Abstract

Nonvolatile holograms are recorded in photorefractive LiTaO3:Fe with laser pulses by use of two-step excitation. Ultraviolet laser pulses (wavelength λ=355 nm) yield a strong increase of absorption (as much as 600 m-1 at λ=633 nm) and sensitize the crystals for subsequent infrared (λ=1064 nm) holographic recording. Refractive-index changes of as much as 1.6×10-4 are achieved for intensities of the infrared light of 1011 W/m2. The saturation values are proportional to the concentration of Fe3+ ions. Nondestructive readout with infrared light is possible, and the holograms remain erasable for ultraviolet light. Typical time constants of recording and erasure are 0.5 µs for intensities of the ultraviolet light of 1011 W/m2. The results can be explained with a two-level charge-transport model.

© 1999 Optical Society of America

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References

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  1. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I and II, Topics in Applied Physics (Springer-Verlag, Heidelberg, 1988 and 1989), Vols. 61 and 62.
  2. S. Breer, H. Vogt, I. Nee, and K. Buse, “Low-crosstalk WDM by Bragg diffraction from thermally fixed reflection holograms in lithium niobate,” Electron. Lett. 34, 2418–2421 (1998).
    [CrossRef]
  3. E. Krätzig and R. Orlowski, “Light-induced charge transport in doped LiNbO3 and LiTaO3,” Ferroelectrics 27, 241–244 (1980).
    [CrossRef]
  4. G. E. Peterson, A. M. Glass, and T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index change,” Appl. Phys. Lett. 19, 130–132 (1971).
    [CrossRef]
  5. W. Phillips and D. L. Staebler, “Control of the Fe2+ concentration in iron-doped lithium niobate,” J. Electron. Mater. 3, 601–617 (1974).
    [CrossRef]
  6. D. von der Linde, A. M. Glass, and K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
    [CrossRef]
  7. H. Vormann and E. Krätzig, “Two step excitation in LiTaO3:Fe for optical data storage,” Solid State Commun. 49, 843–847 (1984).
    [CrossRef]
  8. K. Buse, F. Jermann, and E. Krätzig, “Infrared holographic recording in LiNbO3:Cu,” Appl. Phys. A: Solids Surf. 58, 191–195 (1994).
    [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. E. Krätzig and R. Orlowski, “LiTaO3 as holographic storage material,” Appl. Phys. 15, 133–139 (1978).
    [CrossRef]
  11. J. Baquedano, M. Carrascosa, L. Arizmendi, and J. M. Cabrera, “Erasure kinetics and spectral dependence of the photorefractive effect in Fe:LiNbO3,” J. Opt. Soc. Am. B 4, 309–312 (1987).
    [CrossRef]
  12. L. A. Kappers, K. L. Sweeney, L. E. Halliburton, and J. H. W. Liaw, “Oxygen vacancies in lithium tantalate,” Phys. Rev. B 31, 6792–6794 (1985).
    [CrossRef]
  13. N. V. Kukhtarev, “Kinetics of hologram recording and erasure in electrooptic crystals,” Sov. Tech. Phys. Lett. 2, 438–440 (1976).
  14. K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London) 393, 665–668 (1998).
    [CrossRef]
  15. L. Hesselink, S. Orlov, A. Liu, A. Akella, D. Lande, and R. Neurgaonkar, “Photorefractive materials for nonvolatile volume holographic data storage,” Science 282, 1089–1094 (1998).
    [CrossRef] [PubMed]
  16. K. H. Hellwege, ed. Landolt–Börnstein, Ferro- und Antiferromagnetische Substanzen (Springer-Verlag, 1975), Vol. III.
  17. H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
    [CrossRef]

1998 (3)

S. Breer, H. Vogt, I. Nee, and K. Buse, “Low-crosstalk WDM by Bragg diffraction from thermally fixed reflection holograms in lithium niobate,” Electron. Lett. 34, 2418–2421 (1998).
[CrossRef]

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

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

1994 (1)

K. Buse, F. Jermann, and E. Krätzig, “Infrared holographic recording in LiNbO3:Cu,” Appl. Phys. A: Solids Surf. 58, 191–195 (1994).
[CrossRef]

1993 (1)

1987 (1)

1985 (1)

L. A. Kappers, K. L. Sweeney, L. E. Halliburton, and J. H. W. Liaw, “Oxygen vacancies in lithium tantalate,” Phys. Rev. B 31, 6792–6794 (1985).
[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]

