Abstract

Propagation of the light beam in a thin photorefractive crystal with the diffusion-type mechanism of nonlinearity has been studied both experimentally and theoretically. Total internal reflections of fanned beams from the crystal’s side surfaces and their coupling with the pump beam result in the light-intensity redistribution and in the generation of the photorefractive surface wave. We propose a theoretical model of the intensity redistribution that considers the light-energy flow from the pump beam to the fanning beam and backward after the fanning beam reflection. A numerical simulation shows that the total internal reflection off the surface, toward which the flow of the light energy is directed, is responsible for the light-energy self-concentration.

© 1996 Optical Society of America

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References

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  1. S. I. Stepanov, “Application of photorefractive crystals,” Rep. Prog. Phys. 57, 39–116 (1994).
    [Crossref]
  2. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefactive media,” Phys. Rev. Lett. 68, 923–926 (1992).
    [Crossref] [PubMed]
  3. B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. J. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
    [Crossref]
  4. O. V. Lyubomudrov and V. V. Shkunov, “Self-bending specklons in photorefractive crystals,” J. Opt. Soc. Am. B 11, 1403–1408 (1994).
    [Crossref]
  5. D. N. Christodoulides and M. I. Carvalho, “Compression, self-bending, and collapse of Gaussian beams in photorefractive crystals,” Opt. Lett. 19, 1714–1716 (1994).
    [Crossref] [PubMed]
  6. A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67, 3242–3244 (1995).
    [Crossref]
  7. M. Cronin-Golomb, “Photorefractive surface waves,” Opt. Lett. 20, 2075–2077 (1995).
    [Crossref] [PubMed]
  8. G. S. Garcia-Quirino, J. J. Sanchez-Mondragon, and S. I. Stepanov, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51, 1571–1577 (1995).
    [Crossref] [PubMed]
  9. S. I. Stepanov, S. M. Shandarov, and N. D. Hat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).
  10. S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
    [Crossref]
  11. A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
    [Crossref]
  12. C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
    [Crossref]
  13. V. V. Voronov, I. R. Dorosh, Y. S. Kuzminov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium nobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
    [Crossref]
  14. M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
    [Crossref]
  15. R. A. Vazquez, F. Vachss, R. R. Neurgaonkar, and M. D. Ewbank, “Large photorefractive coupling coefficient in a thin cerium-doped strontium barium niobate crystal,” J. Opt. Soc. Am. B 8, 1932–1941 (1991).
    [Crossref]
  16. Q. B. He and P. Yeh, “Fanning noise reduction in photorefractive amplifiers using incoherent erasures,” Appl. Opt. 33, 283–287 (1994).
    [Crossref] [PubMed]
  17. S. I. Stepanov and M. P. Petrov, “Nonstationary holographic recording for efficient amplification and phase conjugation,” in Photorefractive Materials and Their Applications I, Vol. 61 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 263–290.
    [Crossref]
  18. Y. Ding and H. J. Eichler, “Crystal orientation dependence of the photorefractive four-wave mixing in compound semiconductors of symmetry group 43m,” Opt. Commun. 110, 456–464 (1994).
    [Crossref]
  19. A. Marrakchi, R. V. Johnson, and A. R. Tanguay, “Polarization properties of photorefractive diffraction in electro-optic and optically active sillenite crystals (Bragg regime),” J. Opt. Soc. Am. B 3, 321–336 (1986).
    [Crossref]
  20. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1992).
  21. S. L. Sochava, E. V. Mokrushina, V. V. Prokofiev, and S. I. Stepanov, “Experimental comparison of the ac field and the moving-grating holographic-recording techniques for Bi12SiO20 and Bi12TiO20 photorefractive crystals,” J. Opt. Soc. Am. B 10, 1600–1604 (1993).
    [Crossref]

1995 (3)

A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67, 3242–3244 (1995).
[Crossref]

