Abstract

Nonlinear light propagation in photorefractive media can be analyzed by numerical methods. The presented numerical approach has regard to the effects of time nonlocality. Two algorithms are presented, and compared in terms of physical results and computing times. The possibility to address the issue of time nonlocality in two ways is attributed to the fact that, it is possible to completely separate carrier dynamics evaluation and wave equation calculation. This in turn, allows to choose a short integration time for carrier dynamics and a longer one to solve the wave equation. The tests of the methods were carried out for a one-carrier model that describes most of photorefractive media, and for a model with bipolar transport and hot electron effect, used in descriptions of semiconductor materials.

© 2014 Optical Society of America

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  22. H. Leblond and N. Fressengeas, “Theory of photorefractive resonance for localized beams in two-carrier photorefractive systems,” Phys. Rev. A 80(3), 033837 (2009).
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  36. N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
    [Crossref]
  37. D. Wolfersberger, N. Khelfaoui, C. Dan, N. Fressengeas, and H. Leblond, “Fast photorefractive self-focusing in InP:Fe semiconductor at infrared wavelengths,” Appl. Phys. Lett. 92(2), 021106 (2008).
    [Crossref]
  38. D. Wolfersberger, F. Lhomme, N. Fressengeas, and G. Kugel, “Simulation of the temporal behavior of one single laser pulse in a photorefractive medium,” Opt. Commun. 222(1-6), 383–391 (2003).
    [Crossref]
  39. P. A. M. Aguilar, J. J. S. Mondragon, S. Stepanov, and V. Vysloukh, “Transient self-bending of laser beams in photorefractive crystals with drift nonlinearity,” Phys. Rev. A 54(4), R2563–R2566 (1996).
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    [Crossref]

2014 (2)

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

A. Ziółkowski, “Self-bending of light in photorefractive semiconductors with hot-electron effect,” Opt. Express 22(4), 4599–4605 (2014).
[Crossref] [PubMed]

2013 (2)

N. Fressengeas, C. Dan, and D. Wolfersberger, “Microsecond infrared beam bending in photorefractive iron doped indium phosphide,” Opt. Laser Technol. 48, 96–101 (2013).
[Crossref]

M. Wichtowski and A. Ziółkowski, “Interband photorefractive effect in semiconductors with hot-electron transport at arbitrary modulation depth,” Opt. Commun. 300, 257–264 (2013).
[Crossref]

2012 (1)

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

2011 (1)

C. Dan, D. Wolfersberger, and N. Fressengeas, “Experimental control of steady state photorefractive self-focusing in InP:Fe at infrared wavelengths,” Appl. Phys. B 104(4), 887–895 (2011).
[Crossref]

2009 (3)

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

H. Leblond and N. Fressengeas, “Theory of photorefractive resonance for localized beams in two-carrier photorefractive systems,” Phys. Rev. A 80(3), 033837 (2009).
[Crossref]

F. Devaux and M. Chauvet, “Three-dimensional numerical model of the dynamics of photorefractive beam self-focusing in InP:Fe,” Phys. Rev. A 79(3), 033823 (2009).
[Crossref]

2008 (2)

F. Devaux, V. Coda, M. Chauvet, and R. Passier, “New time-dependent photorefractive three-dimensional model: application to self-trapped beam with large bending,” J. Opt. Soc. Am. B 25(6), 1081–1086 (2008).
[Crossref]

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

2007 (2)

N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
[Crossref]

A. Ziółkowski and E. Weinert-Raczka, “Dark screening solitons in multiple quantum well planar waveguide,” J. Opt. A, Pure Appl. Opt. 9(7), 688–698 (2007).
[Crossref]

2006 (1)

2005 (1)

A. Ziółkowski and E. Weinert-Raczka, “Spatial solitons in biased photorefractive media with quadratic electro-optic effect,” Opto-electronics Rev. 13, 135–140 (2005).

