Abstract

We report the use of actively stabilized holographic recording in high-diffraction-efficiency crystals in which strong energy coupling occurs. We use this technique to characterize the photorefractive properties of a Ti-doped (KxNa1−x)2m(SryBa1−y)1−mNb2O6 crystal and compare our results with available data in the literature for other dopants and other crystals.

© 1995 Optical Society of America

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  1. Y. Xu and H. Chen, "Single crystal growth and determination of physical properties of (K1−xNax)0.4.(Sr1−yBay) 0.8 Nb2O6," Ferroelectrics 54, 123–126 (1984).
    [CrossRef]
  2. R. R. Neurgaonkar and W. K. Cory, "Progress in photorefractive tungsten bronze crystals," J. Opt. Soc. Am. B 3, 274–282 (1986).
    [CrossRef]
  3. H. Chen and Y. Xu, "Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6 (KNSBN) single crystals with tungsten-bronze structure," J. Cryst. Growth 96, 357–362 (1989).
    [CrossRef]
  4. D. Zhu, R. Wang, J. Tan, and D. Mo, "A study on the gain coefficient of two-wave coupling in doped KNSBN crystals," Acta Phys. Sin. 41, 1440–1447 (1992).
  5. Y. Tomita, J. Bergquist, and M. A. Shibata, "Photorefractive properties of undoped, Cr-doped, and Cu-doped potassium sodium strontium barium niobate crystals," J. Opt. Soc. Am. B 10, 94–99 (1993).
    [CrossRef]
  6. J. Rodriguez, A. Siahmakoun, G. Salamo, M. J. Miller, W. W. Clark III, and G. L. Wood, "BSKNN as a self-pumped phase conjugator," Appl. Opt. 26, 1732–1735 (1987).
    [CrossRef] [PubMed]
  7. J. Xu, Y. Wu, G. Zhang, D. Sun, Y. Song, and H. Chen, "High-performance self-pumped phase-conjugator with a multichannel in KNSBN:Cu crystal," Opt. Lett. 16, 1255–1257 (1991).
    [CrossRef] [PubMed]
  8. S. Bian, J. Zhang, X. Su, K. Xu, W. Sun, Q. Jiang, H. Chen, and D. Sun, "Self-pumped phase conjugation of 18°-cut Cedoped KNSBN crystal at 632.8 nm," Opt. Lett. 18, 769–771 (1993).
    [CrossRef] [PubMed]
  9. P. A. M. dos Santos, L. Cescato, and J. Frejlich, "Interference term real-time measurement in stabilized two-wave mixing in photorefractives," Opt. Lett. 13, 1014–1016 (1988).
    [CrossRef]
  10. J. Frejlich and P. M. Garcia, "Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals," Appl. Phys. A 55, 49–54 (1992).
    [CrossRef]
  11. A. A. Freschi and J. Frejlich, "Stabilized photorefractive modulation recording beyond 100% diffraction efficiency in LiNbO3:Fe crystals," J. Opt. Soc. Am. B 11, 1837–1841 (1994).
    [CrossRef]
  12. J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, "Self-enhancement in lithium niobate," Opt. Commun. 72, 175–179 (1989).
    [CrossRef]
  13. C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, "Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials," Opt. Commun. 79, 349–352 (1990).
    [CrossRef]
  14. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–961 (1979).
    [CrossRef]
  15. P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484–519 (1989).
    [CrossRef]
  16. J. Frejlich, "Real-time photorefractive hologram phase-shift measurement and self-diffraction effects," Opt. Commun. 107, 260–264 (1994).
    [CrossRef]
  17. P. Günter, "Photorefractive effects and materials," in Photorefractive Materials and Their Applications I, P. Güunter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).
    [CrossRef]
  18. J. Frejlich, L. Cescato, and G. F. Mendes, "Analysis of an active stabilization system for a holographic setup," Appl. Opt. 27, 1967–1976 (1988).
    [CrossRef] [PubMed]
  19. J. Frejlich, P. M. Garcia, and L. Cescato, "Adaptive fringe-locked running hologram in photorefractive crystals," Opt. Lett. 14, 1210–1212 (1989).
    [CrossRef] [PubMed]
  20. J. Frejlich, P. M. Garcia, and L. Cescato, "Adaptive fringelocked running hologram in photorefractive crystals: errata," Opt. Lett. 15, 1247 (1990).
    [CrossRef] [PubMed]
  21. J. Frejlich, "Fringe-locked running hologram and multiple photoactive species in Bi12TiO20," J. Appl. Phys. 68, 3104–3109 (1990).
    [CrossRef]
  22. P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, "Transport length, quantum efficiency, and trap density measurement in Bi12SiO20," J. Appl. Phys. 66, 247–251 (1989).
    [CrossRef]
  23. R. A. Vazquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416–1427 (1992).
    [CrossRef]
  24. M. B. Klein, "Beam coupling in undoped GaAs at 1.06 μm using the photorefractive effect," Opt. Lett. 9, 350–352 (1984).
    [CrossRef] [PubMed]

