Abstract

Gated recording based on two-step excitation with metastable shallow traps is analyzed theoretically. A two-center model, including the tail of the conduction band into the bandgap, is suggested. The tail provides a way to model efficiently excitation from deep to shallow traps and long recombination times back into deep traps. The results are compared with experimental results performed with La3Ga5SiO14, and good agreement is found. Further, the limiting material parameters determining the material sensitivity are identified.

© 2001 Optical Society of America

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References

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  1. J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
    [CrossRef]
  2. F. Micheron and G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
    [CrossRef]
  3. D. von der Linde, A. Glass, and K. Rodgers, “Optical storage using refractive index changes induced by two-step excitation,” J. Appl. Phys. 47, 217–220 (1976).
    [CrossRef]
  4. L. Paraschis, M. Bashaw, A. Liu, and L. Hesselink, “Resonant two-photon processes for nonvolatile holography in photorefractive crystals under continuous-wave illumination,” J. Opt. Soc. Am. B 14, 2670–2680 (1997).
    [CrossRef]
  5. Y. Ming, E. Krätzig, and R. Orlowski, “Photorefractive effects in LiNbO3:Cr induced by two-step excitation,” Phys. Status Solidi 92, 221–229 (1987).
    [CrossRef]
  6. H. Vormann and E. Krätzig, “Two step excitation in LiTaO3:Fe for optical data storage,” Solid State Commun. 49, 843–847 (1984).
    [CrossRef]
  7. Y. Bai, R. Neurgaonkar, and R. Kachru, “Resonant two-photon photorefractive grating in praseodymium-doped strontium barium niobate with cw lasers,” Opt. Lett. 21, 567–569 (1996).
    [CrossRef] [PubMed]
  8. K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665–668 (1998).
    [CrossRef]
  9. F. Jermann and J. Otten, “Light-induced charge transport in LiNbO3:Fe at high light intensities,” J. Opt. Soc. Am. B 10, 2085–2092 (1993).
    [CrossRef]
  10. J. Imbrock, D. Kip, and E. Krätzig, “Nonvolatile holographic storage in iron-doped lithium tantalate with continuous-wave laser light,” Opt. Lett. 24, 1302–1304 (1999).
    [CrossRef]
  11. J. Li, X. H. Li, F. X. Wu, Y. Zhu, X. Wu, and H. F. Wang, “Photorefractive parameters and light-induced absorption in BaTiO3,” Appl. Phys. A 61, 553–557 (1995).
    [CrossRef]
  12. O. V. Kobozev, S. M. Shandarov, A. A. Kamshilin, and V. V. Prokofiev, “Light-induced absorption in a Bi12TiO20 crystal,” J. Opt. A: Pure Appl. Opt. 1, 442–447 (1999).
    [CrossRef]
  13. S. Orlov, M. Segev, A. Yariv, and R. R. Neurgaonkar, “Light-induced absorption in photorefractive strontium barium niobate,” Opt. Lett. 19, 1293–1295 (1994).
    [CrossRef] [PubMed]
  14. A. Liu, M. Lee, and L. Hesselink, “Light-induced absorption of cerium-doped lead barium niobate crystals,” Opt. Lett. 23, 1618–1620 (1998).
    [CrossRef]
  15. O. F. Schirmer, O. Thiemann, and M. Wohlecke, “Defects in LiNbO3. I. Experimental aspects,” J. Phys. Chem. Solids 52, 185–200 (1991).
    [CrossRef]
  16. Y. Bai and R. Kachru, “Nonvolatile holographic storage with two-step recording in lithium niobate using cw lasers,” Phys. Rev. Lett. 78, 2944–2947 (1997).
    [CrossRef]
  17. D. Lande, S. Orlov, A. Akella, L. Hesselink, and R. Neugaonkar, “Digital holographic storage systems incorporating optical fixing,” Opt. Lett. 22, 1722–1724 (1997).
    [CrossRef]
  18. B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer-Verlag, Berlin, 1984).
  19. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  20. T. Nikolajsen, P. M. Johansen, X. Yue, D. Kip, and E. Krätzig, “Two-step two-color recording in a photorefractive praseodymium doped La3Ga5SiO14 crystal,” Appl. Phys. Lett. 74, 4037–4039 (1999).
    [CrossRef]
  21. L. Hesselink, S. S. Orlov, A. Liu, A. Akella, D. Lande, and R. R. Neugaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089–1094 (1998).
    [CrossRef] [PubMed]