2003 (2)

D. Wolfersberger, F. Lhomme, N. Fressengeas, and G. Kugel, “Simulation of the temporal behavior of one single laser pulse in a photorefractive medium,” Opt. Commun. 222(1-6), 383–391 (2003).
[Crossref]

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

2001 (1)

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

1999 (3)

J. Maufoy, N. Fressengeas, D. Wolfersberger, and G. Kugel, “Simulation of the temporal behavior of soliton propagation in photorefractive media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(55 Pt B), 6116–6121 (1999).
[Crossref] [PubMed]

J. G. Murillo, “Photorefractive grating dynamics in Bi12SiO20 using optical pulses,” Opt. Commun. 159(4-6), 293–300 (1999).
[Crossref]

T. Gatlin and N. Singh, “Nonlinear frequency response of a moving grating with an applied field in bismuth silicon oxide,” Opt. Lett. 24(22), 1593–1595 (1999).
[Crossref] [PubMed]

1998 (1)

N. Fressengeas, D. Wolfersberger, J. Maufoy, and G. Kugel, “Build up mechanisms of (1+1)-dimensional photorefractive bright spatial quasi-steady-state and screening solitons,” Opt. Commun. 145(1-6), 393–400 (1998).
[Crossref]

1997 (2)

N. Singh, S. P. Nadar, and P. P. Banerjee, “Time-dependent nonlinear photorefractive response to sinusoidal intensity gratings,” Opt. Commun. 136(5-6), 487–495 (1997).
[Crossref]

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and G. Bryant, “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70(19), 2499–2501 (1997).
[Crossref]

1996 (2)

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and 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]

P. A. M. Aguilar, J. J. S. Mondragon, S. Stepanov, and V. Vysloukh, “Transient self-bending of laser beams in photorefractive crystals with drift nonlinearity,” Phys. Rev. A 54(4), R2563–R2566 (1996).

1995 (1)

1994 (2)

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Q. N. Wang, R. M. Brubaker, and 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]

1993 (1)

G. A. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96(1-3), 113–116 (1993).
[Crossref]

1989 (1)

1972 (1)

M. Reiser, “Large-scale numerical simulation in semiconductor device modelling,” Comput. Methods Appl. Mech. Eng. 1(1), 17–38 (1972).
[Crossref]

Aguilar, P. A. M.

P. A. M. Aguilar, J. J. S. Mondragon, S. Stepanov, and V. Vysloukh, “Transient self-bending of laser beams in photorefractive crystals with drift nonlinearity,” Phys. Rev. A 54(4), R2563–R2566 (1996).

Balasubramanian, S.

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

Banerjee, P. P.

N. Singh, S. P. Nadar, and P. P. Banerjee, “Time-dependent nonlinear photorefractive response to sinusoidal intensity gratings,” Opt. Commun. 136(5-6), 487–495 (1997).
[Crossref]

Bliss, D. F.

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and G. Bryant, “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70(19), 2499–2501 (1997).
[Crossref]

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and 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]

Brost, G. A.

G. A. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96(1-3), 113–116 (1993).
[Crossref]

Brubaker, R. M.

Bryant, G.

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and G. Bryant, “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70(19), 2499–2501 (1997).
[Crossref]

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and 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]

Carvalho, M. I.

Chauvet, M.

F. Devaux and M. Chauvet, “Three-dimensional numerical model of the dynamics of photorefractive beam self-focusing in InP:Fe,” Phys. Rev. A 79(3), 033823 (2009).
[Crossref]

F. Devaux, V. Coda, M. Chauvet, and R. Passier, “New time-dependent photorefractive three-dimensional model: application to self-trapped beam with large bending,” J. Opt. Soc. Am. B 25(6), 1081–1086 (2008).
[Crossref]

N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
[Crossref]

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and G. Bryant, “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70(19), 2499–2501 (1997).
[Crossref]

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and 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]

Christodoulides, D. N.

Coda, V.

Crosignani, B.

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

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Dan, C.