1980 (1)

E. Krätzig and R. Orlowski, “Light-induced charge transport in doped LiNbO3 and LiTaO3,” Ferroelectrics 27, 241–244 (1980).
[CrossRef]

1978 (1)

E. Krätzig and R. Orlowski, “LiTaO3 as holographic storage material,” Appl. Phys. 15, 133–139 (1978).
[CrossRef]

1977 (1)

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

1976 (1)

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

1974 (2)

W. Phillips and D. L. Staebler, “Control of the Fe2+ concentration in iron-doped lithium niobate,” J. Electron. Mater. 3, 601–617 (1974).
[CrossRef]

D. von der Linde, A. M. Glass, and K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

1971 (1)

G. E. Peterson, A. M. Glass, and T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index change,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

Adibi, A.

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

Akella, A.

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

Arizmendi, L.

Baquedano, J.

Breer, S.

S. Breer, H. Vogt, I. Nee, and K. Buse, “Low-crosstalk WDM by Bragg diffraction from thermally fixed reflection holograms in lithium niobate,” Electron. Lett. 34, 2418–2421 (1998).
[CrossRef]

Buse, K.

S. Breer, H. Vogt, I. Nee, and K. Buse, “Low-crosstalk WDM by Bragg diffraction from thermally fixed reflection holograms in lithium niobate,” Electron. Lett. 34, 2418–2421 (1998).
[CrossRef]

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

K. Buse, F. Jermann, and E. Krätzig, “Infrared holographic recording in LiNbO3:Cu,” Appl. Phys. A: Solids Surf. 58, 191–195 (1994).
[CrossRef]

Cabrera, J. M.

Carrascosa, M.

Dischler, B.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Engelmann, H.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Glass, A. M.

D. von der Linde, A. M. Glass, and K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

G. E. Peterson, A. M. Glass, and T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index change,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

Gonser, U.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Halliburton, L. E.

L. A. Kappers, K. L. Sweeney, L. E. Halliburton, and J. H. W. Liaw, “Oxygen vacancies in lithium tantalate,” Phys. Rev. B 31, 6792–6794 (1985).
[CrossRef]

Hesselink, L.

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

Jermann, F.

K. Buse, F. Jermann, and E. Krätzig, “Infrared holographic recording in LiNbO3:Cu,” Appl. Phys. A: Solids Surf. 58, 191–195 (1994).
[CrossRef]

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]

Kappers, L. A.

L. A. Kappers, K. L. Sweeney, L. E. Halliburton, and J. H. W. Liaw, “Oxygen vacancies in lithium tantalate,” Phys. Rev. B 31, 6792–6794 (1985).
[CrossRef]

Keune, W.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Krätzig, E.

K. Buse, F. Jermann, and E. Krätzig, “Infrared holographic recording in LiNbO3:Cu,” Appl. Phys. A: Solids Surf. 58, 191–195 (1994).
[CrossRef]

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

E. Krätzig and R. Orlowski, “Light-induced charge transport in doped LiNbO3 and LiTaO3,” Ferroelectrics 27, 241–244 (1980).
[CrossRef]

E. Krätzig and R. Orlowski, “LiTaO3 as holographic storage material,” Appl. Phys. 15, 133–139 (1978).
[CrossRef]

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Kukhtarev, N. V.

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

Kurz, H.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Lande, D.

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

Liaw, J. H. W.

L. A. Kappers, K. L. Sweeney, L. E. Halliburton, and J. H. W. Liaw, “Oxygen vacancies in lithium tantalate,” Phys. Rev. B 31, 6792–6794 (1985).
[CrossRef]

Liu, A.

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

Nee, I.

S. Breer, H. Vogt, I. Nee, and K. Buse, “Low-crosstalk WDM by Bragg diffraction from thermally fixed reflection holograms in lithium niobate,” Electron. Lett. 34, 2418–2421 (1998).
[CrossRef]

Negran, T. J.

G. E. Peterson, A. M. Glass, and T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index change,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

Neurgaonkar, R.

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

Orlov, S.

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

Orlowski, R.

E. Krätzig and R. Orlowski, “Light-induced charge transport in doped LiNbO3 and LiTaO3,” Ferroelectrics 27, 241–244 (1980).
[CrossRef]

E. Krätzig and R. Orlowski, “LiTaO3 as holographic storage material,” Appl. Phys. 15, 133–139 (1978).
[CrossRef]

Otten, J.

Peterson, G. E.

