Abstract

Ferroelectric photorefractive Sn2P2S6 crystals become more sensitive to cw radiation of a Nd3+: YAG laser (λ = 1.06 µm) by preexposure with incoherent white light. Space-charge formation and hologram recording are dominated by a diffusionlike charge transport, leading to an ultimate gain factor for transmission gratings that exceeds 6 cm−1 at a laser intensity of approximately 50 W/cm2.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. K. Kwong and A. Yariv, "One-way, real time wave front converters," Appl. Phys. Lett. 48, 564–566 (1986).
    [CrossRef]
  2. M. Cronin-Golomb, J. Paslaski, and A. Yariv, "Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors," Appl. Phys. Lett. 47, 1131–1133 (1985).
    [CrossRef]
  3. S. Weiss, M. Segev, S. Sternklar, and B. Fischer, "Photorefractive dynamic optical interconnects," Appl. Opt. 27, 3422–3427 (1988).
    [CrossRef] [PubMed]
  4. S. MacCormack and R. W. Eason, "Efficient amplification of a single-mode laser diode by photorefractive beam combination using an injection-locked diode-laser array pump," Opt. Lett. 15, 1212–1214 (1990).
    [CrossRef] [PubMed]
  5. S. K. Kwong, M. Cronin-Golomb, and A. Yariv, "Oscillation with photorefractive gain," IEEE J. Quantum Electron. 22, 1508–1523 (1986).
    [CrossRef]
  6. 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]
  7. J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, "Photorefractive gain enhancement in InP:Fe using band-edge resonance and temperature stabilization," Appl. Phys. Lett. 57, 2776–2778 (1991).
    [CrossRef]
  8. G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave-mixing gain enhancement in photorefractive In-P:Fe: a new mechanism of resonance," J. Appl. Phys. 66, 3798–3813 (1989).
    [CrossRef]
  9. G. W. Ross, P. Hribek, R. W. Eason, M. H. Garret, and D. Rytz, "Impurity enhanced self-pumped phase conjugation in the near infrared in 'blue' BaTiO3," Opt. Commun. 101, 60–64 (1993).
    [CrossRef]
  10. B. A. Wechsler, M. B. Klein, C. C. Nelson, and R. N. Schwartz, "Spectroscopic and photorefractive properties of infrared-sensitive rhodium-doped barium titanate," Opt. Lett. 19, 536–538 (1994).
    [CrossRef] [PubMed]
  11. A. A. Grabar, R. I. Muzhikash, A. D. Kostyuk, and Yu. M. Vysochanskiy, "Investigation of the switching process in the domain structure of ferroelectric Sn2P2S6 by the dynamic holographic method," Sov. Phys. Solid State 33, 1314–1316 (1991).
  12. A. A. Grabar, Yu. M. Vysochanskiy, I. M. Stoyka, M. M. Danko, and V. Yu. Slivka, "Influence of the domain structure on photorefractive properties of a ferroelectric Sn2P2S6," Ukr. Phys. J. 39, 941–942 (1994).
  13. A. N. Shumelyuk, U. Hellwig, R. A. Rupp, S. G. Odoulov, and A. A. Grabar, "Infrared recording in photorefractivetin-hypothiodiphosphate (Sn2P2S6)," in Photorefractive Materials, Effects, and Devices Topical Meeting (Optical Society of America, Washington, D.C., 1995), pp. 80–83.
  14. A. A. Grabar, Y. M. Vysochanskiy, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, "Thermooptic investigations of ferroelectric Sn2P2S6," Sov. Phys. Solid State 26, 2087–2089 (1984).
  15. C. D. Carpentier and R. Nitsche, "Vapour growth and crystal data of the thio(seleno)-hypodiphosphates Sn2P2S6, Sn2P2Se6, Pb2P2S6, Pb2P2Se6 and their mixed crystals," Mater. Res. Bull. 9, 401–410 (1974).
    [CrossRef]
  16. M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korda, and V. Yu. Slivka, "Optical properties of Sn2P2S6 crystals," Sov. Phys. Solid State 19, 1794–1795 (1977).
  17. Yu. M. Vysochanskiy and V. Yu. Slivka, Ferroelectrics of the Sn2P2S6 Family. Properties in the Vicinity of the Lifshits Point, 1st ed. (Scientific Edition, L'vov, 1994), Chap. 10, p. 244 (in Russian).
  18. G. Dittmar and H. Schaefer, "The crystal structure of Sn2P2S6," Z. Naturforsch. 29b, 312–317 (1974).
  19. C. D. Carpentier and R. Nitsche, "Ferroelectricity in Sn2P2S6," Mater. Res. Bull. 9, 1097–1100 (1974).
    [CrossRef]
  20. G. A. Brost, R. A. Motes, and J. R. Rotge, "Intensity-dependent absorption and photorefractive effects in barium titanate," J. Opt. Soc. Am. B 5, 1879–1885 (1988).
    [CrossRef]
  21. R. L. Townsend and J. T. LaMacchia, "Optically induced refractive index changes in BaTiO3," J. Appl. Phys. 41, 5188–5192 (1970).
    [CrossRef]
  22. S. Zhivkova and M. Miteva, "Holographic recording in pho-torefractive crystals with simultaneous electron-hole transport and two active centers," J. Appl. Phys. 68, 3099–3103 (1990).
    [CrossRef]
  23. M. B. Klein and G. C. Valley, "Beam coupling in BaTiO3/sub> at 442 nm," J. Appl. Phys. 57, 4901–4905 (1987).
    [CrossRef]
  24. N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vi-netskii, "Holographic storage in electrooptic crystals," Fer-roelectrics 22, 949–964 (1979).
    [CrossRef]
  25. J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hell-warth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297–1305 (1980).
    [CrossRef]
  26. Until now the signs of movable charges responsible for the fast and the slow gratings were not established. The attribution of the fast component to electrons and of the slow component to holes still has to be proved by independent experiments.
  27. S. I. Stepanov and M. P. Petrov, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 263.
    [CrossRef]
  28. M. P. Petrov, S. J. Stepanov, A. V. Khomenko, Photorefrac-tive Crystals in Coherent Optical Systems, Vol. 59 of Optical Sciences (Springer-Verlag, Berlin, 1991).
    [CrossRef]
  29. M. B. Klein, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 195.
    [CrossRef]
  30. A. A. Volkov, G. V. Kozlov, N. I. Afanasieva, Yu. M. Vysoch-anskiy, A. A. Grabar, and V. Yu. Slivka, "Low-frequency modes in the infrared spectrum of an Sn2P2S6 crystal," Sov. Phys. Solid State 25, 1482–1483 (1983).
  31. N. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438–440 (1976).
  32. S. G. Odoulov, A. N. Shumelyuk, G. A. Brost, and K. M. Magde, "Enhancement of beam coupling in near infrared for tin hypothiodiphosphate," Appl. Phys. Lett. (to be published).
  33. A. M. Glass and J. Strait, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 237.
    [CrossRef]