1994 (2)

A. A. Freschi and J. Frejlich, "Stabilized photorefractive modulation recording beyond 100% diffraction efficiency in LiNbO3:Fe crystals," J. Opt. Soc. Am. B 11, 1837–1841 (1994).
[CrossRef]

J. Frejlich, "Real-time photorefractive hologram phase-shift measurement and self-diffraction effects," Opt. Commun. 107, 260–264 (1994).
[CrossRef]

1993 (2)

1992 (3)

D. Zhu, R. Wang, J. Tan, and D. Mo, "A study on the gain coefficient of two-wave coupling in doped KNSBN crystals," Acta Phys. Sin. 41, 1440–1447 (1992).

J. Frejlich and P. M. Garcia, "Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals," Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

R. A. Vazquez, R. R. Neurgaonkar, and M. D. Ewbank, "Photorefractive properties of SBN:60 systematically doped with rhodium," J. Opt. Soc. Am. B 9, 1416–1427 (1992).
[CrossRef]

1991 (1)

1990 (3)

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, "Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials," Opt. Commun. 79, 349–352 (1990).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, "Adaptive fringelocked running hologram in photorefractive crystals: errata," Opt. Lett. 15, 1247 (1990).
[CrossRef] [PubMed]

J. Frejlich, "Fringe-locked running hologram and multiple photoactive species in Bi12TiO20," J. Appl. Phys. 68, 3104–3109 (1990).
[CrossRef]

1989 (5)

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, "Transport length, quantum efficiency, and trap density measurement in Bi12SiO20," J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, "Adaptive fringe-locked running hologram in photorefractive crystals," Opt. Lett. 14, 1210–1212 (1989).
[CrossRef] [PubMed]

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, "Self-enhancement in lithium niobate," Opt. Commun. 72, 175–179 (1989).
[CrossRef]

H. Chen and Y. Xu, "Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6 (KNSBN) single crystals with tungsten-bronze structure," J. Cryst. Growth 96, 357–362 (1989).
[CrossRef]

1988 (3)

1987 (1)

1986 (1)

1984 (2)

Y. Xu and H. Chen, "Single crystal growth and determination of physical properties of (K1−xNax)0.4.(Sr1−yBay) 0.8 Nb2O6," Ferroelectrics 54, 123–126 (1984).
[CrossRef]

M. B. Klein, "Beam coupling in undoped GaAs at 1.06 μm using the photorefractive effect," Opt. Lett. 9, 350–352 (1984).
[CrossRef] [PubMed]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Bergquist, J.

Bian, S.

Cescato, L.

Chen, H.