N. Fressengeas, C. Dan, and D. Wolfersberger, “Microsecond infrared beam bending in photorefractive iron doped indium phosphide,” Opt. Laser Technol. 48, 96–101 (2013).
[Crossref]

C. Dan, D. Wolfersberger, and N. Fressengeas, “Experimental control of steady state photorefractive self-focusing in InP:Fe at infrared wavelengths,” Appl. Phys. B 104(4), 887–895 (2011).
[Crossref]

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

N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
[Crossref]

Dari-Salisburgo, C.

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

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

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

Devaux, F.

F. Devaux and M. Chauvet, “Three-dimensional numerical model of the dynamics of photorefractive beam self-focusing in InP:Fe,” Phys. Rev. A 79(3), 033823 (2009).
[Crossref]

F. Devaux, V. Coda, M. Chauvet, and R. Passier, “New time-dependent photorefractive three-dimensional model: application to self-trapped beam with large bending,” J. Opt. Soc. Am. B 25(6), 1081–1086 (2008).
[Crossref]

Di Porto, P.

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

DiPorto, P.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Fressengeas, N.

N. Fressengeas, C. Dan, and D. Wolfersberger, “Microsecond infrared beam bending in photorefractive iron doped indium phosphide,” Opt. Laser Technol. 48, 96–101 (2013).
[Crossref]

C. Dan, D. Wolfersberger, and N. Fressengeas, “Experimental control of steady state photorefractive self-focusing in InP:Fe at infrared wavelengths,” Appl. Phys. B 104(4), 887–895 (2011).
[Crossref]

H. Leblond and N. Fressengeas, “Theory of photorefractive resonance for localized beams in two-carrier photorefractive systems,” Phys. Rev. A 80(3), 033837 (2009).
[Crossref]

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

N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
[Crossref]

D. Wolfersberger, F. Lhomme, N. Fressengeas, and G. Kugel, “Simulation of the temporal behavior of one single laser pulse in a photorefractive medium,” Opt. Commun. 222(1-6), 383–391 (2003).
[Crossref]

J. Maufoy, N. Fressengeas, D. Wolfersberger, and G. Kugel, “Simulation of the temporal behavior of soliton propagation in photorefractive media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(55 Pt B), 6116–6121 (1999).
[Crossref] [PubMed]

N. Fressengeas, D. Wolfersberger, J. Maufoy, and G. Kugel, “Build up mechanisms of (1+1)-dimensional photorefractive bright spatial quasi-steady-state and screening solitons,” Opt. Commun. 145(1-6), 393–400 (1998).
[Crossref]

Gatlin, T.

Gravey, P.

Hawkins, S. A.

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and G. Bryant, “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70(19), 2499–2501 (1997).
[Crossref]

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and 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]

Khelfaoui, N.

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

N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
[Crossref]

Kugel, G.

D. Wolfersberger, F. Lhomme, N. Fressengeas, and G. Kugel, “Simulation of the temporal behavior of one single laser pulse in a photorefractive medium,” Opt. Commun. 222(1-6), 383–391 (2003).
[Crossref]

J. Maufoy, N. Fressengeas, D. Wolfersberger, and G. Kugel, “Simulation of the temporal behavior of soliton propagation in photorefractive media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(55 Pt B), 6116–6121 (1999).
[Crossref] [PubMed]

N. Fressengeas, D. Wolfersberger, J. Maufoy, and G. Kugel, “Build up mechanisms of (1+1)-dimensional photorefractive bright spatial quasi-steady-state and screening solitons,” Opt. Commun. 145(1-6), 393–400 (1998).
[Crossref]

Leblond, H.

H. Leblond and N. Fressengeas, “Theory of photorefractive resonance for localized beams in two-carrier photorefractive systems,” Phys. Rev. A 80(3), 033837 (2009).
[Crossref]

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

N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
[Crossref]

Lhomme, F.

D. Wolfersberger, F. Lhomme, N. Fressengeas, and G. Kugel, “Simulation of the temporal behavior of one single laser pulse in a photorefractive medium,” Opt. Commun. 222(1-6), 383–391 (2003).
[Crossref]

Maufoy, J.

