Abstract

This article analyzes nonlinear light propagation in semiconductors with bipolar conductivity and nonlinear transport of electrons. We show how the competition between electron and hole conductivity can influence light propagation, leading to the self-bending effect of optical beam trajectory, which depending on the value of trap compensation coefficient may be stationary or transient.

© 2014 Optical Society of America

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References

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  1. Z. Chen, M. Segev, D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
    [CrossRef] [PubMed]
  2. Y. S. Kivshar, G. I. Stegeman, “Spatial optical solitons: Guiding light for future technologies,” Opt. Photonics News 13(2), 59–63 (2002).
    [CrossRef]
  3. E. DelRe, P. Di Porto, B. Crosignani, “Photorefractive solitons and their underlying nonlocal physics,” Prog. Opt. 53, 153–200 (2009).
    [CrossRef]
  4. S. Lan, M. F. Shih, M. Segev, “Self-trapping of one-dimensional and two-dimensional optical beams and induced waveguides in photorefractive KNbO3.,” Opt. Lett. 22(19), 1467–1469 (1997).
    [CrossRef] [PubMed]
  5. S. Lan, E. Delre, Z. G. Chen, M. F. Shih, M. Segev, “Directional coupler with soliton-induced waveguides,” Opt. Lett. 24(7), 475–477 (1999).
    [CrossRef] [PubMed]
  6. K. Pismennaya, O. Kashin, V. Matusevich, A. Kiessling, R. Kowarschik, “Beam self-trapping and self-bending dynamics in a strontium barium niobate crystal,” J. Opt. Soc. Am. B 25(2), 136–139 (2008).
    [CrossRef]
  7. J. Petter, C. Weilnau, C. Denz, A. Stepken, F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170(4-6), 291–297 (1999).
    [CrossRef]
  8. P. Günter and J. P. Huignard, Photorefractive Materials and Their Applications (Springer, 2007), Vol. III, Chap. 11.
  9. D. Wolfersberger, N. Khelfaoui, C. Dan, N. Fressengeas, H. Leblond, “Fast photorefractive self-focusing in InP:Fe semiconductor at infrared wavelengths,” Appl. Phys. Lett. 92(2), 021106 (2008).
    [CrossRef]
  10. M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, G. Bryant, “Self-trapping of planar optical beams by use of the photorefractive effect in InP:Fe,” Opt. Lett. 21(17), 1333–1335 (1996).
    [CrossRef] [PubMed]
  11. T. Schwartz, Y. Ganor, T. Carmon, R. Uzdin, S. Shwartz, M. Segev, U. El-Hanany, “Photorefractive Solitons and Light-induced resonance control in semiconductor CdZnTe,” Opt. Lett. 27(14), 1229–1231 (2002).
    [CrossRef] [PubMed]
  12. K. Seeger, Semiconductor Physics (Springer, 2004), Chap. 4.
  13. S. M. Sze, Physics of Semiconductor Devices (Wiley-Interscience, 2006), Chap. 11.
  14. D. D. Nolte, S. Balasubramanian, M. R. Melloch, “Nonlinear charge transport in photorefractive semiconductor quantum wells,” Opt. Mater. 18(1), 199–203 (2001).
    [CrossRef]
  15. Q. N. Wang, R. M. Brubaker, D. D. Nolte, “Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures,” J. Opt. Soc. Am. B 11(9), 1773–1779 (1994).
    [CrossRef]
  16. M. Wichtowski, E. Weinert-Rączka, “Temporal response of photorefractive multiple quantum wells in Franz–Keldysh geometry,” Opt. Commun. 281(5), 1233–1243 (2008).
    [CrossRef]
  17. A. Ziółkowski, “Temporal analysis of solitons in photorefractive semiconductors,” J. Opt. 14(3), 035202 (2012).
    [CrossRef]
  18. A. Ziółkowski, “A numerical approach to nonlinear propagation of light in photorefractive media,” Comput. Phys. Commun. 185(2), 504–511 (2014).
    [CrossRef]
  19. D. D. Nolte, Photorefractive Effects and Materials (Kluwer, 1995).
  20. S. Balasubramanian, I. Lahiri, Y. Ding, M. Melloch, D. Nolte, “Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68(5), 863–869 (1999).
    [CrossRef]
  21. C. Dari-Salisburgo, E. DelRe, E. Palange, “Molding and stretched evolution of optical solitons in cumulative nonlinearities,” Phys. Rev. Lett. 91(26), 263903 (2003).
    [CrossRef] [PubMed]
  22. E. DelRe, E. Palange, “Optical nonlinearity and existence conditions for quasi-steady-state photorefractive solitons,” J. Opt. Soc. Am. B 23(11), 2323–2327 (2006).
    [CrossRef]
  23. N. Fressengeas, J. Maufoy, G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(6), 6866–6875 (1996).
    [CrossRef] [PubMed]
  24. E. DelRe, A. D’Ercole, E. Palange, “Mechanisms supporting long propagation regimes of photorefractive solitons,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 71(3), 036610 (2005).
    [CrossRef] [PubMed]