S. Bian, J. Zhang, X. Su, K. Xu, W. Sun, Q. Jiang, H. Chen, and D. Sun, "Self-pumped phase conjugation of 18°-cut Cedoped KNSBN crystal at 632.8 nm," Opt. Lett. 18, 769–771 (1993).
[CrossRef] [PubMed]

J. Xu, Y. Wu, G. Zhang, D. Sun, Y. Song, and H. Chen, "High-performance self-pumped phase-conjugator with a multichannel in KNSBN:Cu crystal," Opt. Lett. 16, 1255–1257 (1991).
[CrossRef] [PubMed]

H. Chen and Y. Xu, "Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6 (KNSBN) single crystals with tungsten-bronze structure," J. Cryst. Growth 96, 357–362 (1989).
[CrossRef]

Y. Xu and H. Chen, "Single crystal growth and determination of physical properties of (K1−xNax)0.4.(Sr1−yBay) 0.8 Nb2O6," Ferroelectrics 54, 123–126 (1984).
[CrossRef]

Clark, W. W.

Cory, W. K.

Ewbank, M. D.

Frejlich, J.

A. A. Freschi and J. Frejlich, "Stabilized photorefractive modulation recording beyond 100% diffraction efficiency in LiNbO3:Fe crystals," J. Opt. Soc. Am. B 11, 1837–1841 (1994).
[CrossRef]

J. Frejlich, "Real-time photorefractive hologram phase-shift measurement and self-diffraction effects," Opt. Commun. 107, 260–264 (1994).
[CrossRef]

J. Frejlich and P. M. Garcia, "Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals," Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

J. Frejlich, "Fringe-locked running hologram and multiple photoactive species in Bi12TiO20," J. Appl. Phys. 68, 3104–3109 (1990).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, "Adaptive fringelocked running hologram in photorefractive crystals: errata," Opt. Lett. 15, 1247 (1990).
[CrossRef] [PubMed]

J. Frejlich, P. M. Garcia, and L. Cescato, "Adaptive fringe-locked running hologram in photorefractive crystals," Opt. Lett. 14, 1210–1212 (1989).
[CrossRef] [PubMed]

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, "Transport length, quantum efficiency, and trap density measurement in Bi12SiO20," J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

P. A. M. dos Santos, L. Cescato, and J. Frejlich, "Interference term real-time measurement in stabilized two-wave mixing in photorefractives," Opt. Lett. 13, 1014–1016 (1988).
[CrossRef]

J. Frejlich, L. Cescato, and G. F. Mendes, "Analysis of an active stabilization system for a holographic setup," Appl. Opt. 27, 1967–1976 (1988).
[CrossRef] [PubMed]

Freschi, A. A.

Garcia, P. M.

J. Frejlich and P. M. Garcia, "Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals," Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, "Adaptive fringelocked running hologram in photorefractive crystals: errata," Opt. Lett. 15, 1247 (1990).
[CrossRef] [PubMed]

J. Frejlich, P. M. Garcia, and L. Cescato, "Adaptive fringe-locked running hologram in photorefractive crystals," Opt. Lett. 14, 1210–1212 (1989).
[CrossRef] [PubMed]

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, "Transport length, quantum efficiency, and trap density measurement in Bi12SiO20," J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

Günter, P.

P. Günter, "Photorefractive effects and materials," in Photorefractive Materials and Their Applications I, P. Güunter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).
[CrossRef]

Jiang, Q.

Klein, M. B.

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Kwak, C. H.

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, "Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials," Opt. Commun. 79, 349–352 (1990).
[CrossRef]

Lee, E.-H.

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, "Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials," Opt. Commun. 79, 349–352 (1990).
[CrossRef]

Lee, H. K.

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, "Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials," Opt. Commun. 79, 349–352 (1990).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Mendes, G. F.

Miller, M. J.

Mo, D.

D. Zhu, R. Wang, J. Tan, and D. Mo, "A study on the gain coefficient of two-wave coupling in doped KNSBN crystals," Acta Phys. Sin. 41, 1440–1447 (1992).

Neurgaonkar, R. R.

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Otten, J.

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, "Self-enhancement in lithium niobate," Opt. Commun. 72, 175–179 (1989).
[CrossRef]

Ozols, A.