1995

A. N. Shumelyuk, U. Hellwig, R. A. Rupp, S. G. Odoulov, and A. A. Grabar, "Infrared recording in photorefractivetin-hypothiodiphosphate (Sn2P2S6)," in Photorefractive Materials, Effects, and Devices Topical Meeting (Optical Society of America, Washington, D.C., 1995), pp. 80–83.

1994

A. A. Grabar, Yu. M. Vysochanskiy, I. M. Stoyka, M. M. Danko, and V. Yu. Slivka, "Influence of the domain structure on photorefractive properties of a ferroelectric Sn2P2S6," Ukr. Phys. J. 39, 941–942 (1994).

B. A. Wechsler, M. B. Klein, C. C. Nelson, and R. N. Schwartz, "Spectroscopic and photorefractive properties of infrared-sensitive rhodium-doped barium titanate," Opt. Lett. 19, 536–538 (1994).
[CrossRef] [PubMed]

1993

G. W. Ross, P. Hribek, R. W. Eason, M. H. Garret, and D. Rytz, "Impurity enhanced self-pumped phase conjugation in the near infrared in 'blue' BaTiO3," Opt. Commun. 101, 60–64 (1993).
[CrossRef]

1991

A. A. Grabar, R. I. Muzhikash, A. D. Kostyuk, and Yu. M. Vysochanskiy, "Investigation of the switching process in the domain structure of ferroelectric Sn2P2S6 by the dynamic holographic method," Sov. Phys. Solid State 33, 1314–1316 (1991).

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, "Photorefractive gain enhancement in InP:Fe using band-edge resonance and temperature stabilization," Appl. Phys. Lett. 57, 2776–2778 (1991).
[CrossRef]

1990

S. Zhivkova and M. Miteva, "Holographic recording in pho-torefractive crystals with simultaneous electron-hole transport and two active centers," J. Appl. Phys. 68, 3099–3103 (1990).
[CrossRef]

S. MacCormack and R. W. Eason, "Efficient amplification of a single-mode laser diode by photorefractive beam combination using an injection-locked diode-laser array pump," Opt. Lett. 15, 1212–1214 (1990).
[CrossRef] [PubMed]

1989

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave-mixing gain enhancement in photorefractive In-P:Fe: a new mechanism of resonance," J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

1988

1987

M. B. Klein and G. C. Valley, "Beam coupling in BaTiO3/sub> at 442 nm," J. Appl. Phys. 57, 4901–4905 (1987).
[CrossRef]

1986

S. K. Kwong and A. Yariv, "One-way, real time wave front converters," Appl. Phys. Lett. 48, 564–566 (1986).
[CrossRef]

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, "Oscillation with photorefractive gain," IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

1985

M. Cronin-Golomb, J. Paslaski, and A. Yariv, "Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors," Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

1984

A. A. Grabar, Y. M. Vysochanskiy, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, "Thermooptic investigations of ferroelectric Sn2P2S6," Sov. Phys. Solid State 26, 2087–2089 (1984).

1983

A. A. Volkov, G. V. Kozlov, N. I. Afanasieva, Yu. M. Vysoch-anskiy, A. A. Grabar, and V. Yu. Slivka, "Low-frequency modes in the infrared spectrum of an Sn2P2S6 crystal," Sov. Phys. Solid State 25, 1482–1483 (1983).