2014

A. Ziółkowski, “A numerical approach to nonlinear propagation of light in photorefractive media,” Comput. Phys. Commun. 185(2), 504–511 (2014).
[CrossRef]

2012

A. Ziółkowski, “Temporal analysis of solitons in photorefractive semiconductors,” J. Opt. 14(3), 035202 (2012).
[CrossRef]

Z. Chen, M. Segev, D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[CrossRef] [PubMed]

2009

E. DelRe, P. Di Porto, B. Crosignani, “Photorefractive solitons and their underlying nonlocal physics,” Prog. Opt. 53, 153–200 (2009).
[CrossRef]

2008

K. Pismennaya, O. Kashin, V. Matusevich, A. Kiessling, R. Kowarschik, “Beam self-trapping and self-bending dynamics in a strontium barium niobate crystal,” J. Opt. Soc. Am. B 25(2), 136–139 (2008).
[CrossRef]

D. Wolfersberger, N. Khelfaoui, C. Dan, N. Fressengeas, H. Leblond, “Fast photorefractive self-focusing in InP:Fe semiconductor at infrared wavelengths,” Appl. Phys. Lett. 92(2), 021106 (2008).
[CrossRef]

M. Wichtowski, E. Weinert-Rączka, “Temporal response of photorefractive multiple quantum wells in Franz–Keldysh geometry,” Opt. Commun. 281(5), 1233–1243 (2008).
[CrossRef]

2006

2005

E. DelRe, A. D’Ercole, E. Palange, “Mechanisms supporting long propagation regimes of photorefractive solitons,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 71(3), 036610 (2005).
[CrossRef] [PubMed]

2003

C. Dari-Salisburgo, E. DelRe, E. Palange, “Molding and stretched evolution of optical solitons in cumulative nonlinearities,” Phys. Rev. Lett. 91(26), 263903 (2003).
[CrossRef] [PubMed]

2002

2001

D. D. Nolte, S. Balasubramanian, M. R. Melloch, “Nonlinear charge transport in photorefractive semiconductor quantum wells,” Opt. Mater. 18(1), 199–203 (2001).
[CrossRef]

1999

S. Lan, E. Delre, Z. G. Chen, M. F. Shih, M. Segev, “Directional coupler with soliton-induced waveguides,” Opt. Lett. 24(7), 475–477 (1999).
[CrossRef] [PubMed]

S. Balasubramanian, I. Lahiri, Y. Ding, M. Melloch, D. Nolte, “Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68(5), 863–869 (1999).
[CrossRef]

J. Petter, C. Weilnau, C. Denz, A. Stepken, F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170(4-6), 291–297 (1999).
[CrossRef]

1997

1996

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, G. Bryant, “Self-trapping of planar optical beams by use of the photorefractive effect in InP:Fe,” Opt. Lett. 21(17), 1333–1335 (1996).
[CrossRef] [PubMed]

N. Fressengeas, J. Maufoy, G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(6), 6866–6875 (1996).
[CrossRef] [PubMed]

1994

Balasubramanian, S.

D. D. Nolte, S. Balasubramanian, M. R. Melloch, “Nonlinear charge transport in photorefractive semiconductor quantum wells,” Opt. Mater. 18(1), 199–203 (2001).
[CrossRef]

S. Balasubramanian, I. Lahiri, Y. Ding, M. Melloch, D. Nolte, “Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68(5), 863–869 (1999).
[CrossRef]

Bliss, D. F.

Brubaker, R. M.

Bryant, G.

Carmon, T.

Chauvet, M.

Chen, Z.

Z. Chen, M. Segev, D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[CrossRef] [PubMed]

Chen, Z. G.

Christodoulides, D. N.

Z. Chen, M. Segev, D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[CrossRef] [PubMed]

Crosignani, B.

E. DelRe, P. Di Porto, B. Crosignani, “Photorefractive solitons and their underlying nonlocal physics,” Prog. Opt. 53, 153–200 (2009).
[CrossRef]

D’Ercole, A.