G. E. Peterson, A. M. Glass, and T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index change,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

Phillips, W.

W. Phillips and D. L. Staebler, “Control of the Fe2+ concentration in iron-doped lithium niobate,” J. Electron. Mater. 3, 601–617 (1974).
[CrossRef]

Psaltis, D.

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

Räuber, A.

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Rodgers, K. F.

D. von der Linde, A. M. Glass, and K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

Staebler, D. L.

W. Phillips and D. L. Staebler, “Control of the Fe2+ concentration in iron-doped lithium niobate,” J. Electron. Mater. 3, 601–617 (1974).
[CrossRef]

Sweeney, K. L.

L. A. Kappers, K. L. Sweeney, L. E. Halliburton, and J. H. W. Liaw, “Oxygen vacancies in lithium tantalate,” Phys. Rev. B 31, 6792–6794 (1985).
[CrossRef]

Vogt, H.

S. Breer, H. Vogt, I. Nee, and K. Buse, “Low-crosstalk WDM by Bragg diffraction from thermally fixed reflection holograms in lithium niobate,” Electron. Lett. 34, 2418–2421 (1998).
[CrossRef]

von der Linde, D.

D. von der Linde, A. M. Glass, and K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[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]

Appl. Phys. (2)

E. Krätzig and R. Orlowski, “LiTaO3 as holographic storage material,” Appl. Phys. 15, 133–139 (1978).
[CrossRef]

H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, and A. Räuber, “Photorefractive centers in LiNbO3, studied by optical-, Mössbauer- and EPR-methods,” Appl. Phys. 12, 355–368 (1977).
[CrossRef]

Appl. Phys. A: Solids Surf. (1)

K. Buse, F. Jermann, and E. Krätzig, “Infrared holographic recording in LiNbO3:Cu,” Appl. Phys. A: Solids Surf. 58, 191–195 (1994).
[CrossRef]

Appl. Phys. Lett. (2)

D. von der Linde, A. M. Glass, and K. F. Rodgers, “Multiphoton photorefractive processes for optical storage in LiNbO3,” Appl. Phys. Lett. 25, 155–157 (1974).
[CrossRef]

G. E. Peterson, A. M. Glass, and T. J. Negran, “Control of the susceptibility of lithium niobate to laser-induced refractive index change,” Appl. Phys. Lett. 19, 130–132 (1971).
[CrossRef]

Electron. Lett. (1)

S. Breer, H. Vogt, I. Nee, and K. Buse, “Low-crosstalk WDM by Bragg diffraction from thermally fixed reflection holograms in lithium niobate,” Electron. Lett. 34, 2418–2421 (1998).
[CrossRef]

Ferroelectrics (1)

E. Krätzig and R. Orlowski, “Light-induced charge transport in doped LiNbO3 and LiTaO3,” Ferroelectrics 27, 241–244 (1980).
[CrossRef]

J. Electron. Mater. (1)

W. Phillips and D. L. Staebler, “Control of the Fe2+ concentration in iron-doped lithium niobate,” J. Electron. Mater. 3, 601–617 (1974).
[CrossRef]

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

Nature (London) (1)

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

Phys. Rev. B (1)

L. A. Kappers, K. L. Sweeney, L. E. Halliburton, and J. H. W. Liaw, “Oxygen vacancies in lithium tantalate,” Phys. Rev. B 31, 6792–6794 (1985).
[CrossRef]

Science (1)

L. Hesselink, S. Orlov, A. Liu, A. Akella, D. Lande, and R. Neurgaonkar, “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]

Sov. Tech. Phys. Lett. (1)

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

Other (2)

K. H. Hellwege, ed. Landolt–Börnstein, Ferro- und Antiferromagnetische Substanzen (Springer-Verlag, 1975), Vol. III.

P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications I and II, Topics in Applied Physics (Springer-Verlag, Heidelberg, 1988 and 1989), Vols. 61 and 62.

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Figures (8)

Fig. 1
Fig. 1

Schematic drawing of the holographic setup.

Fig. 2
Fig. 2

Light-induced absorption coefficient αli (wavelength, λ=633 nm) versus intensity IUV of the ultraviolet light. The sample contains 0.02 wt. % Fe with a concentration ratio NFe2+/NFe3+ of 2.6. The line is a linear fit.

Fig. 3
Fig. 3

Slope A of the light-induced absorption coefficient αli as a function of the Fe2+ concentration NFe2+ for two probe-laser wavelengths. The lines are linear fits to the measured values.

