Abstract

We study experimentally the aging of optical spatial solitons in a dipolar glass hosted by a nanodisordered sample of photorefractive potassium-sodium-tantalate-niobate (KNTN). As the system ages, the waves erratically explore varying strengths of the nonlinear response, causing them to break up and scatter. We show that this process can still lead to solitons, but in a generalized form for which the changing response is compensated by changing the normalized wave size and intensity so as to maintain fixed the optical waveform.

© 2013 Optical Society of America

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    [CrossRef]
  2. L. Leuzzi and T. M. Nieuwenhuizen, Thermodynamics of the Glassy State (Taylor and Francis, 2008).
  3. C. A. Angell, “Glass-formers and viscous liquid slowdown since David Turnbull: Enduring puzzles and new twists,” MRS Bull.33, 544–555 (2008).
    [CrossRef]
  4. N. Gofraniha, C. Conti, and G. Ruocco, “Aging of the nonlinear optical susceptibility in doped colloidal suspensions,” Phys. Rev. B75, 224203 (2007).
    [CrossRef]
  5. N. Gofraniha, C. Conti, G. Ruocco, and F. Zamponi, “Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material,” Phys. Rev. Lett.102, 038303 (2009).
    [CrossRef]
  6. G. A. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys. Condens. Matter15, R367–R411 (2003).
    [CrossRef]
  7. A. Bokov, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci.41, 31–52 (2006).
    [CrossRef]
  8. P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B70, 132104 (2004).
    [CrossRef]
  9. A. Gumennik, Y. Kurzweil-Segev, and A. J. Agranat, “Electrooptical effects in glass forming liquids of dipolar nano-clusters embedded in a paraelectric environment,” Opt. Mater. Express1, 332–343 (2011).
    [CrossRef]
  10. Y. Chang, C. Wang, S. Yin, R. C. Hoffman, and A. G. Mott, “Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals,” Opt. Express21, 17760–17768 (2013).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics5, 39–42 (2011).
    [CrossRef]
  14. E. DelRe and C. Conti, “Scale-free optics,” in Nonlinear Photonics and Novel Optical Phenomena, Vol. 170 of Springer Series in Optical Sciences (Springer, 2012), Chap. 8, pp. 207–230.
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  15. J. Parravicini, F. Di Mei, C. Conti, A.J. Agranat, and E. DelRe, “Diffraction cancellation over multiple wavelengths in photorefractive dipolar glasses,” Opt. Express19, 24109–24114 (2011).
    [CrossRef] [PubMed]
  16. J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time,” Opt. Express20, 27382–27387 (2012).
    [CrossRef] [PubMed]
  17. J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Programming scale-free optics in disordered ferroelectrics,” Opt. Lett.37, 2355–2357 (2012).
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  18. J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett.101, 111104 (2012).
    [CrossRef]
  19. 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, 3211–3214 (1994).
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    [CrossRef]
  26. M. Morin, G. Duree, G. Salamo, and M. Segev, “Wave-guides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett.20, 2066–2068 (1995).
    [CrossRef] [PubMed]
  27. E. DelRe and E. Palange, “Optical nonlinearity and existence conditions for quasi-steady-state photorefractive solitons,” J. Opt. Soc. Am. B23, 2323–2327 (2006).
    [CrossRef]
  28. C. Dari-Salisburgo, E. DelRe, and E. Palange, “Molding and stretched evolution of optical solitons in cumulative nonlinearities,” Phys. Rev. Lett.91, 263903 (2003).
    [CrossRef]
  29. M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun.120, 311–315 (1995).
    [CrossRef]
  30. Z. G. Chen, M. Asaro, O. Ostroverkhova, and W. E. Moerner, “Self-trapping of light in an organic photorefractive glass,” Opt. Lett.28, 2509–2511 (2003).
    [CrossRef] [PubMed]
  31. M. Asaro, M. Sheldon, Z. G. Chen, O. Ostroverkhova, and W. E. Moerner, “Soliton-induced waveguides in an organic photorefractive glass,” Opt. Lett.30, 519–521 (2005).
    [CrossRef] [PubMed]