E. DelRe, A. D’Ercole, E. Palange, “Mechanisms supporting long propagation regimes of photorefractive solitons,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 71(3), 036610 (2005).
[CrossRef] [PubMed]

Dan, C.

D. Wolfersberger, N. Khelfaoui, C. Dan, N. Fressengeas, H. Leblond, “Fast photorefractive self-focusing in InP:Fe semiconductor at infrared wavelengths,” Appl. Phys. Lett. 92(2), 021106 (2008).
[CrossRef]

Dari-Salisburgo, C.

C. Dari-Salisburgo, E. DelRe, E. Palange, “Molding and stretched evolution of optical solitons in cumulative nonlinearities,” Phys. Rev. Lett. 91(26), 263903 (2003).
[CrossRef] [PubMed]

DelRe, E.

E. DelRe, P. Di Porto, B. Crosignani, “Photorefractive solitons and their underlying nonlocal physics,” Prog. Opt. 53, 153–200 (2009).
[CrossRef]

E. DelRe, E. Palange, “Optical nonlinearity and existence conditions for quasi-steady-state photorefractive solitons,” J. Opt. Soc. Am. B 23(11), 2323–2327 (2006).
[CrossRef]

E. DelRe, A. D’Ercole, E. Palange, “Mechanisms supporting long propagation regimes of photorefractive solitons,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 71(3), 036610 (2005).
[CrossRef] [PubMed]

C. Dari-Salisburgo, E. DelRe, E. Palange, “Molding and stretched evolution of optical solitons in cumulative nonlinearities,” Phys. Rev. Lett. 91(26), 263903 (2003).
[CrossRef] [PubMed]

S. Lan, E. Delre, Z. G. Chen, M. F. Shih, M. Segev, “Directional coupler with soliton-induced waveguides,” Opt. Lett. 24(7), 475–477 (1999).
[CrossRef] [PubMed]

Denz, C.

J. Petter, C. Weilnau, C. Denz, A. Stepken, F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170(4-6), 291–297 (1999).
[CrossRef]

Di Porto, P.

E. DelRe, P. Di Porto, B. Crosignani, “Photorefractive solitons and their underlying nonlocal physics,” Prog. Opt. 53, 153–200 (2009).
[CrossRef]

Ding, Y.

S. Balasubramanian, I. Lahiri, Y. Ding, M. Melloch, D. Nolte, “Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68(5), 863–869 (1999).
[CrossRef]

El-Hanany, U.

Fressengeas, N.

D. Wolfersberger, N. Khelfaoui, C. Dan, N. Fressengeas, H. Leblond, “Fast photorefractive self-focusing in InP:Fe semiconductor at infrared wavelengths,” Appl. Phys. Lett. 92(2), 021106 (2008).
[CrossRef]

N. Fressengeas, J. Maufoy, G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(6), 6866–6875 (1996).
[CrossRef] [PubMed]

Ganor, Y.

Hawkins, S. A.

Kaiser, F.

J. Petter, C. Weilnau, C. Denz, A. Stepken, F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170(4-6), 291–297 (1999).
[CrossRef]

Kashin, O.

Khelfaoui, N.

D. Wolfersberger, N. Khelfaoui, C. Dan, N. Fressengeas, H. Leblond, “Fast photorefractive self-focusing in InP:Fe semiconductor at infrared wavelengths,” Appl. Phys. Lett. 92(2), 021106 (2008).
[CrossRef]

Kiessling, A.

Kivshar, Y. S.

Y. S. Kivshar, G. I. Stegeman, “Spatial optical solitons: Guiding light for future technologies,” Opt. Photonics News 13(2), 59–63 (2002).
[CrossRef]

Kowarschik, R.

Kugel, G.

N. Fressengeas, J. Maufoy, G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(6), 6866–6875 (1996).
[CrossRef] [PubMed]

Lahiri, I.

S. Balasubramanian, I. Lahiri, Y. Ding, M. Melloch, D. Nolte, “Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68(5), 863–869 (1999).
[CrossRef]

Lan, S.

Leblond, H.

D. Wolfersberger, N. Khelfaoui, C. Dan, N. Fressengeas, H. Leblond, “Fast photorefractive self-focusing in InP:Fe semiconductor at infrared wavelengths,” Appl. Phys. Lett. 92(2), 021106 (2008).
[CrossRef]

Matusevich, V.

Maufoy, J.

N. Fressengeas, J. Maufoy, G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(6), 6866–6875 (1996).
[CrossRef] [PubMed]

Melloch, M.