1980

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hell-warth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

1979

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vi-netskii, "Holographic storage in electrooptic crystals," Fer-roelectrics 22, 949–964 (1979).
[CrossRef]

1977

M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korda, and V. Yu. Slivka, "Optical properties of Sn2P2S6 crystals," Sov. Phys. Solid State 19, 1794–1795 (1977).

1976

N. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438–440 (1976).

1974

G. Dittmar and H. Schaefer, "The crystal structure of Sn2P2S6," Z. Naturforsch. 29b, 312–317 (1974).

C. D. Carpentier and R. Nitsche, "Ferroelectricity in Sn2P2S6," Mater. Res. Bull. 9, 1097–1100 (1974).
[CrossRef]

C. D. Carpentier and R. Nitsche, "Vapour growth and crystal data of the thio(seleno)-hypodiphosphates Sn2P2S6, Sn2P2Se6, Pb2P2S6, Pb2P2Se6 and their mixed crystals," Mater. Res. Bull. 9, 401–410 (1974).
[CrossRef]

1970

R. L. Townsend and J. T. LaMacchia, "Optically induced refractive index changes in BaTiO3," J. Appl. Phys. 41, 5188–5192 (1970).
[CrossRef]

Khomenko, A. V.

M. P. Petrov, S. J. Stepanov, A. V. Khomenko, Photorefrac-tive Crystals in Coherent Optical Systems, Vol. 59 of Optical Sciences (Springer-Verlag, Berlin, 1991).
[CrossRef]

Klein, M. B.

M. B. Klein, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 195.
[CrossRef]

Stepanov, S. J.

M. P. Petrov, S. J. Stepanov, A. V. Khomenko, Photorefrac-tive Crystals in Coherent Optical Systems, Vol. 59 of Optical Sciences (Springer-Verlag, Berlin, 1991).
[CrossRef]

Afanasieva, N. I.

A. A. Volkov, G. V. Kozlov, N. I. Afanasieva, Yu. M. Vysoch-anskiy, A. A. Grabar, and V. Yu. Slivka, "Low-frequency modes in the infrared spectrum of an Sn2P2S6 crystal," Sov. Phys. Solid State 25, 1482–1483 (1983).

Boggess, T. F.

Brost, G. A.

G. A. Brost, R. A. Motes, and J. R. Rotge, "Intensity-dependent absorption and photorefractive effects in barium titanate," J. Opt. Soc. Am. B 5, 1879–1885 (1988).
[CrossRef]

S. G. Odoulov, A. N. Shumelyuk, G. A. Brost, and K. M. Magde, "Enhancement of beam coupling in near infrared for tin hypothiodiphosphate," Appl. Phys. Lett. (to be published).

Buturlakin, A. P.

M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korda, and V. Yu. Slivka, "Optical properties of Sn2P2S6 crystals," Sov. Phys. Solid State 19, 1794–1795 (1977).

Carpentier, C. D.

C. D. Carpentier and R. Nitsche, "Vapour growth and crystal data of the thio(seleno)-hypodiphosphates Sn2P2S6, Sn2P2Se6, Pb2P2S6, Pb2P2Se6 and their mixed crystals," Mater. Res. Bull. 9, 401–410 (1974).
[CrossRef]

C. D. Carpentier and R. Nitsche, "Ferroelectricity in Sn2P2S6," Mater. Res. Bull. 9, 1097–1100 (1974).
[CrossRef]

Cronin-Golomb, M.

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, "Oscillation with photorefractive gain," IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

M. Cronin-Golomb, J. Paslaski, and A. Yariv, "Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors," Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

Danko, M. M.

A. A. Grabar, Yu. M. Vysochanskiy, I. M. Stoyka, M. M. Danko, and V. Yu. Slivka, "Influence of the domain structure on photorefractive properties of a ferroelectric Sn2P2S6," Ukr. Phys. J. 39, 941–942 (1994).

Dittmar, G.

G. Dittmar and H. Schaefer, "The crystal structure of Sn2P2S6," Z. Naturforsch. 29b, 312–317 (1974).

Eason, R. W.

G. W. Ross, P. Hribek, R. W. Eason, M. H. Garret, and D. Rytz, "Impurity enhanced self-pumped phase conjugation in the near infrared in 'blue' BaTiO3," Opt. Commun. 101, 60–64 (1993).
[CrossRef]

S. MacCormack and R. W. Eason, "Efficient amplification of a single-mode laser diode by photorefractive beam combination using an injection-locked diode-laser array pump," Opt. Lett. 15, 1212–1214 (1990).
[CrossRef] [PubMed]

Feinberg, J.

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hell-warth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Fischer, B.

Garmire, E. M.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, "Photorefractive gain enhancement in InP:Fe using band-edge resonance and temperature stabilization," Appl. Phys. Lett. 57, 2776–2778 (1991).
[CrossRef]

Garret, M. H.

G. W. Ross, P. Hribek, R. W. Eason, M. H. Garret, and D. Rytz, "Impurity enhanced self-pumped phase conjugation in the near infrared in 'blue' BaTiO3," Opt. Commun. 101, 60–64 (1993).
[CrossRef]

Gerasimenko, V. S.

M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korda, and V. Yu. Slivka, "Optical properties of Sn2P2S6 crystals," Sov. Phys. Solid State 19, 1794–1795 (1977).