J. Maufoy, N. Fressengeas, D. Wolfersberger, and G. Kugel, “Simulation of the temporal behavior of soliton propagation in photorefractive media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(55 Pt B), 6116–6121 (1999).
[Crossref] [PubMed]

N. Fressengeas, D. Wolfersberger, J. Maufoy, and G. Kugel, “Build up mechanisms of (1+1)-dimensional photorefractive bright spatial quasi-steady-state and screening solitons,” Opt. Commun. 145(1-6), 393–400 (1998).
[Crossref]

Melloch, M. R.

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

Mondragon, J. J. S.

P. A. M. Aguilar, J. J. S. Mondragon, S. Stepanov, and V. Vysloukh, “Transient self-bending of laser beams in photorefractive crystals with drift nonlinearity,” Phys. Rev. A 54(4), R2563–R2566 (1996).

Montemezzani, G.

N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
[Crossref]

Murillo, J. G.

J. G. Murillo, “Photorefractive grating dynamics in Bi12SiO20 using optical pulses,” Opt. Commun. 159(4-6), 293–300 (1999).
[Crossref]

Nadar, S. P.

N. Singh, S. P. Nadar, and P. P. Banerjee, “Time-dependent nonlinear photorefractive response to sinusoidal intensity gratings,” Opt. Commun. 136(5-6), 487–495 (1997).
[Crossref]

Nolte, D. D.

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

Q. N. Wang, R. M. Brubaker, and 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]

Ozkul, C.

Palange, E.

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

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

Passier, R.

Picoli, G.

Reiser, M.

M. Reiser, “Large-scale numerical simulation in semiconductor device modelling,” Comput. Methods Appl. Mech. Eng. 1(1), 17–38 (1972).
[Crossref]

Salamo, G. J.

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and G. Bryant, “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70(19), 2499–2501 (1997).
[Crossref]

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and 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]

Segev, M.

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and G. Bryant, “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70(19), 2499–2501 (1997).
[Crossref]

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and 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]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Singh, N.

T. Gatlin and N. Singh, “Nonlinear frequency response of a moving grating with an applied field in bismuth silicon oxide,” Opt. Lett. 24(22), 1593–1595 (1999).
[Crossref] [PubMed]

N. Singh, S. P. Nadar, and P. P. Banerjee, “Time-dependent nonlinear photorefractive response to sinusoidal intensity gratings,” Opt. Commun. 136(5-6), 487–495 (1997).
[Crossref]

Stepanov, S.

P. A. M. Aguilar, J. J. S. Mondragon, S. Stepanov, and V. Vysloukh, “Transient self-bending of laser beams in photorefractive crystals with drift nonlinearity,” Phys. Rev. A 54(4), R2563–R2566 (1996).

Valley, G. C.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Vysloukh, V.

P. A. M. Aguilar, J. J. S. Mondragon, S. Stepanov, and V. Vysloukh, “Transient self-bending of laser beams in photorefractive crystals with drift nonlinearity,” Phys. Rev. A 54(4), R2563–R2566 (1996).

Wang, Q. N.

Weinert-Raczka, E.

A. Ziółkowski and E. Weinert-Raczka, “Dark screening solitons in multiple quantum well planar waveguide,” J. Opt. A, Pure Appl. Opt. 9(7), 688–698 (2007).
[Crossref]

A. Ziółkowski and E. Weinert-Raczka, “Spatial solitons in biased photorefractive media with quadratic electro-optic effect,” Opto-electronics Rev. 13, 135–140 (2005).

Wichtowski, M.

M. Wichtowski and A. Ziółkowski, “Interband photorefractive effect in semiconductors with hot-electron transport at arbitrary modulation depth,” Opt. Commun. 300, 257–264 (2013).
[Crossref]

Wolfersberger, D.