S. Balasubramanian, I. Lahiri, Y. Ding, M. Melloch, D. Nolte, “Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68(5), 863–869 (1999).
[CrossRef]

Melloch, M. R.

D. D. Nolte, S. Balasubramanian, M. R. Melloch, “Nonlinear charge transport in photorefractive semiconductor quantum wells,” Opt. Mater. 18(1), 199–203 (2001).
[CrossRef]

Nolte, D.

S. Balasubramanian, I. Lahiri, Y. Ding, M. Melloch, D. Nolte, “Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68(5), 863–869 (1999).
[CrossRef]

Nolte, D. D.

D. D. Nolte, S. Balasubramanian, M. R. Melloch, “Nonlinear charge transport in photorefractive semiconductor quantum wells,” Opt. Mater. 18(1), 199–203 (2001).
[CrossRef]

Q. N. Wang, R. M. Brubaker, D. D. Nolte, “Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures,” J. Opt. Soc. Am. B 11(9), 1773–1779 (1994).
[CrossRef]

Palange, E.

E. DelRe, E. Palange, “Optical nonlinearity and existence conditions for quasi-steady-state photorefractive solitons,” J. Opt. Soc. Am. B 23(11), 2323–2327 (2006).
[CrossRef]

E. DelRe, A. D’Ercole, E. Palange, “Mechanisms supporting long propagation regimes of photorefractive solitons,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 71(3), 036610 (2005).
[CrossRef] [PubMed]

C. Dari-Salisburgo, E. DelRe, E. Palange, “Molding and stretched evolution of optical solitons in cumulative nonlinearities,” Phys. Rev. Lett. 91(26), 263903 (2003).
[CrossRef] [PubMed]

Petter, J.

J. Petter, C. Weilnau, C. Denz, A. Stepken, F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170(4-6), 291–297 (1999).
[CrossRef]

Pismennaya, K.

Salamo, G. J.

Schwartz, T.

Segev, M.

Shih, M. F.

Shwartz, S.

Stegeman, G. I.

Y. S. Kivshar, G. I. Stegeman, “Spatial optical solitons: Guiding light for future technologies,” Opt. Photonics News 13(2), 59–63 (2002).
[CrossRef]

Stepken, A.

J. Petter, C. Weilnau, C. Denz, A. Stepken, F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170(4-6), 291–297 (1999).
[CrossRef]

Uzdin, R.

Wang, Q. N.

Weilnau, C.

J. Petter, C. Weilnau, C. Denz, A. Stepken, F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170(4-6), 291–297 (1999).
[CrossRef]

Weinert-Raczka, E.

M. Wichtowski, E. Weinert-Rączka, “Temporal response of photorefractive multiple quantum wells in Franz–Keldysh geometry,” Opt. Commun. 281(5), 1233–1243 (2008).
[CrossRef]

Wichtowski, M.

M. Wichtowski, E. Weinert-Rączka, “Temporal response of photorefractive multiple quantum wells in Franz–Keldysh geometry,” Opt. Commun. 281(5), 1233–1243 (2008).
[CrossRef]

Wolfersberger, D.

D. Wolfersberger, N. Khelfaoui, C. Dan, N. Fressengeas, H. Leblond, “Fast photorefractive self-focusing in InP:Fe semiconductor at infrared wavelengths,” Appl. Phys. Lett. 92(2), 021106 (2008).
[CrossRef]

Ziólkowski, A.

A. Ziółkowski, “A numerical approach to nonlinear propagation of light in photorefractive media,” Comput. Phys. Commun. 185(2), 504–511 (2014).
[CrossRef]

A. Ziółkowski, “Temporal analysis of solitons in photorefractive semiconductors,” J. Opt. 14(3), 035202 (2012).
[CrossRef]

Appl. Phys. B

S. Balasubramanian, I. Lahiri, Y. Ding, M. Melloch, D. Nolte, “Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings,” Appl. Phys. B 68(5), 863–869 (1999).
[CrossRef]

Appl. Phys. Lett.

D. Wolfersberger, N. Khelfaoui, C. Dan, N. Fressengeas, H. Leblond, “Fast photorefractive self-focusing in InP:Fe semiconductor at infrared wavelengths,” Appl. Phys. Lett. 92(2), 021106 (2008).
[CrossRef]

Comput. Phys. Commun.