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, "Self-enhancement in lithium niobate," Opt. Commun. 72, 175–179 (1989).
[CrossRef]

Park, S. Y.

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, "Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials," Opt. Commun. 79, 349–352 (1990).
[CrossRef]

Reinfelde, M.

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, "Self-enhancement in lithium niobate," Opt. Commun. 72, 175–179 (1989).
[CrossRef]

Ringhofer, K. H.

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, "Self-enhancement in lithium niobate," Opt. Commun. 72, 175–179 (1989).
[CrossRef]

Rodriguez, J.

Salamo, G.

Santos, P. A. M. dos

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, "Transport length, quantum efficiency, and trap density measurement in Bi12SiO20," J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

P. A. M. dos Santos, L. Cescato, and J. Frejlich, "Interference term real-time measurement in stabilized two-wave mixing in photorefractives," Opt. Lett. 13, 1014–1016 (1988).
[CrossRef]

Shibata, M. A.

Siahmakoun, A.

Song, Y.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Su, X.

Sun, D.

Sun, W.

Tan, J.

D. Zhu, R. Wang, J. Tan, and D. Mo, "A study on the gain coefficient of two-wave coupling in doped KNSBN crystals," Acta Phys. Sin. 41, 1440–1447 (1992).

Tomita, Y.

Vazquez, R. A.

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Wang, R.

D. Zhu, R. Wang, J. Tan, and D. Mo, "A study on the gain coefficient of two-wave coupling in doped KNSBN crystals," Acta Phys. Sin. 41, 1440–1447 (1992).

Wood, G. L.

Wu, Y.

Xu, J.

Xu, K.

Xu, Y.

H. Chen and Y. Xu, "Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6 (KNSBN) single crystals with tungsten-bronze structure," J. Cryst. Growth 96, 357–362 (1989).
[CrossRef]

Y. Xu and H. Chen, "Single crystal growth and determination of physical properties of (K1−xNax)0.4.(Sr1−yBay) 0.8 Nb2O6," Ferroelectrics 54, 123–126 (1984).
[CrossRef]

Yeh, P.

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

Zhang, G.

Zhang, J.

Zhu, D.

D. Zhu, R. Wang, J. Tan, and D. Mo, "A study on the gain coefficient of two-wave coupling in doped KNSBN crystals," Acta Phys. Sin. 41, 1440–1447 (1992).

Acta Phys. Sin. (1)

D. Zhu, R. Wang, J. Tan, and D. Mo, "A study on the gain coefficient of two-wave coupling in doped KNSBN crystals," Acta Phys. Sin. 41, 1440–1447 (1992).

Appl. Opt. (2)

Appl. Phys. A (1)

J. Frejlich and P. M. Garcia, "Quasipermanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals," Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

Ferroelectrics (2)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals," Ferroelectrics 22, 949–961 (1979).
[CrossRef]

Y. Xu and H. Chen, "Single crystal growth and determination of physical properties of (K1−xNax)0.4.(Sr1−yBay) 0.8 Nb2O6," Ferroelectrics 54, 123–126 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

J. Appl. Phys. (2)

J. Frejlich, "Fringe-locked running hologram and multiple photoactive species in Bi12TiO20," J. Appl. Phys. 68, 3104–3109 (1990).
[CrossRef]

P. A. M. dos Santos, P. M. Garcia, and J. Frejlich, "Transport length, quantum efficiency, and trap density measurement in Bi12SiO20," J. Appl. Phys. 66, 247–251 (1989).
[CrossRef]

J. Cryst. Growth (1)

H. Chen and Y. Xu, "Growth and some properties of undoped and doped (K1−xNax)0.4(Sr1−yBay)0.8Nb2O6 (KNSBN) single crystals with tungsten-bronze structure," J. Cryst. Growth 96, 357–362 (1989).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Commun. (3)

J. Otten, A. Ozols, M. Reinfelde, and K. H. Ringhofer, "Self-enhancement in lithium niobate," Opt. Commun. 72, 175–179 (1989).
[CrossRef]

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, "Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials," Opt. Commun. 79, 349–352 (1990).
[CrossRef]

J. Frejlich, "Real-time photorefractive hologram phase-shift measurement and self-diffraction effects," Opt. Commun. 107, 260–264 (1994).
[CrossRef]

Opt. Lett. (6)

Other (1)

P. Günter, "Photorefractive effects and materials," in Photorefractive Materials and Their Applications I, P. Güunter and J.-P. Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Intensity absorption coefficient measured for a Ti-doped (0.36 wt. %) KNSBN crystal with extraordinarily polarized light.