N. Fressengeas, C. Dan, and D. Wolfersberger, “Microsecond infrared beam bending in photorefractive iron doped indium phosphide,” Opt. Laser Technol. 48, 96–101 (2013).
[Crossref]

C. Dan, D. Wolfersberger, and N. Fressengeas, “Experimental control of steady state photorefractive self-focusing in InP:Fe at infrared wavelengths,” Appl. Phys. B 104(4), 887–895 (2011).
[Crossref]

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

N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
[Crossref]

D. Wolfersberger, F. Lhomme, N. Fressengeas, and G. Kugel, “Simulation of the temporal behavior of one single laser pulse in a photorefractive medium,” Opt. Commun. 222(1-6), 383–391 (2003).
[Crossref]

J. Maufoy, N. Fressengeas, D. Wolfersberger, and G. Kugel, “Simulation of the temporal behavior of soliton propagation in photorefractive media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(55 Pt B), 6116–6121 (1999).
[Crossref] [PubMed]

N. Fressengeas, D. Wolfersberger, J. Maufoy, and G. Kugel, “Build up mechanisms of (1+1)-dimensional photorefractive bright spatial quasi-steady-state and screening solitons,” Opt. Commun. 145(1-6), 393–400 (1998).
[Crossref]

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

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, “Self-bending of light in photorefractive semiconductors with hot-electron effect,” Opt. Express 22(4), 4599–4605 (2014).
[Crossref] [PubMed]

M. Wichtowski and A. Ziółkowski, “Interband photorefractive effect in semiconductors with hot-electron transport at arbitrary modulation depth,” Opt. Commun. 300, 257–264 (2013).
[Crossref]

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

A. Ziółkowski and E. Weinert-Raczka, “Dark screening solitons in multiple quantum well planar waveguide,” J. Opt. A, Pure Appl. Opt. 9(7), 688–698 (2007).
[Crossref]

A. Ziółkowski and E. Weinert-Raczka, “Spatial solitons in biased photorefractive media with quadratic electro-optic effect,” Opto-electronics Rev. 13, 135–140 (2005).

Appl. Phys. B (1)

C. Dan, D. Wolfersberger, and N. Fressengeas, “Experimental control of steady state photorefractive self-focusing in InP:Fe at infrared wavelengths,” Appl. Phys. B 104(4), 887–895 (2011).
[Crossref]

Appl. Phys. Lett. (2)

M. Chauvet, S. A. Hawkins, G. J. Salamo, M. Segev, D. F. Bliss, and G. Bryant, “Self-trapping of two-dimensional optical beams and light-induced waveguiding in photorefractive InP at telecommunication wavelengths,” Appl. Phys. Lett. 70(19), 2499–2501 (1997).
[Crossref]

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

Comput. Methods Appl. Mech. Eng. (1)

M. Reiser, “Large-scale numerical simulation in semiconductor device modelling,” Comput. Methods Appl. Mech. Eng. 1(1), 17–38 (1972).
[Crossref]

Comput. Phys. Commun. (1)

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

J. Opt. (1)

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

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

A. Ziółkowski and E. Weinert-Raczka, “Dark screening solitons in multiple quantum well planar waveguide,” J. Opt. A, Pure Appl. Opt. 9(7), 688–698 (2007).
[Crossref]

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

Opt. Commun. (6)

N. Fressengeas, D. Wolfersberger, J. Maufoy, and G. Kugel, “Build up mechanisms of (1+1)-dimensional photorefractive bright spatial quasi-steady-state and screening solitons,” Opt. Commun. 145(1-6), 393–400 (1998).
[Crossref]

G. A. Brost, “Numerical analysis of photorefractive grating formation dynamics at large modulation in BSO,” Opt. Commun. 96(1-3), 113–116 (1993).
[Crossref]

N. Singh, S. P. Nadar, and P. P. Banerjee, “Time-dependent nonlinear photorefractive response to sinusoidal intensity gratings,” Opt. Commun. 136(5-6), 487–495 (1997).
[Crossref]