2013

C. Hu, H. Tian, B. Yaoa, Z. Zhou, and D. Chen, “Large quadratic electro-optic effect in K0.99Li0.01Ta0.60Nb0.40O3 single crystal,” Curr. Appl. Phys.13, 785–788 (2013).
[CrossRef]

Y. Chang, C. Wang, S. Yin, R. C. Hoffman, and A. G. Mott, “Kovacs effect enhanced broadband large field of view electro-optic modulators in nanodisordered KTN crystals,” Opt. Express21, 17760–17768 (2013).
[CrossRef] [PubMed]

2012

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Programming scale-free optics in disordered ferroelectrics,” Opt. Lett.37, 2355–2357 (2012).
[CrossRef] [PubMed]

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time,” Opt. Express20, 27382–27387 (2012).
[CrossRef] [PubMed]

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett.101, 111104 (2012).
[CrossRef]

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

2011

2009

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

N. Gofraniha, C. Conti, G. Ruocco, and F. Zamponi, “Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material,” Phys. Rev. Lett.102, 038303 (2009).
[CrossRef]

2008

C. A. Angell, “Glass-formers and viscous liquid slowdown since David Turnbull: Enduring puzzles and new twists,” MRS Bull.33, 544–555 (2008).
[CrossRef]

2007

N. Gofraniha, C. Conti, and G. Ruocco, “Aging of the nonlinear optical susceptibility in doped colloidal suspensions,” Phys. Rev. B75, 224203 (2007).
[CrossRef]

2006

2005

2004

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B70, 132104 (2004).
[CrossRef]

2003

G. A. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys. Condens. Matter15, R367–R411 (2003).
[CrossRef]

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

Z. G. Chen, M. Asaro, O. Ostroverkhova, and W. E. Moerner, “Self-trapping of light in an organic photorefractive glass,” Opt. Lett.28, 2509–2511 (2003).
[CrossRef] [PubMed]

2002

G. Bitton, Y. Feldman, and A. J. Agranat, “Relaxation processes of off-center impurities in KTN:Li crystals,” J. Non-Cryst. Solids305, 362–367 (2002).
[CrossRef]

1998

1995

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun.120, 311–315 (1995).
[CrossRef]

M. Morin, G. Duree, G. Salamo, and M. Segev, “Wave-guides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett.20, 2066–2068 (1995).
[CrossRef] [PubMed]

1994

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, 3211–3214 (1994).
[CrossRef] [PubMed]

Agranat, A.

Agranat, A. J.

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time,” Opt. Express20, 27382–27387 (2012).
[CrossRef] [PubMed]

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Programming scale-free optics in disordered ferroelectrics,” Opt. Lett.37, 2355–2357 (2012).
[CrossRef] [PubMed]

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett.101, 111104 (2012).
[CrossRef]

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics5, 39–42 (2011).
[CrossRef]

A. Gumennik, Y. Kurzweil-Segev, and A. J. Agranat, “Electrooptical effects in glass forming liquids of dipolar nano-clusters embedded in a paraelectric environment,” Opt. Mater. Express1, 332–343 (2011).
[CrossRef]

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B70, 132104 (2004).
[CrossRef]

G. Bitton, Y. Feldman, and A. J. Agranat, “Relaxation processes of off-center impurities in KTN:Li crystals,” J. Non-Cryst. Solids305, 362–367 (2002).
[CrossRef]

Agranat, A.J.

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2012).

Angell, C. A.

C. A. Angell, “Glass-formers and viscous liquid slowdown since David Turnbull: Enduring puzzles and new twists,” MRS Bull.33, 544–555 (2008).
[CrossRef]

Asaro, M.

Ben Ishai, P.