Fig. 2
Fig. 2

Actively stabilized holographic recording setup: BS, beam splitter; M, mirror; LA 1, LA 2, lock-in amplifiers tuned to Ω and 2Ω frequencies, respectively; HV, high-voltage source; OSC, oscillator at frequency Ω; D, photodetector.

Fig. 3
Fig. 3

(Circles) Evolution of the I-term data in actively stabilized recording conditions and (solid curve) monoexponential function fit.

Fig. 4
Fig. 4

Steady-state values for I as a function of the external incidence angles θ.

Fig. 5
Fig. 5

Exponential gain coefficient Γ as a function of the external incidence angle θ.

Fig. 6
Fig. 6

Photorefractive sensitivity S as a function of the external incidence angle θ.

Fig. 7
Fig. 7

Hologram response rate τH−1 dependence on the total incident light intensity inside the crystal.

Tables (2)

Tables Icon

Table 1 Experimental Data

Tables Icon

Table 2 Comparative Dataa

Equations (20)

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

cos θ i R z = i π n 1 λ exp ( i ϕ ) m S ,
cos θ i S z = i π n 1 λ exp ( - i ϕ ) m * R ,
I S = I S 0 1 + β 2 1 + β 2 exp ( - Γ d ) ,
ψ S ( d ) - ψ S ( 0 ) = Δ ψ S = 1 2 tan ϕ ln 1 + β 2 exp ( - Γ d ) 1 + β 2 ,
Γ = 4 π n 1 sin ϕ λ cos θ i ,
n 1 sin ϕ = n 3 r eff ζ 2 E D 1 + K 2 l S 2 cos 2 θ i .
I S = S 0 1 - η exp [ i ψ d sin ( Ω t ) ] + i R 0 η exp ( - i φ ) 2 .
I Ω = 2 ψ d [ I S 0 I R 0 η ( 1 - η ) ] 1 / 2 cos φ ,
I 2 Ω = ( ψ d 2 / 2 ) [ I S 0 I R 0 η ( 1 - η ) ] 1 / 2 sin φ .
η = β 2 [ exp ( Γ d / 2 ) - 1 ] 2 ( 1 + β 2 ) [ β 2 + exp ( Γ d ) ] .
I Ω = 0 ,
I 2 Ω = ( ψ d 2 / 4 ) I S 0 I R 0 exp ( Γ d ) - 1 exp ( Γ d ) + 1 .
S = 1 I 0 α ( n 1 t ) t = 0
S = ( n 3 r eff ζ ) ( Φ μ τ ) ( k B T 2 h ν ɛ 0 K cos 2 θ i 1 + K 2 L D 2 )
σ d σ ph = q μ τ Φ α I 0 h ν ,             α d 1 ,
τ SC - 1 = σ d + q μ τ Φ α I 0 / h ν ɛ 0 1 + K 2 l S 2 1 + K 2 L D 2 ,
I 2 Ω t = I 2 Ω η η Γ Γ n 1 n 1 t ,
( I 2 Ω η η Γ Γ n 1 ) t = 0 = π ψ d 2 d I S 0 I R 0 2 λ cos θ i .
S = 2 λ cos θ i π k D ψ d 2 α I 0 d I S 0 I R 0 ( I 2 Ω t ) t = 0 ,
I 2 Ω = [ I 2 Ω ] S [ 1 - exp ( - t / τ H ) ]

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