J. G. Murillo, “Photorefractive grating dynamics in Bi12SiO20 using optical pulses,” Opt. Commun. 159(4-6), 293–300 (1999).
[Crossref]

M. Wichtowski and A. Ziółkowski, “Interband photorefractive effect in semiconductors with hot-electron transport at arbitrary modulation depth,” Opt. Commun. 300, 257–264 (2013).
[Crossref]

D. Wolfersberger, F. Lhomme, N. Fressengeas, and G. Kugel, “Simulation of the temporal behavior of one single laser pulse in a photorefractive medium,” Opt. Commun. 222(1-6), 383–391 (2003).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

N. Fressengeas, C. Dan, and D. Wolfersberger, “Microsecond infrared beam bending in photorefractive iron doped indium phosphide,” Opt. Laser Technol. 48, 96–101 (2013).
[Crossref]

Opt. Lett. (3)

Opt. Mater. (Amst) (1)

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

Opto-electronics Rev. (1)

A. Ziółkowski and E. Weinert-Raczka, “Spatial solitons in biased photorefractive media with quadratic electro-optic effect,” Opto-electronics Rev. 13, 135–140 (2005).

Phys. Rev. A (4)

P. A. M. Aguilar, J. J. S. Mondragon, S. Stepanov, and V. Vysloukh, “Transient self-bending of laser beams in photorefractive crystals with drift nonlinearity,” Phys. Rev. A 54(4), R2563–R2566 (1996).

H. Leblond and N. Fressengeas, “Theory of photorefractive resonance for localized beams in two-carrier photorefractive systems,” Phys. Rev. A 80(3), 033837 (2009).
[Crossref]

F. Devaux and M. Chauvet, “Three-dimensional numerical model of the dynamics of photorefractive beam self-focusing in InP:Fe,” Phys. Rev. A 79(3), 033823 (2009).
[Crossref]

N. Fressengeas, N. Khelfaoui, C. Dan, D. Wolfersberger, G. Montemezzani, H. Leblond, and M. Chauvet, “Roles of resonance and dark irradiance for infrared photorefractive self-focusing and solitons in bipolar InP:Fe,” Phys. Rev. A 75(6), 063834 (2007).
[Crossref]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

J. Maufoy, N. Fressengeas, D. Wolfersberger, and G. Kugel, “Simulation of the temporal behavior of soliton propagation in photorefractive media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 59(55 Pt B), 6116–6121 (1999).
[Crossref] [PubMed]

Phys. Rev. Lett. (2)

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

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73(24), 3211–3214 (1994).
[Crossref] [PubMed]

Prog. Opt. (1)

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

Other (9)

S. Selberherr, Analysis and Simulation of Semiconductor Devices (Springer-Verlag, 1984).

S. M. Sze and K. N. Kwok, “Physics and Properties of Semiconductors - A Review,” in Physics of Semiconductor Devices (John Wiley & Sons, 2002).

K. Seeger, Semiconductor Physics - An Introduction (Springer-Verlag, 2004).

R. W. Boyd, Nonlinear Optics, Electronics & Electrical (Elsevier Science, 2003).

P. Yeh, Introduction to Photorefractive Nonlinear Optics (John Wiley & Sons, 1993).

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

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Clarendon, 1996).

P. Günter and J. P. Huignard, Photorefractive Materials and Their Applications 2: Materials (Springer-Verlag, 2006).

P. Günter and J. P. Huignard, Photorefractive Materials and Their Applications 3: Applications (Springer-Verlag, 2007).

Supplementary Material (2)

» Media 1: MOV (332 KB)     
» Media 2: MOV (1851 KB)     

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Figures (7)

Fig. 1
Fig. 1 Computing algorithm: time local version; numerical procedure I.

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Fig. 2
Fig. 2 Block diagram of a computing algorithm: time nonlocal version; a) numerical procedure II, b) numerical procedure III.