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B70, 132104 (2004).
[CrossRef]

Bitton, G.

G. Bitton, Y. Feldman, and A. J. Agranat, “Relaxation processes of off-center impurities in KTN:Li crystals,” J. Non-Cryst. Solids305, 362–367 (2002).
[CrossRef]

Bokov, A.

A. Bokov, “Recent progress in relaxor ferroelectrics with perovskite structure,” J. Mater. Sci.41, 31–52 (2006).
[CrossRef]

Carvalho, M. I.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun.120, 311–315 (1995).
[CrossRef]

Chang, Y.

Chen, D.

C. Hu, H. Tian, B. Yaoa, Z. Zhou, and D. Chen, “Large quadratic electro-optic effect in K0.99Li0.01Ta0.60Nb0.40O3 single crystal,” Curr. Appl. Phys.13, 785–788 (2013).
[CrossRef]

Chen, Z.

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

Chen, Z. G.

Christodoulides, D.

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

Christodoulides, D. N.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun.120, 311–315 (1995).
[CrossRef]

Conti, C.

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time,” Opt. Express20, 27382–27387 (2012).
[CrossRef] [PubMed]

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Programming scale-free optics in disordered ferroelectrics,” Opt. Lett.37, 2355–2357 (2012).
[CrossRef] [PubMed]

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett.101, 111104 (2012).
[CrossRef]

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics5, 39–42 (2011).
[CrossRef]

J. Parravicini, F. Di Mei, C. Conti, A.J. Agranat, and E. DelRe, “Diffraction cancellation over multiple wavelengths in photorefractive dipolar glasses,” Opt. Express19, 24109–24114 (2011).
[CrossRef] [PubMed]

N. Gofraniha, C. Conti, G. Ruocco, and F. Zamponi, “Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material,” Phys. Rev. Lett.102, 038303 (2009).
[CrossRef]

N. Gofraniha, C. Conti, and G. Ruocco, “Aging of the nonlinear optical susceptibility in doped colloidal suspensions,” Phys. Rev. B75, 224203 (2007).
[CrossRef]

E. DelRe and C. Conti, “Scale-free optics,” in Nonlinear Photonics and Novel Optical Phenomena, Vol. 170 of Springer Series in Optical Sciences (Springer, 2012), Chap. 8, pp. 207–230.
[CrossRef]

Crosignani, B.

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

E. DelRe, B. Crosignani, M. Tamburrini, M. Segev, M. Mitchell, E. Refaeli, and A. Agranat, “One-dimensional steady-state photorefractive spatial solitons in centrosymmetric paraelectric potassium lithium tantalate niobate,” Opt. Lett.23, 421–423 (1998).
[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, 3211–3214 (1994).
[CrossRef] [PubMed]

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, 263903 (2003).
[CrossRef]

De Olivera, C. E. M.

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B70, 132104 (2004).
[CrossRef]

DelRe, E.

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Rejuvenation in scale-free optics and enhanced diffraction cancellation life-time,” Opt. Express20, 27382–27387 (2012).
[CrossRef] [PubMed]

J. Parravicini, C. Conti, A. J. Agranat, and E. DelRe, “Programming scale-free optics in disordered ferroelectrics,” Opt. Lett.37, 2355–2357 (2012).
[CrossRef] [PubMed]

J. Parravicini, A. J. Agranat, C. Conti, and E. DelRe, “Equalizing disordered ferroelectrics for diffraction cancellation,” Appl. Phys. Lett.101, 111104 (2012).
[CrossRef]

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics5, 39–42 (2011).
[CrossRef]

J. Parravicini, F. Di Mei, C. Conti, A.J. Agranat, and E. DelRe, “Diffraction cancellation over multiple wavelengths in photorefractive dipolar glasses,” Opt. Express19, 24109–24114 (2011).
[CrossRef] [PubMed]

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. B23, 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, 263903 (2003).
[CrossRef]