Fig. 4
Fig. 4

Diffraction efficiency η for a typical write–read–erase cycle. Squares, measured values; dashed curve, monoexponential fits. The sample contains 0.02 wt. % Fe with a concentration ratio NFe2+/NFe3+=0.4. The solid curve shows numerical fits with light absorption (α355 nm=3470 m-1) and depth-dependent time constants taken into account. The time scale corresponds to the exposure time. The intensities of infrared and ultraviolet light pulses are IIR=90 GW/m2 and IUV=27 GW/m2, respectively.

Fig. 5
Fig. 5

Saturation values ΔnS of refractive-index changes as a function of the intensity IUV of the ultraviolet light for a sample containing 0.01 wt. % Fe with a concentration ratio of NFe2+/NFe3+=2.5. The intensity of the infrared light is IIR=21 GW/m2, and the curve is a fit according to ΔnS=a/(1+bIUV), where a and b represent free parameters.

Fig. 6
Fig. 6

Saturation values ΔnS of refractive-index changes as a function of the intensity IIR of the infrared light for the same sample as in Fig. 5. The intensity of the ultraviolet light is IUV=17 GW/m2. The curve is a fit according to ΔnS=aIIR+bIIR2, where a and b represent free parameters.

Fig. 7
Fig. 7

Saturation values ΔnS of refractive-index changes normalized to the intensity of the ultraviolet and infrared light as a function of the Fe3+ concentration NFe3+. Solid curve, a linear fit.

Fig. 8
Fig. 8

Inverse time constants τf-1 at the crystal’s front side for writing and erasing a hologram. The sample contains 0.02 wt. % Fe with a concentration ratio NFe2+/NFe3+ of 0.3. For hologram writing the intensity of the infrared light is approximately IIR=45 GW/m2. Curves, linear fits to the measured values.

Tables (2)

Tables Icon

Table 1 Parameters of LiTaO3 and LiNbO3

Tables Icon

Table 2 Abbreviations for Parameters to Describe Generation and Recombination of Free Charge Carriers in LiTaO3 within a Two-Level Model

Equations (25)

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

AFe2+=α400o×2.13×1021m-2,
NFe3+=α310o×5.33×1020m-2.
NX0t=(sFeXUVqFeXUVIUVNFe2++γXNe)NX+-(βX+sXUVqXUVIUV+γXFeNFe3+)NX0,
Net=sFeUVqFeUVIUVNFe2++sXUVqXUVIUVNX0+sXIRqXIRIIRNX0+βXNX0-(γXNX++γFeNFe3+)Ne.
αlip(IUV)=(sXp-sFep-sFeXpNX+)NX0,
NX0=sFeXUVqFeXUVIUVNFe2+NX+t,
αlip(IUV)=(sXp-sFep-sFeXpNX+)sFeXUVqFeXUVIUVNFe2+NX+t.
IIR(z)=IIR,0[1+m cos(Kz)],
m=2IIRRIIRSIIRR+IIRS,
j(z, t)=σph,0E(z, t)+κXIRNX0IIR(z)+κFeUVNFe2+IUV+κXUVNX0IUV,
Δn(z, t)o(e)=-1/2no(e)3r113(333)ESC(z, t),
Δn(t)=ΔnS[1-exp(-t/τw)].
Δn(t)=Δn0 exp[-(t-t0)/τe],
Δn0=Δn(t0),
ΔnS=no(e)3r113(333)κXIRNX0mIIR2σph,0,
τw=0σph,0,τe=0σph,0UV.
σph,0=eμeNe=eμe sFeUVqFeUVIUVNFe2++sXUVqXUVIUVNX0+sXIRqXIRIIR,0NX0+βXNX0γFeNFe3++γXNX+,
σph,0=NFe2+NFe3+IUV(a+bIUVNX+cIIRNX),
a=eμe sFeUVqFeUVγFe,
b=eμe sXUVqXUVsFeXUVqFeXUVτPUVγFe,
c=eμe sXIRqXIRsFeXUVqFeXUVτPUVγFe,
ΔnS=dNFe3+NXmIIR(a+bIUVNX+cIIRNX)-1,
τw=NFe3+NFe2+IUV-10(a+bIUVNX+cIIRNX)-1,
τe=NFe3+NFe2+IUV-10(a+bIUVNX)-1,
d=1/2no(e)3r113(333)κXIRsFeXUVqFeXUVτPUV.

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