1999 (3)

O. V. Kobozev, S. M. Shandarov, A. A. Kamshilin, and V. V. Prokofiev, “Light-induced absorption in a Bi12TiO20 crystal,” J. Opt. A: Pure Appl. Opt. 1, 442–447 (1999).
[CrossRef]

T. Nikolajsen, P. M. Johansen, X. Yue, D. Kip, and E. Krätzig, “Two-step two-color recording in a photorefractive praseodymium doped La3Ga5SiO14 crystal,” Appl. Phys. Lett. 74, 4037–4039 (1999).
[CrossRef]

J. Imbrock, D. Kip, and E. Krätzig, “Nonvolatile holographic storage in iron-doped lithium tantalate with continuous-wave laser light,” Opt. Lett. 24, 1302–1304 (1999).
[CrossRef]

1998 (3)

L. Hesselink, S. S. Orlov, A. Liu, A. Akella, D. Lande, and R. R. Neugaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089–1094 (1998).
[CrossRef] [PubMed]

A. Liu, M. Lee, and L. Hesselink, “Light-induced absorption of cerium-doped lead barium niobate crystals,” Opt. Lett. 23, 1618–1620 (1998).
[CrossRef]

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665–668 (1998).
[CrossRef]

1997 (3)

1996 (1)

1995 (1)

J. Li, X. H. Li, F. X. Wu, Y. Zhu, X. Wu, and H. F. Wang, “Photorefractive parameters and light-induced absorption in BaTiO3,” Appl. Phys. A 61, 553–557 (1995).
[CrossRef]

1994 (1)

1993 (1)

1991 (1)

O. F. Schirmer, O. Thiemann, and M. Wohlecke, “Defects in LiNbO3. I. Experimental aspects,” J. Phys. Chem. Solids 52, 185–200 (1991).
[CrossRef]

1987 (1)

Y. Ming, E. Krätzig, and R. Orlowski, “Photorefractive effects in LiNbO3:Cr induced by two-step excitation,” Phys. Status Solidi 92, 221–229 (1987).
[CrossRef]

1984 (1)

H. Vormann and E. Krätzig, “Two step excitation in LiTaO3:Fe for optical data storage,” Solid State Commun. 49, 843–847 (1984).
[CrossRef]

1976 (1)

D. von der Linde, A. Glass, and K. Rodgers, “Optical storage using refractive index changes induced by two-step excitation,” J. Appl. Phys. 47, 217–220 (1976).
[CrossRef]

1972 (1)

F. Micheron and G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

1971 (1)

J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Adibi, A.

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665–668 (1998).
[CrossRef]

Akella, A.

L. Hesselink, S. S. Orlov, A. Liu, A. Akella, D. Lande, and R. R. Neugaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089–1094 (1998).
[CrossRef] [PubMed]

D. Lande, S. Orlov, A. Akella, L. Hesselink, and R. Neugaonkar, “Digital holographic storage systems incorporating optical fixing,” Opt. Lett. 22, 1722–1724 (1997).
[CrossRef]

Amodei, J. J.

J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Bai, Y.

Y. Bai and R. Kachru, “Nonvolatile holographic storage with two-step recording in lithium niobate using cw lasers,” Phys. Rev. Lett. 78, 2944–2947 (1997).
[CrossRef]

Y. Bai, R. Neurgaonkar, and R. Kachru, “Resonant two-photon photorefractive grating in praseodymium-doped strontium barium niobate with cw lasers,” Opt. Lett. 21, 567–569 (1996).
[CrossRef] [PubMed]

Bashaw, M.