Glass, A. M.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, "Photorefractive gain enhancement in InP:Fe using band-edge resonance and temperature stabilization," Appl. Phys. Lett. 57, 2776–2778 (1991).
[CrossRef]

A. M. Glass and J. Strait, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 237.
[CrossRef]

Grabar, A. A.

A. N. Shumelyuk, U. Hellwig, R. A. Rupp, S. G. Odoulov, and A. A. Grabar, "Infrared recording in photorefractivetin-hypothiodiphosphate (Sn2P2S6)," in Photorefractive Materials, Effects, and Devices Topical Meeting (Optical Society of America, Washington, D.C., 1995), pp. 80–83.

A. A. Grabar, Yu. M. Vysochanskiy, I. M. Stoyka, M. M. Danko, and V. Yu. Slivka, "Influence of the domain structure on photorefractive properties of a ferroelectric Sn2P2S6," Ukr. Phys. J. 39, 941–942 (1994).

A. A. Grabar, R. I. Muzhikash, A. D. Kostyuk, and Yu. M. Vysochanskiy, "Investigation of the switching process in the domain structure of ferroelectric Sn2P2S6 by the dynamic holographic method," Sov. Phys. Solid State 33, 1314–1316 (1991).

A. A. Grabar, Y. M. Vysochanskiy, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, "Thermooptic investigations of ferroelectric Sn2P2S6," Sov. Phys. Solid State 26, 2087–2089 (1984).

A. A. Volkov, G. V. Kozlov, N. I. Afanasieva, Yu. M. Vysoch-anskiy, A. A. Grabar, and V. Yu. Slivka, "Low-frequency modes in the infrared spectrum of an Sn2P2S6 crystal," Sov. Phys. Solid State 25, 1482–1483 (1983).

Gravey, P.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave-mixing gain enhancement in photorefractive In-P:Fe: a new mechanism of resonance," J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

Gurzan, M. I.

A. A. Grabar, Y. M. Vysochanskiy, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, "Thermooptic investigations of ferroelectric Sn2P2S6," Sov. Phys. Solid State 26, 2087–2089 (1984).

M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korda, and V. Yu. Slivka, "Optical properties of Sn2P2S6 crystals," Sov. Phys. Solid State 19, 1794–1795 (1977).

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hell-warth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Hell-warth, R. W.

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hell-warth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Hellwig, U.

A. N. Shumelyuk, U. Hellwig, R. A. Rupp, S. G. Odoulov, and A. A. Grabar, "Infrared recording in photorefractivetin-hypothiodiphosphate (Sn2P2S6)," in Photorefractive Materials, Effects, and Devices Topical Meeting (Optical Society of America, Washington, D.C., 1995), pp. 80–83.

Hribek, P.

G. W. Ross, P. Hribek, R. W. Eason, M. H. Garret, and D. Rytz, "Impurity enhanced self-pumped phase conjugation in the near infrared in 'blue' BaTiO3," Opt. Commun. 101, 60–64 (1993).
[CrossRef]

Klein, M. B.

B. A. Wechsler, M. B. Klein, C. C. Nelson, and R. N. Schwartz, "Spectroscopic and photorefractive properties of infrared-sensitive rhodium-doped barium titanate," Opt. Lett. 19, 536–538 (1994).
[CrossRef] [PubMed]

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, "Photorefractive gain enhancement in InP:Fe using band-edge resonance and temperature stabilization," Appl. Phys. Lett. 57, 2776–2778 (1991).
[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]

M. B. Klein and G. C. Valley, "Beam coupling in BaTiO3/sub> at 442 nm," J. Appl. Phys. 57, 4901–4905 (1987).
[CrossRef]

Koehler, S. D.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, "Photorefractive gain enhancement in InP:Fe using band-edge resonance and temperature stabilization," Appl. Phys. Lett. 57, 2776–2778 (1991).
[CrossRef]

Korda, N. F.

M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korda, and V. Yu. Slivka, "Optical properties of Sn2P2S6 crystals," Sov. Phys. Solid State 19, 1794–1795 (1977).

Kostyuk, A. D.

A. A. Grabar, R. I. Muzhikash, A. D. Kostyuk, and Yu. M. Vysochanskiy, "Investigation of the switching process in the domain structure of ferroelectric Sn2P2S6 by the dynamic holographic method," Sov. Phys. Solid State 33, 1314–1316 (1991).

Kozlov, G. V.

A. A. Volkov, G. V. Kozlov, N. I. Afanasieva, Yu. M. Vysoch-anskiy, A. A. Grabar, and V. Yu. Slivka, "Low-frequency modes in the infrared spectrum of an Sn2P2S6 crystal," Sov. Phys. Solid State 25, 1482–1483 (1983).

Kukhtarev, N.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vi-netskii, "Holographic storage in electrooptic crystals," Fer-roelectrics 22, 949–964 (1979).
[CrossRef]

N. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438–440 (1976).

Kwong, S. K.

S. K. Kwong and A. Yariv, "One-way, real time wave front converters," Appl. Phys. Lett. 48, 564–566 (1986).
[CrossRef]

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, "Oscillation with photorefractive gain," IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

LaMacchia, J. T.