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Fig. 3
Fig. 3 Time evolution of a soliton beam in a material described by the model (1a)-(1d), determined by procedure II. The results present transition states for a) 0 ms, b) 0.3 ms, c) 0.9 ms, d) 1.65 ms, e) 2.55 ms, f) 9 ms. For more effective illustration, the process has been recorded (Media 1).

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Fig. 4
Fig. 4 a) Comparison of diffraction coefficient changes during self-trapping of light beam, determined by algorithms I and II. b) Comparison of time evolution of the diffraction coefficient for low dynamics of self-trapping. Computed results produced by algorithms I and II for propagation lengths Z = 3.5 mm (Z/LD = 1.6).

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Fig. 5
Fig. 5 a) Comparison of the diffraction coefficient obtained by algorithm II for various time steps dt = 1x10−7s and 3x10−7s. b) Comparison of the diffraction coefficient obtained by algorithm III for various values of parameter H to results obtained by numerical procedures I and II.

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Fig. 6
Fig. 6 Time evolution of a Gaussian beam in a material described by the model (5a)- (5f), determined by algorithm III for H = 20. The results present transition states for a) 0 μs, b) 2 μs, c) 4.8 μs, d) 12.8 μs, e) 25.2 μs, f) 41 μs. For better illustration, the process is shown in a movie (Media 2).

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Fig. 7
Fig. 7 Time evolution of light intensity distribution collected at the output of computing field for algorithm I and III (H = 20). The computation results present transition states for a) 0 μs, b) 2 μs, c) 4 μs, d) 8 μs, e) 16 μs, f) 20 μs, g) 24 μs, h) 32 μs, i) 48 μs.

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Tables (3)

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Table 1 Material parameters used in computations based on model (1a)-(1d).

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Table 2 Material parameters used in computations based on model (5a) – (5f).

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Table 3 Computing times determined by the numerical procedure III.

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Equations (33)