E. DelRe, B. Crosignani, M. Tamburrini, M. Segev, M. Mitchell, E. Refaeli, and A. Agranat, “One-dimensional steady-state photorefractive spatial solitons in centrosymmetric paraelectric potassium lithium tantalate niobate,” Opt. Lett.23, 421–423 (1998).
[CrossRef]

E. DelRe and C. Conti, “Scale-free optics,” in Nonlinear Photonics and Novel Optical Phenomena, Vol. 170 of Springer Series in Optical Sciences (Springer, 2012), Chap. 8, pp. 207–230.
[CrossRef]

Di Mei, F.

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, 3211–3214 (1994).
[CrossRef] [PubMed]

Donth, E.

E. Donth, The Glass Transition (Springer, 2001).
[CrossRef]

Duree, G.

Feldman, Y.

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B70, 132104 (2004).
[CrossRef]

G. Bitton, Y. Feldman, and A. J. Agranat, “Relaxation processes of off-center impurities in KTN:Li crystals,” J. Non-Cryst. Solids305, 362–367 (2002).
[CrossRef]

Gofraniha, N.

N. Gofraniha, C. Conti, G. Ruocco, and F. Zamponi, “Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material,” Phys. Rev. Lett.102, 038303 (2009).
[CrossRef]

N. Gofraniha, C. Conti, and G. Ruocco, “Aging of the nonlinear optical susceptibility in doped colloidal suspensions,” Phys. Rev. B75, 224203 (2007).
[CrossRef]

Gumennik, A.

Hoffman, R. C.

Hu, C.

C. Hu, H. Tian, B. Yaoa, Z. Zhou, and D. Chen, “Large quadratic electro-optic effect in K0.99Li0.01Ta0.60Nb0.40O3 single crystal,” Curr. Appl. Phys.13, 785–788 (2013).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

Kurzweil-Segev, Y.

Leuzzi, L.

L. Leuzzi and T. M. Nieuwenhuizen, Thermodynamics of the Glassy State (Taylor and Francis, 2008).

Mitchell, M.

Moerner, W. E.

Morin, M.

Mott, A. G.

Nieuwenhuizen, T. M.

L. Leuzzi and T. M. Nieuwenhuizen, Thermodynamics of the Glassy State (Taylor and Francis, 2008).

Ostroverkhova, O.

Palange, E.

E. DelRe and E. Palange, “Optical nonlinearity and existence conditions for quasi-steady-state photorefractive solitons,” J. Opt. Soc. Am. B23, 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, 263903 (2003).
[CrossRef]

Parravicini, J.

Refaeli, E.

Ruocco, G.

N. Gofraniha, C. Conti, G. Ruocco, and F. Zamponi, “Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material,” Phys. Rev. Lett.102, 038303 (2009).
[CrossRef]

N. Gofraniha, C. Conti, and G. Ruocco, “Aging of the nonlinear optical susceptibility in doped colloidal suspensions,” Phys. Rev. B75, 224203 (2007).
[CrossRef]

Ryabov, Y.

P. Ben Ishai, C. E. M. De Olivera, Y. Ryabov, Y. Feldman, and A. J. Agranat, “Glass-forming liquid kinetics manifested in a KTN:Cu crystal,” Phys. Rev. B70, 132104 (2004).
[CrossRef]

Salamo, G.

Samara, G. A.

G. A. Samara, “The relaxational properties of compositionally disordered ABO3 perovskites,” J. Phys. Condens. Matter15, R367–R411 (2003).
[CrossRef]

Segev, M.

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

E. DelRe, B. Crosignani, M. Tamburrini, M. Segev, M. Mitchell, E. Refaeli, and A. Agranat, “One-dimensional steady-state photorefractive spatial solitons in centrosymmetric paraelectric potassium lithium tantalate niobate,” Opt. Lett.23, 421–423 (1998).
[CrossRef]

M. Morin, G. Duree, G. Salamo, and M. Segev, “Wave-guides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett.20, 2066–2068 (1995).
[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, 3211–3214 (1994).
[CrossRef] [PubMed]

Sheldon, M.