R. L. Townsend and J. T. LaMacchia, "Optically induced refractive index changes in BaTiO3," J. Appl. Phys. 41, 5188–5192 (1970).
[CrossRef]

MacCormack, S.

Magde, K. M.

S. G. Odoulov, A. N. Shumelyuk, G. A. Brost, and K. M. Magde, "Enhancement of beam coupling in near infrared for tin hypothiodiphosphate," Appl. Phys. Lett. (to be published).

Markov, V.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vi-netskii, "Holographic storage in electrooptic crystals," Fer-roelectrics 22, 949–964 (1979).
[CrossRef]

McCahon, S. W.

Millerd, J. E.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, "Photorefractive gain enhancement in InP:Fe using band-edge resonance and temperature stabilization," Appl. Phys. Lett. 57, 2776–2778 (1991).
[CrossRef]

Miteva, M.

S. Zhivkova and M. Miteva, "Holographic recording in pho-torefractive crystals with simultaneous electron-hole transport and two active centers," J. Appl. Phys. 68, 3099–3103 (1990).
[CrossRef]

Motes, R. A.

Muzhikash, R. I.

A. A. Grabar, R. I. Muzhikash, A. D. Kostyuk, and Yu. M. Vysochanskiy, "Investigation of the switching process in the domain structure of ferroelectric Sn2P2S6 by the dynamic holographic method," Sov. Phys. Solid State 33, 1314–1316 (1991).

Nelson, C. C.

Nitsche, R.

C. D. Carpentier and R. Nitsche, "Vapour growth and crystal data of the thio(seleno)-hypodiphosphates Sn2P2S6, Sn2P2Se6, Pb2P2S6, Pb2P2Se6 and their mixed crystals," Mater. Res. Bull. 9, 401–410 (1974).
[CrossRef]

C. D. Carpentier and R. Nitsche, "Ferroelectricity in Sn2P2S6," Mater. Res. Bull. 9, 1097–1100 (1974).
[CrossRef]

Odoulov, S.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vi-netskii, "Holographic storage in electrooptic crystals," Fer-roelectrics 22, 949–964 (1979).
[CrossRef]

Odoulov, S. G.

A. N. Shumelyuk, U. Hellwig, R. A. Rupp, S. G. Odoulov, and A. A. Grabar, "Infrared recording in photorefractivetin-hypothiodiphosphate (Sn2P2S6)," in Photorefractive Materials, Effects, and Devices Topical Meeting (Optical Society of America, Washington, D.C., 1995), pp. 80–83.

S. G. Odoulov, A. N. Shumelyuk, G. A. Brost, and K. M. Magde, "Enhancement of beam coupling in near infrared for tin hypothiodiphosphate," Appl. Phys. Lett. (to be published).

Ozkul, C.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave-mixing gain enhancement in photorefractive In-P:Fe: a new mechanism of resonance," J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

Partovi, A.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, "Photorefractive gain enhancement in InP:Fe using band-edge resonance and temperature stabilization," Appl. Phys. Lett. 57, 2776–2778 (1991).
[CrossRef]

Paslaski, J.

M. Cronin-Golomb, J. Paslaski, and A. Yariv, "Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors," Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

Perechinskii, S. I.

A. A. Grabar, Y. M. Vysochanskiy, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, "Thermooptic investigations of ferroelectric Sn2P2S6," Sov. Phys. Solid State 26, 2087–2089 (1984).

Petrov, M. P.

M. P. Petrov, S. J. Stepanov, A. V. Khomenko, Photorefrac-tive Crystals in Coherent Optical Systems, Vol. 59 of Optical Sciences (Springer-Verlag, Berlin, 1991).
[CrossRef]

S. I. Stepanov and M. P. Petrov, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 263.
[CrossRef]

Picoli, G.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave-mixing gain enhancement in photorefractive In-P:Fe: a new mechanism of resonance," J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

Ross, G. W.

G. W. Ross, P. Hribek, R. W. Eason, M. H. Garret, and D. Rytz, "Impurity enhanced self-pumped phase conjugation in the near infrared in 'blue' BaTiO3," Opt. Commun. 101, 60–64 (1993).
[CrossRef]

Rotge, J. R.

Rupp, R. A.

A. N. Shumelyuk, U. Hellwig, R. A. Rupp, S. G. Odoulov, and A. A. Grabar, "Infrared recording in photorefractivetin-hypothiodiphosphate (Sn2P2S6)," in Photorefractive Materials, Effects, and Devices Topical Meeting (Optical Society of America, Washington, D.C., 1995), pp. 80–83.

Rytz, D.

G. W. Ross, P. Hribek, R. W. Eason, M. H. Garret, and D. Rytz, "Impurity enhanced self-pumped phase conjugation in the near infrared in 'blue' BaTiO3," Opt. Commun. 101, 60–64 (1993).
[CrossRef]

Salo, L. A.

A. A. Grabar, Y. M. Vysochanskiy, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, "Thermooptic investigations of ferroelectric Sn2P2S6," Sov. Phys. Solid State 26, 2087–2089 (1984).

Schaefer, H.

G. Dittmar and H. Schaefer, "The crystal structure of Sn2P2S6," Z. Naturforsch. 29b, 312–317 (1974).

Schwartz, R. N.