Bismuth, G.

F. Micheron and G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

Buse, K.

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665–668 (1998).
[CrossRef]

Glass, A.

D. von der Linde, A. Glass, and K. Rodgers, “Optical storage using refractive index changes induced by two-step excitation,” J. Appl. Phys. 47, 217–220 (1976).
[CrossRef]

Hesselink, L.

Imbrock, J.

Jermann, F.

Johansen, P. M.

T. Nikolajsen, P. M. Johansen, X. Yue, D. Kip, and E. Krätzig, “Two-step two-color recording in a photorefractive praseodymium doped La3Ga5SiO14 crystal,” Appl. Phys. Lett. 74, 4037–4039 (1999).
[CrossRef]

Kachru, R.

Y. Bai and R. Kachru, “Nonvolatile holographic storage with two-step recording in lithium niobate using cw lasers,” Phys. Rev. Lett. 78, 2944–2947 (1997).
[CrossRef]

Y. Bai, R. Neurgaonkar, and R. Kachru, “Resonant two-photon photorefractive grating in praseodymium-doped strontium barium niobate with cw lasers,” Opt. Lett. 21, 567–569 (1996).
[CrossRef] [PubMed]

Kamshilin, A. A.

O. V. Kobozev, S. M. Shandarov, A. A. Kamshilin, and V. V. Prokofiev, “Light-induced absorption in a Bi12TiO20 crystal,” J. Opt. A: Pure Appl. Opt. 1, 442–447 (1999).
[CrossRef]

Kip, D.

T. Nikolajsen, P. M. Johansen, X. Yue, D. Kip, and E. Krätzig, “Two-step two-color recording in a photorefractive praseodymium doped La3Ga5SiO14 crystal,” Appl. Phys. Lett. 74, 4037–4039 (1999).
[CrossRef]

J. Imbrock, D. Kip, and E. Krätzig, “Nonvolatile holographic storage in iron-doped lithium tantalate with continuous-wave laser light,” Opt. Lett. 24, 1302–1304 (1999).
[CrossRef]

Kobozev, O. V.

O. V. Kobozev, S. M. Shandarov, A. A. Kamshilin, and V. V. Prokofiev, “Light-induced absorption in a Bi12TiO20 crystal,” J. Opt. A: Pure Appl. Opt. 1, 442–447 (1999).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Krätzig, E.

T. Nikolajsen, P. M. Johansen, X. Yue, D. Kip, and E. Krätzig, “Two-step two-color recording in a photorefractive praseodymium doped La3Ga5SiO14 crystal,” Appl. Phys. Lett. 74, 4037–4039 (1999).
[CrossRef]

J. Imbrock, D. Kip, and E. Krätzig, “Nonvolatile holographic storage in iron-doped lithium tantalate with continuous-wave laser light,” Opt. Lett. 24, 1302–1304 (1999).
[CrossRef]

Y. Ming, E. Krätzig, and R. Orlowski, “Photorefractive effects in LiNbO3:Cr induced by two-step excitation,” Phys. Status Solidi 92, 221–229 (1987).
[CrossRef]

H. Vormann and E. Krätzig, “Two step excitation in LiTaO3:Fe for optical data storage,” Solid State Commun. 49, 843–847 (1984).
[CrossRef]

Lande, D.

L. Hesselink, S. S. Orlov, A. Liu, A. Akella, D. Lande, and R. R. Neugaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089–1094 (1998).
[CrossRef] [PubMed]

D. Lande, S. Orlov, A. Akella, L. Hesselink, and R. Neugaonkar, “Digital holographic storage systems incorporating optical fixing,” Opt. Lett. 22, 1722–1724 (1997).
[CrossRef]

Lee, M.

Li, J.

