ 1 exp ( γ 1 t ) + b 2 γ 2 exp ( γ 2 t ) ] = y s - [ b 0 + b 1 exp ( γ 1 t ) + b 2 exp ( γ 2 t ) ] + β [ a 0 + a 1 exp ( γ 1 t ) + a 2 exp ( γ 2 t ) ] .
z s = a 0 - α b 0 ,             y s = b 0 - β a 0 .
a 0 = z s + α y s 1 - α β ,             b 0 = y s + β z s 1 - α β .
a 1 ( 1 + γ 1 τ z ) = α b 1 ,             a 2 ( 1 + γ 2 τ z ) = α b 2 ,
b 1 ( 1 + γ 1 τ y ) = β a 1 ,             b 2 ( 1 + γ 2 τ y ) = β a 2 .
y ( 2 Δ t ) = y ( 0 ) ,             z ( 2 Δ t ) = z ( 0 )
y ( Δ t ) = y * ( 0 ) ,             z ( Δ t ) = z * ( 0 ) ,
a 0 + a 1 exp ( γ 1 Δ t ) + a 2 exp ( γ 2 Δ t ) = a 0 * + a 1 * + a 2 * ,
b 0 + b 1 exp ( γ 1 Δ t ) + b 2 exp ( γ 2 Δ t ) = b 0 * + b 1 * + b 2 * .
Re ( a 0 + a 1 + a 2 + b 0 + b 1 + b 2 ) .
0 2 Δ t d y = 0 = 0 2 Δ t 1 τ y ( - y + y s + β z ) d t ,
0 2 Δ t d z = 0 = 0 2 Δ t 1 τ z ( - z + z s + α y ) d t .

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