Segev, M.

Shumelyuk, A. N.

A. N. Shumelyuk, U. Hellwig, R. A. Rupp, S. G. Odoulov, and A. A. Grabar, "Infrared recording in photorefractivetin-hypothiodiphosphate (Sn2P2S6)," in Photorefractive Materials, Effects, and Devices Topical Meeting (Optical Society of America, Washington, D.C., 1995), pp. 80–83.

S. G. Odoulov, A. N. Shumelyuk, G. A. Brost, and K. M. Magde, "Enhancement of beam coupling in near infrared for tin hypothiodiphosphate," Appl. Phys. Lett. (to be published).

Slivka, V. Yu.

A. A. Grabar, Yu. M. Vysochanskiy, I. M. Stoyka, M. M. Danko, and V. Yu. Slivka, "Influence of the domain structure on photorefractive properties of a ferroelectric Sn2P2S6," Ukr. Phys. J. 39, 941–942 (1994).

A. A. Grabar, Y. M. Vysochanskiy, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, "Thermooptic investigations of ferroelectric Sn2P2S6," Sov. Phys. Solid State 26, 2087–2089 (1984).

A. A. Volkov, G. V. Kozlov, N. I. Afanasieva, Yu. M. Vysoch-anskiy, A. A. Grabar, and V. Yu. Slivka, "Low-frequency modes in the infrared spectrum of an Sn2P2S6 crystal," Sov. Phys. Solid State 25, 1482–1483 (1983).

M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korda, and V. Yu. Slivka, "Optical properties of Sn2P2S6 crystals," Sov. Phys. Solid State 19, 1794–1795 (1977).

Yu. M. Vysochanskiy and V. Yu. Slivka, Ferroelectrics of the Sn2P2S6 Family. Properties in the Vicinity of the Lifshits Point, 1st ed. (Scientific Edition, L'vov, 1994), Chap. 10, p. 244 (in Russian).

Soskin, M.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vi-netskii, "Holographic storage in electrooptic crystals," Fer-roelectrics 22, 949–964 (1979).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov and M. P. Petrov, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 263.
[CrossRef]

Sternklar, S.

Stoyka, I. M.

A. A. Grabar, Yu. M. Vysochanskiy, I. M. Stoyka, M. M. Danko, and V. Yu. Slivka, "Influence of the domain structure on photorefractive properties of a ferroelectric Sn2P2S6," Ukr. Phys. J. 39, 941–942 (1994).

Strait, J.

A. M. Glass and J. Strait, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 237.
[CrossRef]

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hell-warth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Townsend, R. L.

R. L. Townsend and J. T. LaMacchia, "Optically induced refractive index changes in BaTiO3," J. Appl. Phys. 41, 5188–5192 (1970).
[CrossRef]

Valley, G. C.

Vieux, V.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave-mixing gain enhancement in photorefractive In-P:Fe: a new mechanism of resonance," J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

Vi-netskii, V.

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vi-netskii, "Holographic storage in electrooptic crystals," Fer-roelectrics 22, 949–964 (1979).
[CrossRef]

Volkov, A. A.

A. A. Volkov, G. V. Kozlov, N. I. Afanasieva, Yu. M. Vysoch-anskiy, A. A. Grabar, and V. Yu. Slivka, "Low-frequency modes in the infrared spectrum of an Sn2P2S6 crystal," Sov. Phys. Solid State 25, 1482–1483 (1983).

Vysochanskiy, Y. M.

A. A. Grabar, Y. M. Vysochanskiy, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, "Thermooptic investigations of ferroelectric Sn2P2S6," Sov. Phys. Solid State 26, 2087–2089 (1984).

Vysochanskiy, Yu. M.

A. A. Grabar, Yu. M. Vysochanskiy, I. M. Stoyka, M. M. Danko, and V. Yu. Slivka, "Influence of the domain structure on photorefractive properties of a ferroelectric Sn2P2S6," Ukr. Phys. J. 39, 941–942 (1994).

A. A. Grabar, R. I. Muzhikash, A. D. Kostyuk, and Yu. M. Vysochanskiy, "Investigation of the switching process in the domain structure of ferroelectric Sn2P2S6 by the dynamic holographic method," Sov. Phys. Solid State 33, 1314–1316 (1991).

Yu. M. Vysochanskiy and V. Yu. Slivka, Ferroelectrics of the Sn2P2S6 Family. Properties in the Vicinity of the Lifshits Point, 1st ed. (Scientific Edition, L'vov, 1994), Chap. 10, p. 244 (in Russian).

Vysoch-anskiy, Yu. M.

A. A. Volkov, G. V. Kozlov, N. I. Afanasieva, Yu. M. Vysoch-anskiy, A. A. Grabar, and V. Yu. Slivka, "Low-frequency modes in the infrared spectrum of an Sn2P2S6 crystal," Sov. Phys. Solid State 25, 1482–1483 (1983).

Wechsler, B. A.

Weiss, S.

Yariv, A.

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, "Oscillation with photorefractive gain," IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

S. K. Kwong and A. Yariv, "One-way, real time wave front converters," Appl. Phys. Lett. 48, 564–566 (1986).
[CrossRef]

M. Cronin-Golomb, J. Paslaski, and A. Yariv, "Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors," Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

Zhivkova, S.