M. Cronin-Golomb, “Photorefractive surface waves,” Opt. Lett. 20, 2075–2077 (1995).
[Crossref] [PubMed]

G. S. Garcia-Quirino, J. J. Sanchez-Mondragon, and S. I. Stepanov, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51, 1571–1577 (1995).
[Crossref] [PubMed]

1994 (5)

1993 (3)

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefactive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[Crossref] [PubMed]

1991 (1)

1990 (1)

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

1989 (1)

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[Crossref]

1987 (1)

S. I. Stepanov, S. M. Shandarov, and N. D. Hat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

1986 (1)

1985 (1)

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

1980 (1)

V. V. Voronov, I. R. Dorosh, Y. S. Kuzminov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium nobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Carvalho, M. I.

Christodoulides, D. N.

Cronin-Golomb, M.

Crosignani, B.

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. J. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
[Crossref]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefactive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[Crossref] [PubMed]

Di Porto, P.

Ding, Y.

Y. Ding and H. J. Eichler, “Crystal orientation dependence of the photorefractive four-wave mixing in compound semiconductors of symmetry group 43m,” Opt. Commun. 110, 456–464 (1994).
[Crossref]

Dorosh, I. R.

V. V. Voronov, I. R. Dorosh, Y. S. Kuzminov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium nobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Eichler, H. J.

Y. Ding and H. J. Eichler, “Crystal orientation dependence of the photorefractive four-wave mixing in compound semiconductors of symmetry group 43m,” Opt. Commun. 110, 456–464 (1994).
[Crossref]

Engin, D.

Ewbank, M. D.

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefactive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[Crossref] [PubMed]

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

Garcia-Quirino, G. S.

G. S. Garcia-Quirino, J. J. Sanchez-Mondragon, and S. I. Stepanov, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51, 1571–1577 (1995).
[Crossref] [PubMed]

Hall, T. J.

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[Crossref]

Hat’kov, N. D.

S. I. Stepanov, S. M. Shandarov, and N. D. Hat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

He, Q. B.

Jaaskelainen, T.

A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67, 3242–3244 (1995).
[Crossref]

Johnson, R. V.

Kamshilin, A. A.

A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67, 3242–3244 (1995).
[Crossref]

Kuzminov, Y. S.

V. V. Voronov, I. R. Dorosh, Y. S. Kuzminov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium nobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Lyubomudrov, O. V.

Marrakchi, A.

Mokrushina, E. V.

Neurgaonkar, R. R.

Ophir, Y.

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

Petrov, M. P.

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

S. I. Stepanov and M. P. Petrov, “Nonstationary holographic recording for efficient amplification and phase conjugation,” in Photorefractive Materials and Their Applications I, Vol. 61 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 263–290.
[Crossref]

Powell, A. K.

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[Crossref]

Prokofiev, V. V.

A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67, 3242–3244 (1995).
[Crossref]

S. L. Sochava, E. V. Mokrushina, V. V. Prokofiev, and S. I. Stepanov, “Experimental comparison of the ac field and the moving-grating holographic-recording techniques for Bi12SiO20 and Bi12TiO20 photorefractive crystals,” J. Opt. Soc. Am. B 10, 1600–1604 (1993).
[Crossref]

Raita, E.

A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67, 3242–3244 (1995).
[Crossref]

Salamo, G. J.

Sanchez-Mondragon, J. J.

G. S. Garcia-Quirino, J. J. Sanchez-Mondragon, and S. I. Stepanov, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51, 1571–1577 (1995).
[Crossref] [PubMed]

Segev, M.

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. J. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
[Crossref]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefactive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[Crossref] [PubMed]

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

Shandarov, S. M.

S. I. Stepanov, S. M. Shandarov, and N. D. Hat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

Shkunov, V. V.

Sochava, S. L.

Stace, C.

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[Crossref]

Stepanov, S. I.