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

∂ N D + ∂ t = [ β n + S n ( I + I B ) ] ( N D − N D + ) − γ n n N D + ,
J n = q μ n n E + μ n k B T   grad   n ,
∂ ∂ t ( N D + − N A − − n ) = 1 q div   J n ,
div   E = −   div ( grad φ ) = q ε ε o ( N D + − N A − − n ) ,
T n ( E ) = T L + 2 q τ r v n ( E ) 3 k B E ,
μ n ( E ) = μ n l f ( E ) + μ n u [ 1 − f ( E ) ] ,
f ( E ) = { 1 + R   exp [ − Δ U k B T n ( E ) ] } − 1 ,
∂ n ∂ t − 1 q div   J n = [ S n ( I + I B ) + β n ] ( N D − N D + ) − γ n n N D +   ,
∂ p ∂ t   + 1 q div   J p = [ S p ( I + I B ) + β p ] N D + − γ p p ( N D − N D + )   ,
J n = q μ n ( E ) n E + k B grad [ μ n ( E ) T n ( E ) n   ] ,
J p = q μ p p E − k B μ p T L grad   p   ,
∂ ∂ t ( n + N A − − p − N D + ) = 1 q div ( J n + J p ) ,
div E = −   div ( grad φ ) = q ε ε o ( N D + + p − n − N A − ) ,
( ∂ ∂ z + i 2 k ∂ 2 ∂ x 2 ) A ( x , z ) + i k n b Δ n ( E ) A ( x , z ) = 0   ,
μ n = μ n l ,     T n = T L .
n = [ S n ( I + I B ) + β n ] ( N D − N D + ) γ n N D + ,   p = [ S p ( I + I B ) + β p ] N D + γ p ( N D − N D + ) .
∂ ∂ x ( J n + J p ) = − ε ε 0 ∂ 2 E ∂ t ∂ x .
∂ E ∂ t + 1 τ D ( 1 + I I B + I d ) E = E 0 τ D .
τ D = ε ε 0 q ( μ n a n + μ p a p ) I B + q ( μ n b n + μ p b p ) ,
a n = S n ( N D − N A ) γ n N A ,   a p = S p N A γ p ( N D − N A ) , b n = β n ( N D − N A ) γ n N A ,   b p = β p N A γ p ( N D − N A ) .
I d = μ n b n + μ p b p μ n a n + μ p a p .
E ( t ) = E 0 exp [ − 1 τ D ∫ 0 t ( 1 + I I B + I D ) d t ′ ] { 1 + 1 τ D ∫ 0 t d t ′ exp [ 1 τ D ∫ 0 t ′ ( 1 + I I B + I D ) d t ″ ] } .
E ( t ) = E 0 exp [ − t τ D ( 1 + I I B + I D ) ] + E 0 ( 1 + I I B + I D ) − 1 { 1 − exp [ − t τ D ( 1 + I I B + I D ) ] } ,
τ n = 1 γ n N A ,   τ p = 1 γ p ( N D − N A ) .
n 0 = ( S n I B + β n ) ( N D − N A ) γ n N A ,   N D + 0 = N A + n 0 ,   E 0 = φ 0 L .
∂ N D + ∂ t = ( ∂ n ∂ t − 1 q ∂ J n ∂ x ) − ( ∂ p ∂ t + 1 q ∂ J p ∂ x ) .
N D + j s + 1 = N D + j s + N D [ ​ S n ( I j s + I B ) + β n + γ p p j s ] d t ​ − ​ N D + j s [ S p ( I j s + I B ) + β p + γ n n j s ] d t 1 + [ S n ( I j s + I B ) + β n + γ p p j s ] d t ,
A + p j + 1 s + 1 + B + p j s + 1 + C + p j − 1 s + 1 = A   p j + 1 s + B   p j s + C   p j − 1 s + D ,
A + = ξ ( μ p 2 d x E j + 1 s − D p d x 2 ) ,   B + = 1 d t + ξ 2 D p d x 2 ,   C + = ξ ( − μ p 2 d x E j − 1 s − D p d x 2 ) , A = ( ξ − 1 ) ( μ p 2 d x E j + 1 s − D p d x 2 ) ,   B = 1 d t + ( ξ − 1 ) 2 D p d x 2 − γ p ( N D − N D + j s ) , C = ( ξ − 1 ) ( − μ p 2 d x E j − 1 s − D p d x 2 ) ,   D = N D + [ S p ( I j s + I B ) + β p ] ,
F + n j + 1 s + 1 + G + n j s + 1 + H + n j − 1 s + 1 = F   n j + 1 s + G   n j s + H   n j − 1 s + M ,
F + = ξ ( − μ n j + 1 s 2 d x E j + 1 s + D n ( j + 1 / 2 ) d x 2 ) ,   G + = 1 d t − ξ D n ( j + 1 / 2 ) + D n ( j − 1 / 2 ) d x 2 , H + = ξ ( μ n j − 1 s 2 d x E j − 1 s + D n ( j − 1 / 2 ) d x 2 ) ,   F = ( μ n j + 1 s 2 d x E j + 1 s − D n ( j + 1 / 2 ) d x 2 ) , G = 1 d t − ( 1 − ξ ) D n ( j + 1 / 2 ) + D n ( j − 1 / 2 ) d x 2 − γ n N D + j s ,   H = ( ξ − 1 ) ( μ n j − 1 s 2 d x E j − 1 s + D n ( j − 1 / 2 ) d x 2 ) , M = [ S n ( I j s + I B ) + β n ] ( N D − N D + j s ) ,   D n ( j + 1 / 2 ) ≈ D n j + 1 + D n j 2 ,   D n ( j − 1 / 2 ) ≈ D n j + D n j − 1 2 .
f ( E ) = [ 1 + ( E E C ) 5.6 ] − 1 4 ,
φ j + 1 s + 1 − 2 φ j s + 1 + φ j − 1 s + 1 = − q d x 2 ε ε 0 ( N D j s + 1 + p j s + 1 − n j s + 1 − N A ) ,

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