J. Li, X. H. Li, F. X. Wu, Y. Zhu, X. Wu, and H. F. Wang, “Photorefractive parameters and light-induced absorption in BaTiO3,” Appl. Phys. A 61, 553–557 (1995).
[CrossRef]

Li, X. H.

J. Li, X. H. Li, F. X. Wu, Y. Zhu, X. Wu, and H. F. Wang, “Photorefractive parameters and light-induced absorption in BaTiO3,” Appl. Phys. A 61, 553–557 (1995).
[CrossRef]

Liu, A.

Micheron, F.

F. Micheron and G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

Ming, Y.

Y. Ming, E. Krätzig, and R. Orlowski, “Photorefractive effects in LiNbO3:Cr induced by two-step excitation,” Phys. Status Solidi 92, 221–229 (1987).
[CrossRef]

Neugaonkar, R.

Neugaonkar, R. R.

L. Hesselink, S. S. Orlov, A. Liu, A. Akella, D. Lande, and R. R. Neugaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089–1094 (1998).
[CrossRef] [PubMed]

Neurgaonkar, R.

Neurgaonkar, R. R.

Nikolajsen, T.

T. Nikolajsen, P. M. Johansen, X. Yue, D. Kip, and E. Krätzig, “Two-step two-color recording in a photorefractive praseodymium doped La3Ga5SiO14 crystal,” Appl. Phys. Lett. 74, 4037–4039 (1999).
[CrossRef]

Orlov, S.

Orlov, S. S.

L. Hesselink, S. S. Orlov, A. Liu, A. Akella, D. Lande, and R. R. Neugaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089–1094 (1998).
[CrossRef] [PubMed]

Orlowski, R.

Y. Ming, E. Krätzig, and R. Orlowski, “Photorefractive effects in LiNbO3:Cr induced by two-step excitation,” Phys. Status Solidi 92, 221–229 (1987).
[CrossRef]

Otten, J.

Paraschis, L.

Prokofiev, V. V.

O. V. Kobozev, S. M. Shandarov, A. A. Kamshilin, and V. V. Prokofiev, “Light-induced absorption in a Bi12TiO20 crystal,” J. Opt. A: Pure Appl. Opt. 1, 442–447 (1999).
[CrossRef]

Psaltis, D.

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665–668 (1998).
[CrossRef]

Rodgers, K.

D. von der Linde, A. Glass, and K. Rodgers, “Optical storage using refractive index changes induced by two-step excitation,” J. Appl. Phys. 47, 217–220 (1976).
[CrossRef]

Schirmer, O. F.

O. F. Schirmer, O. Thiemann, and M. Wohlecke, “Defects in LiNbO3. I. Experimental aspects,” J. Phys. Chem. Solids 52, 185–200 (1991).
[CrossRef]

Segev, M.

Shandarov, S. M.

O. V. Kobozev, S. M. Shandarov, A. A. Kamshilin, and V. V. Prokofiev, “Light-induced absorption in a Bi12TiO20 crystal,” J. Opt. A: Pure Appl. Opt. 1, 442–447 (1999).
[CrossRef]

Staebler, D. L.

J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Thiemann, O.

O. F. Schirmer, O. Thiemann, and M. Wohlecke, “Defects in LiNbO3. I. Experimental aspects,” J. Phys. Chem. Solids 52, 185–200 (1991).
[CrossRef]

von der Linde, D.

D. von der Linde, A. Glass, and K. Rodgers, “Optical storage using refractive index changes induced by two-step excitation,” J. Appl. Phys. 47, 217–220 (1976).
[CrossRef]

Vormann, H.

H. Vormann and E. Krätzig, “Two step excitation in LiTaO3:Fe for optical data storage,” Solid State Commun. 49, 843–847 (1984).
[CrossRef]

Wang, H. F.

J. Li, X. H. Li, F. X. Wu, Y. Zhu, X. Wu, and H. F. Wang, “Photorefractive parameters and light-induced absorption in BaTiO3,” Appl. Phys. A 61, 553–557 (1995).
[CrossRef]

Wohlecke, M.