G. S. Garcia-Quirino, J. J. Sanchez-Mondragon, and S. I. Stepanov, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51, 1571–1577 (1995).
[Crossref] [PubMed]

S. I. Stepanov, “Application of photorefractive crystals,” Rep. Prog. Phys. 57, 39–116 (1994).
[Crossref]

S. L. Sochava, E. V. Mokrushina, V. V. Prokofiev, and S. I. Stepanov, “Experimental comparison of the ac field and the moving-grating holographic-recording techniques for Bi12SiO20 and Bi12TiO20 photorefractive crystals,” J. Opt. Soc. Am. B 10, 1600–1604 (1993).
[Crossref]

S. I. Stepanov, S. M. Shandarov, and N. D. Hat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

S. I. Stepanov and M. P. Petrov, “Nonstationary holographic recording for efficient amplification and phase conjugation,” in Photorefractive Materials and Their Applications I, Vol. 61 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 263–290.
[Crossref]

Tanguay, A. R.

Tkachenko, N. V.

V. V. Voronov, I. R. Dorosh, Y. S. Kuzminov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium nobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Vachss, F.

Vazquez, R. A.

Voronov, V. V.

V. V. Voronov, I. R. Dorosh, Y. S. Kuzminov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium nobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Walsh, K.

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[Crossref]

Yariv, A.

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. J. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B 10, 446–453 (1993).
[Crossref]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefactive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[Crossref] [PubMed]

Yeh, P.

Zozulya, A. A.

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. A. Kamshilin, E. Raita, V. V. Prokofiev, and T. Jaaskelainen, “Nonlinear self-channeling of a laser beam at the surface of a photorefractive fiber,” Appl. Phys. Lett. 67, 3242–3244 (1995).
[Crossref]

IEEE J. Quantum Electron. (1)

A. A. Zozulya, “Fanning and photorefractive self-pumped four-wave mixing geometries,” IEEE J. Quantum Electron. 29, 538–555 (1993).
[Crossref]

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

Opt. Commun. (4)

Y. Ding and H. J. Eichler, “Crystal orientation dependence of the photorefractive four-wave mixing in compound semiconductors of symmetry group 43m,” Opt. Commun. 110, 456–464 (1994).
[Crossref]

C. Stace, A. K. Powell, K. Walsh, and T. J. Hall, “Coupling modulation in photorefractive materials by applying ac electric fields,” Opt. Commun. 70, 509–514 (1989).
[Crossref]

S. I. Stepanov and M. P. Petrov, “Efficient unstationary holographic recording in photorefractive crystals under an external alternating electric field,” Opt. Commun. 53, 292–295 (1985).
[Crossref]

M. Segev, Y. Ophir, and B. Fischer, “Nonlinear multi two-wave mixing, the fanning process and its bleaching in photorefractive media,” Opt. Commun. 77, 265–274 (1990).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

G. S. Garcia-Quirino, J. J. Sanchez-Mondragon, and S. I. Stepanov, “Nonlinear surface optical waves in photorefractive crystals with a diffusion mechanism of nonlinearity,” Phys. Rev. A 51, 1571–1577 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefactive media,” Phys. Rev. Lett. 68, 923–926 (1992).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

S. I. Stepanov, “Application of photorefractive crystals,” Rep. Prog. Phys. 57, 39–116 (1994).
[Crossref]

Sov. J. Quantum Electron. (1)

V. V. Voronov, I. R. Dorosh, Y. S. Kuzminov, and N. V. Tkachenko, “Photoinduced light scattering in cerium-doped barium strontium nobate crystals,” Sov. J. Quantum Electron. 10, 1346–1349 (1980).
[Crossref]

Sov. Phys. Solid State (1)

S. I. Stepanov, S. M. Shandarov, and N. D. Hat’kov, “Photoelastic contribution to the photorefractive effect in cubic crystals,” Sov. Phys. Solid State 29, 1754–1756 (1987).