S. Zhivkova and M. Miteva, "Holographic recording in pho-torefractive crystals with simultaneous electron-hole transport and two active centers," J. Appl. Phys. 68, 3099–3103 (1990).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. E. Millerd, S. D. Koehler, E. M. Garmire, A. Partovi, A. M. Glass, and M. B. Klein, "Photorefractive gain enhancement in InP:Fe using band-edge resonance and temperature stabilization," Appl. Phys. Lett. 57, 2776–2778 (1991).
[CrossRef]

S. K. Kwong and A. Yariv, "One-way, real time wave front converters," Appl. Phys. Lett. 48, 564–566 (1986).
[CrossRef]

M. Cronin-Golomb, J. Paslaski, and A. Yariv, "Vibration resistance, short coherence length operation, and mode-locked pumping in passive phase conjugate mirrors," Appl. Phys. Lett. 47, 1131–1133 (1985).
[CrossRef]

Fer-roelectrics

N. Kukhtarev, V. Markov, S. Odoulov, M. Soskin, and V. Vi-netskii, "Holographic storage in electrooptic crystals," Fer-roelectrics 22, 949–964 (1979).
[CrossRef]

IEEE J. Quantum Electron.

S. K. Kwong, M. Cronin-Golomb, and A. Yariv, "Oscillation with photorefractive gain," IEEE J. Quantum Electron. 22, 1508–1523 (1986).
[CrossRef]

J. Appl. Phys.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, "Theory of two-wave-mixing gain enhancement in photorefractive In-P:Fe: a new mechanism of resonance," J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, and R. W. Hell-warth, "Photorefractive effects and light-induced charge migration in barium titanate," J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

R. L. Townsend and J. T. LaMacchia, "Optically induced refractive index changes in BaTiO3," J. Appl. Phys. 41, 5188–5192 (1970).
[CrossRef]

S. Zhivkova and M. Miteva, "Holographic recording in pho-torefractive crystals with simultaneous electron-hole transport and two active centers," J. Appl. Phys. 68, 3099–3103 (1990).
[CrossRef]

M. B. Klein and G. C. Valley, "Beam coupling in BaTiO3/sub> at 442 nm," J. Appl. Phys. 57, 4901–4905 (1987).
[CrossRef]

J. Opt. Soc. Am. B

Mater. Res. Bull.

C. D. Carpentier and R. Nitsche, "Ferroelectricity in Sn2P2S6," Mater. Res. Bull. 9, 1097–1100 (1974).
[CrossRef]

C. D. Carpentier and R. Nitsche, "Vapour growth and crystal data of the thio(seleno)-hypodiphosphates Sn2P2S6, Sn2P2Se6, Pb2P2S6, Pb2P2Se6 and their mixed crystals," Mater. Res. Bull. 9, 401–410 (1974).
[CrossRef]

Opt. Commun.

G. W. Ross, P. Hribek, R. W. Eason, M. H. Garret, and D. Rytz, "Impurity enhanced self-pumped phase conjugation in the near infrared in 'blue' BaTiO3," Opt. Commun. 101, 60–64 (1993).
[CrossRef]

Opt. Lett.

Sov. Phys. Solid State

A. A. Volkov, G. V. Kozlov, N. I. Afanasieva, Yu. M. Vysoch-anskiy, A. A. Grabar, and V. Yu. Slivka, "Low-frequency modes in the infrared spectrum of an Sn2P2S6 crystal," Sov. Phys. Solid State 25, 1482–1483 (1983).

A. A. Grabar, R. I. Muzhikash, A. D. Kostyuk, and Yu. M. Vysochanskiy, "Investigation of the switching process in the domain structure of ferroelectric Sn2P2S6 by the dynamic holographic method," Sov. Phys. Solid State 33, 1314–1316 (1991).

M. I. Gurzan, A. P. Buturlakin, V. S. Gerasimenko, N. F. Korda, and V. Yu. Slivka, "Optical properties of Sn2P2S6 crystals," Sov. Phys. Solid State 19, 1794–1795 (1977).

A. A. Grabar, Y. M. Vysochanskiy, S. I. Perechinskii, L. A. Salo, M. I. Gurzan, and V. Yu. Slivka, "Thermooptic investigations of ferroelectric Sn2P2S6," Sov. Phys. Solid State 26, 2087–2089 (1984).

Sov. Tech. Phys. Lett.

N. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438–440 (1976).

Ukr. Phys. J.

A. A. Grabar, Yu. M. Vysochanskiy, I. M. Stoyka, M. M. Danko, and V. Yu. Slivka, "Influence of the domain structure on photorefractive properties of a ferroelectric Sn2P2S6," Ukr. Phys. J. 39, 941–942 (1994).

Z. Naturforsch.

G. Dittmar and H. Schaefer, "The crystal structure of Sn2P2S6," Z. Naturforsch. 29b, 312–317 (1974).

Other

Until now the signs of movable charges responsible for the fast and the slow gratings were not established. The attribution of the fast component to electrons and of the slow component to holes still has to be proved by independent experiments.