A. Ziółkowski, “A numerical approach to nonlinear propagation of light in photorefractive media,” Comput. Phys. Commun. 185(2), 504–511 (2014).
[CrossRef]

J. Opt.

A. Ziółkowski, “Temporal analysis of solitons in photorefractive semiconductors,” J. Opt. 14(3), 035202 (2012).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

J. Petter, C. Weilnau, C. Denz, A. Stepken, F. Kaiser, “Self-bending of photorefractive solitons,” Opt. Commun. 170(4-6), 291–297 (1999).
[CrossRef]

M. Wichtowski, E. Weinert-Rączka, “Temporal response of photorefractive multiple quantum wells in Franz–Keldysh geometry,” Opt. Commun. 281(5), 1233–1243 (2008).
[CrossRef]

Opt. Lett.

Opt. Mater.

D. D. Nolte, S. Balasubramanian, M. R. Melloch, “Nonlinear charge transport in photorefractive semiconductor quantum wells,” Opt. Mater. 18(1), 199–203 (2001).
[CrossRef]

Opt. Photonics News

Y. S. Kivshar, G. I. Stegeman, “Spatial optical solitons: Guiding light for future technologies,” Opt. Photonics News 13(2), 59–63 (2002).
[CrossRef]

Phys. Rev. E Stat. Nonlinear Soft Matter Phys.

E. DelRe, A. D’Ercole, E. Palange, “Mechanisms supporting long propagation regimes of photorefractive solitons,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 71(3), 036610 (2005).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

N. Fressengeas, J. Maufoy, G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54(6), 6866–6875 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett.

C. Dari-Salisburgo, E. DelRe, E. Palange, “Molding and stretched evolution of optical solitons in cumulative nonlinearities,” Phys. Rev. Lett. 91(26), 263903 (2003).
[CrossRef] [PubMed]

Prog. Opt.

E. DelRe, P. Di Porto, B. Crosignani, “Photorefractive solitons and their underlying nonlocal physics,” Prog. Opt. 53, 153–200 (2009).
[CrossRef]

Rep. Prog. Phys.

Z. Chen, M. Segev, D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[CrossRef] [PubMed]

Other

P. Günter and J. P. Huignard, Photorefractive Materials and Their Applications (Springer, 2007), Vol. III, Chap. 11.

D. D. Nolte, Photorefractive Effects and Materials (Kluwer, 1995).

K. Seeger, Semiconductor Physics (Springer, 2004), Chap. 4.

S. M. Sze, Physics of Semiconductor Devices (Wiley-Interscience, 2006), Chap. 11.

Supplementary Material (7)

» Media 1: MOV (788 KB)     
» Media 2: MOV (735 KB)     
» Media 3: MOV (738 KB)     
» Media 4: MOV (710 KB)     
» Media 5: MOV (441 KB)     
» Media 6: MOV (262 KB)     
» Media 7: MOV (671 KB)     

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Figures (4)

Fig. 1
Fig. 1

(a) Propagation of a Gaussian beam with a diameter 2w = 29 μm in semi-insulating gallium arsenide with a compensation coefficient r = 0.88 (Media 1). (b) Time evolution of the electric field distribution in the same material (Media 2).

Fig. 2
Fig. 2

Space-time evolution of concentration distribution of: (a) electrons (Media 3), (b) holes in a semi-insulating gallium arsenide with a compensation coefficient r = 0.88 (Media 4).

Fig. 3
Fig. 3

(a) Trajectory of an optical beam propagating in a stationary state in semi-insulating gallium arsenide for various values of the compensation coefficient. (b) Gaussian beam propagation in gallium arsenide with the compensation coefficient r = 0.88, given that the transport of electron is linear (Media 5).

Fig. 4
Fig. 4

(a) Propagation of a Gaussian beam with a diameter 2w = 29 μm in semi-insulating gallium arsenide with the compensation coefficient r = 0.4 (Media 6). (b) Time evolution of the electric field distribution in the same conditions (Media 7).

Equations (10)

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

T n ( E )= T L + 2q τ r v n ( E ) 3 k B E,
μ n (E)= μ nl f(E)+ μ nu [1f(E)],
f(E)= { 1+Rexp[ ΔU k B T n ( E ) ] } 1 ,
n t 1 q div J n =( S n I+ β n ) N A γ n n( N A N A ),
p t + 1 q div J p =( S p I+ β p )( N A N A ) γ p p N A ,
J n =q μ n (E)nE+ k B grad[ μ n (E) T n (E)n ],
J p =q μ p pE k B μ p T L gradp,
t ( n+ N A p N D + )= 1 q div( J n + J p ),
divE= q ε ε o ( N D + +pn N A ),
( z + i 2k 2 )A+ ik n b ΔnA=0,

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