O. F. Schirmer, O. Thiemann, and M. Wohlecke, “Defects in LiNbO3. I. Experimental aspects,” J. Phys. Chem. Solids 52, 185–200 (1991).
[CrossRef]

Wu, F. X.

J. Li, X. H. Li, F. X. Wu, Y. Zhu, X. Wu, and H. F. Wang, “Photorefractive parameters and light-induced absorption in BaTiO3,” Appl. Phys. A 61, 553–557 (1995).
[CrossRef]

Wu, X.

J. Li, X. H. Li, F. X. Wu, Y. Zhu, X. Wu, and H. F. Wang, “Photorefractive parameters and light-induced absorption in BaTiO3,” Appl. Phys. A 61, 553–557 (1995).
[CrossRef]

Yariv, A.

Yue, X.

T. Nikolajsen, P. M. Johansen, X. Yue, D. Kip, and E. Krätzig, “Two-step two-color recording in a photorefractive praseodymium doped La3Ga5SiO14 crystal,” Appl. Phys. Lett. 74, 4037–4039 (1999).
[CrossRef]

Zhu, Y.

J. Li, X. H. Li, F. X. Wu, Y. Zhu, X. Wu, and H. F. Wang, “Photorefractive parameters and light-induced absorption in BaTiO3,” Appl. Phys. A 61, 553–557 (1995).
[CrossRef]

Appl. Phys. A (1)

J. Li, X. H. Li, F. X. Wu, Y. Zhu, X. Wu, and H. F. Wang, “Photorefractive parameters and light-induced absorption in BaTiO3,” Appl. Phys. A 61, 553–557 (1995).
[CrossRef]

Appl. Phys. Lett. (3)

J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

F. Micheron and G. Bismuth, “Electrical control of fixation and erasure of holographic patterns in ferroelectric materials,” Appl. Phys. Lett. 20, 79–81 (1972).
[CrossRef]

T. Nikolajsen, P. M. Johansen, X. Yue, D. Kip, and E. Krätzig, “Two-step two-color recording in a photorefractive praseodymium doped La3Ga5SiO14 crystal,” Appl. Phys. Lett. 74, 4037–4039 (1999).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

J. Appl. Phys. (1)

D. von der Linde, A. Glass, and K. Rodgers, “Optical storage using refractive index changes induced by two-step excitation,” J. Appl. Phys. 47, 217–220 (1976).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

O. V. Kobozev, S. M. Shandarov, A. A. Kamshilin, and V. V. Prokofiev, “Light-induced absorption in a Bi12TiO20 crystal,” J. Opt. A: Pure Appl. Opt. 1, 442–447 (1999).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. Solids (1)

O. F. Schirmer, O. Thiemann, and M. Wohlecke, “Defects in LiNbO3. I. Experimental aspects,” J. Phys. Chem. Solids 52, 185–200 (1991).
[CrossRef]

Nature (1)

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665–668 (1998).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

Y. Bai and R. Kachru, “Nonvolatile holographic storage with two-step recording in lithium niobate using cw lasers,” Phys. Rev. Lett. 78, 2944–2947 (1997).
[CrossRef]

Phys. Status Solidi (1)

Y. Ming, E. Krätzig, and R. Orlowski, “Photorefractive effects in LiNbO3:Cr induced by two-step excitation,” Phys. Status Solidi 92, 221–229 (1987).
[CrossRef]

Science (1)

L. Hesselink, S. S. Orlov, A. Liu, A. Akella, D. Lande, and R. R. Neugaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089–1094 (1998).
[CrossRef] [PubMed]

Solid State Commun. (1)

H. Vormann and E. Krätzig, “Two step excitation in LiTaO3:Fe for optical data storage,” Solid State Commun. 49, 843–847 (1984).
[CrossRef]

Other (1)

B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Springer-Verlag, Berlin, 1984).