S. I. Stepanov and M. P. Petrov, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 263.
[CrossRef]

M. P. Petrov, S. J. Stepanov, A. V. Khomenko, Photorefrac-tive Crystals in Coherent Optical Systems, Vol. 59 of Optical Sciences (Springer-Verlag, Berlin, 1991).
[CrossRef]

M. B. Klein, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 195.
[CrossRef]

A. N. Shumelyuk, U. Hellwig, R. A. Rupp, S. G. Odoulov, and A. A. Grabar, "Infrared recording in photorefractivetin-hypothiodiphosphate (Sn2P2S6)," in Photorefractive Materials, Effects, and Devices Topical Meeting (Optical Society of America, Washington, D.C., 1995), pp. 80–83.

Yu. M. Vysochanskiy and V. Yu. Slivka, Ferroelectrics of the Sn2P2S6 Family. Properties in the Vicinity of the Lifshits Point, 1st ed. (Scientific Edition, L'vov, 1994), Chap. 10, p. 244 (in Russian).

S. G. Odoulov, A. N. Shumelyuk, G. A. Brost, and K. M. Magde, "Enhancement of beam coupling in near infrared for tin hypothiodiphosphate," Appl. Phys. Lett. (to be published).

A. M. Glass and J. Strait, in Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), p. 237.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (19)

Fig. 1
Fig. 1

Absorption spectrum α (λ) of a 2.3-mm-thick SPS sample with light polarization nearly parallel to the axis of the spontaneous polarization.

Fig. 2
Fig. 2

Experimental setup: F1/F2, optical-density filters; λ/2, λ/2 plate; BS, beam splitter; M, Mirror; P1, P2, polarizers; D, detector.

Fig. 3
Fig. 3

Temporal variation of the weak signal wave for two opposite orientations of the ferroelectric axis [(a), (b)]. In the inset the initial part of the recording process is shown. Sample 2: total intensity on the sample, 30 W/cm2; initial intensity ratio, 1:50; grating period, Λ = 2.3 µm.

Fig. 4
Fig. 4

(a) Relaxation time τf and (b) reciprocal quantity (1/τf) of the fast grating versus the light intensity I. The filled points and the open squares correspond to the sample before and after preexposure to white light, respectively.

Fig. 5
Fig. 5

Relaxation time τs of the slow grating versus the light intensity I.

Fig. 6
Fig. 6

Gain factor Γf (corrected for effects of the experimental geometry) versus grating spacing Λ.

Fig. 7
Fig. 7

Gain factors Γf,s (with geometric correction) versus total intensity I of the recording waves.

Fig. 8
Fig. 8

Temporal dependence of the diffraction efficiency. The inset shows the detailed behavior just after the writing wave is blocked.

Fig. 9
Fig. 9

(a) Dependence of the grating spacing on the gain factor, and (b) linearized dependence for evaluation of the effective electro-optic constant and effective trap density. Curves 1 and 2 correspond to the sample after and before preexposure to white light, respectively (with geometric correction).

Fig. 10
Fig. 10

Gain factor Γf (with geometric correction) versus preexposure time.

Fig. 11
Fig. 11

Gain factor versus time after preexposure. The filled squares and circles correspond to the gains Γf for the fast grating and Γs for the slow grating, respectively (with geometric correction).

Fig. 12
Fig. 12

Dynamics of the intensity variation for different temperatures of the sample.

Fig. 13
Fig. 13

Log plot of inverted relaxation time versus inverse temperature (Arrhenius plot) for the cooling process of the crystal.

Fig. 14
Fig. 14

Relaxation time of the fast grating τf versus the intensity for different grating spacings.

Fig. 15
Fig. 15

Erasure time of the slow grating τ2E versus the grating spacing.

Fig. 16
Fig. 16

Scheme of electron transitions and energy levels.

Fig. 17
Fig. 17

Dependence of the product (f)−1 on the grating spatial frequency K.

Fig. 18
Fig. 18

Erasure time of the slow grating τsE versus the grating spatial frequency.

Fig. 19
Fig. 19

Interaction area of the beam inside the crystal: , crystal thickness; θi, angle of incidence inside the crystal; 2x, beam diameter at the height y(x) of the beam cross section.

Tables (1)

Tables Icon

Table 1 Dimensions and Measured Data for Three SPS Samplesa

Equations (10)

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

Γ t = Γ f t Γ s t ,
Γ f t = Γ f 1 exp t / τ f , Γ s t = Γ s 1 exp t / τ s ,
I , t I 0 1 + Γ t
Γ = 4 π 2 n 3 r eff k B T / λ Λ e   cos   θ 1 + S / 2 π Λ 2 1 .
1 / Γ Λ   cos   θ = λ e / 4 π 2 n 3 r eff k B T 1 + S / 2 π Λ 2 ,
S = ε ε 0 k B T / e 2 N R 1 / 2 ,
r eff = λ e / 4 π 2 n 3 k B T / 1 / Γ Λ   cos   θ ,
τ = τ di 1 + K D 2 / 1 + K S 2   1 + κ I / σ d ,
τ f I = ε ε 0 / κ 1 + K D e 2 / 1 + K S e 2 .
τ s E = τ di h 1 + K D h 2 / 1 + K S h 2 .

Metrics