Singh, S. R.

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, “Self-deflection of steady-state bright spatial solitons in biased photorefractive crystals,” Opt. Commun.120, 311–315 (1995).
[CrossRef]

Spinozzi, E.

E. DelRe, E. Spinozzi, A. J. Agranat, and C. Conti, “Scale-free optics and diffractionless waves in nanodisordered ferroelectrics,” Nat. Photonics5, 39–42 (2011).
[CrossRef]

Tamburrini, M.

Tian, H.

C. Hu, H. Tian, B. Yaoa, Z. Zhou, and D. Chen, “Large quadratic electro-optic effect in K0.99Li0.01Ta0.60Nb0.40O3 single crystal,” Curr. Appl. Phys.13, 785–788 (2013).
[CrossRef]

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, 3211–3214 (1994).
[CrossRef] [PubMed]

Wang, C.

Yaoa, B.

C. Hu, H. Tian, B. Yaoa, Z. Zhou, and D. Chen, “Large quadratic electro-optic effect in K0.99Li0.01Ta0.60Nb0.40O3 single crystal,” Curr. Appl. Phys.13, 785–788 (2013).
[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, 3211–3214 (1994).
[CrossRef] [PubMed]

Yin, S.

Zamponi, F.

N. Gofraniha, C. Conti, G. Ruocco, and F. Zamponi, “Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material,” Phys. Rev. Lett.102, 038303 (2009).
[CrossRef]

Zhou, Z.

C. Hu, H. Tian, B. Yaoa, Z. Zhou, and D. Chen, “Large quadratic electro-optic effect in K0.99Li0.01Ta0.60Nb0.40O3 single crystal,” Curr. Appl. Phys.13, 785–788 (2013).
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Figures (2)

Fig. 1
Fig. 1

Conventional PR solitons fail to form. (a) Low frequency normalized dielectric constant εr versus T manifesting thermal hysteresis for the KNTN sample. Dark-green regions indicate the paraelectric (PE) and ferroelectric (FE) ergodic (i.e., where no glassy phenomena emerge) phases, the light-green region indicates the crossing region where glassy physics emerges. (b) Steady-state screening solitons in annealed KNTN and insets reporting transverse intensity distributions of the beam at input (z = 0) and at the output (z = Lz) of the sample at different times. (c) Beam evolution in the same conditions of (b) in quenched KNTN, leading to modulation instability (M.I.) and a large variability in the trajectories (shaded region indicates the values observed in 10 successive experiments). (d) Quasi-steady-state solitons in the annealed case compared to the phenomena observed in the (e) quenched case. The slight systematic asymmetry along x in the annealed and quenched cases is caused by nonlocal terms in the response [29].

Fig. 2
Fig. 2

Solitons that age. (a) Output FWHM indicates a stable soliton following supercooling. (b) E0(t) required to follow the soliton as the susceptibility ages and equivalent εr(t). The shaded region indicates the transient hump in response. (c) Self-similar waveforms during the aging. (Center) Annealed existence curve (blue squares) and equivalent existence conditions for the aging KNTN in the quenched case (green asterix points) at different instants of time, in the conditions of stabilized soliton. Insets, top-left, input (red) and output (blue) beam profiles in the linear case (at t = 0); top-right, output profile for a SS soliton in the annealed case in A; right, profiles of the output at t1, t2, t3.

Equations (2)

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z A ( x , z ) ( i / 2 k ) x x A ( x , z ) = ( i k / n 0 ) Δ n ( I , t ) A ( x , z )
d 2 u ( ξ ) / d ξ 2 = [ ( 1 + u 0 2 ) 1 1 ( 1 + u ( ξ ) 2 ) 2 ] u ( ξ ) ,

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