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Figures (6)

Fig. 1
Fig. 1

Schematic illustration of the tail in the bandgap found in most solid-state materials. From deep traps, electrons can be excited to states in the tail of the conduction band. Once in the tail, electrons relax by phonon-assisted relaxation to the bottom of the tail.

Fig. 2
Fig. 2

Schematic model of the excitation-recombination scheme that constitutes the basis of our model. The tail of the conduction band is divided into a continuous band S in which electrons relax toward the bottom of the tail and a level W that represents electrons near the bottom.

Fig. 3
Fig. 3

Population of the shallow traps as a function of the ratio of gating and writing intensities for three different values of the ratio σWeff/σW.

Fig. 4
Fig. 4

Saturation value of the space-charge field in diffusion-driven recording. It is assumed that Γ˜Gτ and σW=σWgσWr. The space-charge field quickly reaches saturation owing to a saturation in Wo. The saturation is followed by a decrease owing to a decrease in the effective modulation ratio.

Fig. 5
Fig. 5

Dependence of sensitivity on gating intensity. The theoretical expression is compared with experiments performed in La3Ga5SiO14:Pr3+.

Fig. 6
Fig. 6

Dependence of sensitivity on writing intensity. The theoretical expression is compared with experiments performed in La3Ga5SiO14:Pr3+.

Equations (34)

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

Ir=I0r(1+m cos Kx),
nst=τe-1n+σGsIgGo-ns(γGsG++γWsW+),
W+t=(τ-1+ΓW)Wo-γWsW+ns,
G+t=(σGCB+σGs)IgGo-γGsnsG+-τ-1Wo.
ΓW=σWgIg+σWrIr
ρt=-Jx,
J=μkBT nx+μenE+(RgIg+RrIr)Wo+RgGIgGo.
εoεs Ex=ρ,
ρ=-e(Wo+ns+n-Go,av+Go),
nt=ΓWWo-τe-1n+σGCBIgGo+1e Jx,
εsεoe Ex=-(Go+Wo-Go,av+n+ns).
A=A0+AK exp(-iKx)+c.c.,
ns=nτe-1+σGsIgGoγGsG++γWsW+.
n0=τeΓWWo0.
(i)WoO=τΓGGoO,γGsG+γWsW+,
(ii)Wo0=τΓ˜G1+τΓ˜G+τΓWW,γGsG+γWsW+,
ΓG=σGsIg,Γ˜G=γWsγGs Go0G+0σGsIg=σWeffIg.
0=(τ-1+ΓW)WoK+m2σWrI0rWo0-γWs[W+ns]K,
0=ΓWWoK+m2σWrI0rWo0+σGCBIgGoK-nKτe-1,
0=iμkBTKnk+μen0EK+WoK(RgIg+RrI0r)+m2Wo0RrI0r+RgGIgGoK,
G+K-ε0εseiKEK.
EK=-m*2(Epvr+iED)1+EDEq-i Epv*Eq-1,
EK=-m*2 11+d[-Epv*+(1+d)Epvr+idED]1+EDEq W+0W-i Epv*Eq W+0W-1,
d=1+Γ˜GτΓWτ.
S=ηt|t=0,
ηπp3reffL2λ cos θBEK2,
EKt=-1ε0εsJK.
S=πp3reffL2λ cos θB 1ε0εsJKt=0.
S=mπp3reffL4λ cos θBWo0I0r|(Rr+iμτeKkBTσWr)|,
S=πp3reffL4λ cos θb 1εsεo(JRD+JKPV),
JKD=i m2KkBTμτeσWrI0rWo0 1+τΓ˜G1+τΓ˜G+τΓW,
JKpv=m2Wo0 I0r1+τΓ˜G+τΓW×[Rr(1+τΓ˜G+τσWgIg)RgIgσWrτ],
S=SmaxD τΓ˜G(1+τΓ˜G)(1+τΓ˜G+τΓW)2,
SmaxD=mπp3ereffL2εoεsλrEDμτeσWrI0rW

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