Other (2)

S. I. Stepanov and M. P. Petrov, “Nonstationary holographic recording for efficient amplification and phase conjugation,” in Photorefractive Materials and Their Applications I, Vol. 61 of Topics in Applied Physics, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988), pp. 263–290.
[Crossref]

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1992).

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Figures (6)

Fig. 1
Fig. 1

Orientation of the thin photorefractive slab of the BTO crystal.

Fig. 2
Fig. 2

Photographs of the pump-beam intensity distribution at the output face of the photorefractive BTO slab: (a) without bias electric field, (b) after application of an alternating electric field of 43-kV/cm amplitude. Intensity distributions corresponding to the horizontal line in the middle of the photographs are shown in graphs (c) and (d), respectively.

Fig. 3
Fig. 3

Evolution of the fanning light intensity that emerged from the thin BTO crystal for a scattering angle of 7 deg for the ac field amplitude of 25 kV/cm.

Fig. 4
Fig. 4

Dependence of the fanning effect response time on the ac field amplitude for the BTO crystal. The pump-beam intensity was 190 mW/cm2, and the scattering angle was 7 deg.

Fig. 5
Fig. 5

Diagram describing the division of the thin photorefractive slab onto layers and stripes for the numerical calculations of the beams’ interaction. The pump beam, P, travels parallel to the surface of the crystal’s longer side, but fanned plane waves F and R propagate with the angle ±β0 [Eq. (2)] with respect to the pump.

Fig. 6
Fig. 6

Intensity distribution inside the thin crystal slab of 1-mm thickness and of 35-mm length, calculated for different amplitudes of the ac external electric field: (a) 8 kV/cm, (b) 12 kV/cm, (c) 20 kV/cm. All the curves were calculated with the following parameters: The natural optical activity ρ is 6.5 deg/mm, the absorption coefficient α is 0.5 cm-1, the seed-to-pump intensity ratio f is 10-6, and the input pump beam is linearly polarized along the 〈1̅11〉 axis.

Equations (17)

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

I=IST1-exp-tτH,
sinβ02=λLD4π[(LD4+LE2LS2)1/2].
Hl,m=l|Hˆ|m, l,m=s,p.
Δ=n04r410EzEyEz0ExEyEx0=n04r41|E|Hˆ,
HSS=13, HPP=-23, HSP=HPS=0.
M=NWL tan β0.
PP(i,0)=IP(0) cos α1, PS(i,0)=IP(0) sin α1,
FP(i,0)=RP(i,0)=fPP(i,0),
FS(i,0)=RS(i,0)=fPS(i,0).
ddzPP=-αPP-ρPS-iκ0HPPPP-κgI0(HPPFP)×(FP*PP cos β0+FS*PS)+κgI0(HPPRP)×(RP*PP cos β0+RS*PS), ddzPS=-αPS+ρPP-iκ0HSSPS-κgI0(HSSFS)×(FP*PP cos β0+FS*PS)+κgI0(HSSRS)×(RP*PP cos β0+RS*PS), ddzFP=-αFP-ρFS-iκ0HPPFP+κgI0(HPPPP)×(FP*PP cosβ0+FS*PS), ddzFS=-αFS+ρFP-iκ0(HSSFS)+κgI0(HSSPS)×(FP*PP cos β0+FS*PS), ddzRP=-αRP-ρRS-iκ0HPPRP-κgI0(HPPPP)×(RP*PP cos β0+RS*PS), ddzRS=-αRS+ρRP-iκ0HSSRS-κgI0(HSSPS)×(RP*PP cos β0+RS*PS),
I0=|PP|2+|PS|2+|FP|2+|FS|2+|RP|2+|RS|2,
κ0=πn03λr41E0,
κg=πn03λr41ESC,
ESC=ED(1+K2LD2)+E0KLE(1+K2LD2)(1+K2LS2)+K2LELA,
ED=KkBTe,
LD=Dτ, LE=μτE0, LS=0kBTe2NA1/2,
LA=0E0eNA.

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