Abstract

Propagation of ultrashort light pulses in disordered multilayers is studied by using numerical simulations in the time domain. We consider cases of instantaneous and noninstantaneous Kerr nonlinearities of the structure materials. The competitive nature of disorder and nonlinearity is revealed on the long and short time scales. We also pay special attention to the effect of pulse self-trapping in the photonic crystal with relaxing nonlinearity and show the dependence of this effect on the level of disorder. We believe that the results reported here will be useful not only in the field of optics but also from the standpoint of the general problem of classical wave propagation in nonlinear disordered periodic media.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
    [CrossRef]
  2. M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
    [CrossRef]
  3. E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
    [CrossRef]
  4. T. V. Laptyeva, J. T. Bodyfelt, and S. Flach, “Subdiffusion of nonlinear waves in two-dimensional disordered lattices,” Europhys. Lett. 98, 60002 (2012).
    [CrossRef]
  5. M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108, 110604 (2012).
    [CrossRef]
  6. Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Super-diffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
    [CrossRef]
  7. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef]
  8. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
    [CrossRef]
  9. E. Reyes-Gomes, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices,” Phys. Rev. B 85, 195110 (2012).
    [CrossRef]
  10. M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
    [CrossRef]
  11. S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
    [CrossRef]
  12. D. M. Jović, Yu. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
    [CrossRef]
  13. I. V. Shadrivov, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and Yu. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
    [CrossRef]
  14. S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
    [CrossRef]
  15. S. E. Skipetrov, “Instability of speckle patterns in random media with noninstantaneous Kerr nonlinearity,” Opt. Lett. 28, 646–648 (2003).
    [CrossRef]
  16. B. Liu, A. Yamilov, Y. Ling, J. Y. Xu, and H. Cao, “Dynamic nonlinear effect on lasing in a random medium,” Phys. Rev. Lett. 91, 063903 (2003).
    [CrossRef]
  17. C. Conti, L. Angelani, and G. Ruocco, “Light diffusion and localization in three-dimensional nonlinear disordered media,” Phys. Rev. A 75, 033812 (2007).
    [CrossRef]
  18. A. S. Pikovsky and D. L. Shepelyansky, “Destruction of Anderson localization by a weak nonlinearity,” Phys. Rev. Lett. 100, 094101 (2008).
    [CrossRef]
  19. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
    [CrossRef]
  20. S. Flach, D. O. Krimer, and C. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
    [CrossRef]
  21. G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
    [CrossRef]
  22. A. Radosavljević, G. Gligorić, A. Maluckov, M. Stepić, and D. Milović, “Light propagation management by disorder and nonlinearity in one-dimensional photonic lattices,” J. Opt. Soc. Am. B 30, 2340–2347 (2013).
    [CrossRef]
  23. C. Conti, “Solitonization of the Anderson localization,” Phys. Rev. A 86, 061801 (2012).
    [CrossRef]
  24. V. Folli and C. Conti, “Self-induced transparency and the Anderson localization of light,” Opt. Lett. 36, 2830–2832 (2011).
    [CrossRef]
  25. V. Folli and C. Conti, “Anderson localization in nonlocal nonlinear media,” Opt. Lett. 37, 332–334 (2012).
    [CrossRef]
  26. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
    [CrossRef]
  27. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1994).
  28. Yu. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).
    [CrossRef]
  29. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).
  30. D. V. Novitsky, “Pulse trapping inside a one-dimensional photonic crystal with relaxing cubic nonlinearity,” Phys. Rev. A 81, 053814 (2010).
    [CrossRef]
  31. M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
    [CrossRef]
  32. D. V. Novitsky, “Spectral transformations in the regime of pulse self-trapping in a nonlinear photonic crystal,” Phys. Rev. A 84, 053857 (2011).
    [CrossRef]
  33. D. V. Novitsky, “Search for the optimal parameters of relaxing nonlinearity to obtain self-trapping of an ultrashort pulse in a photonic crystal,” J. Nonlinear Opt. Phys. Mater. 21, 1250010 (2012).
  34. D. V. Novitsky, “Asymmetric light transmission through a photonic crystal with relaxing Kerr nonlinearity,” Europhys. Lett. 99, 44001 (2012).
    [CrossRef]
  35. D. V. Novitsky, “Effects of pulse collisions in a multilayer system with noninstantaneous cubic nonlinearity,” J. Opt. 15, 035206 (2013).
    [CrossRef]
  36. S. E. Skipetrov and R. Maynard, “Diffuse waves in nonlinear disordered media,” in Wave Scattering in Complex Media: From Theory to Applications (Springer, 2003).

2013 (2)

2012 (9)

V. Folli and C. Conti, “Anderson localization in nonlocal nonlinear media,” Opt. Lett. 37, 332–334 (2012).
[CrossRef]

C. Conti, “Solitonization of the Anderson localization,” Phys. Rev. A 86, 061801 (2012).
[CrossRef]

D. V. Novitsky, “Search for the optimal parameters of relaxing nonlinearity to obtain self-trapping of an ultrashort pulse in a photonic crystal,” J. Nonlinear Opt. Phys. Mater. 21, 1250010 (2012).

D. V. Novitsky, “Asymmetric light transmission through a photonic crystal with relaxing Kerr nonlinearity,” Europhys. Lett. 99, 44001 (2012).
[CrossRef]

T. V. Laptyeva, J. T. Bodyfelt, and S. Flach, “Subdiffusion of nonlinear waves in two-dimensional disordered lattices,” Europhys. Lett. 98, 60002 (2012).
[CrossRef]

M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108, 110604 (2012).
[CrossRef]

Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Super-diffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
[CrossRef]

S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
[CrossRef]

E. Reyes-Gomes, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices,” Phys. Rev. B 85, 195110 (2012).
[CrossRef]

2011 (3)

D. M. Jović, Yu. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

D. V. Novitsky, “Spectral transformations in the regime of pulse self-trapping in a nonlinear photonic crystal,” Phys. Rev. A 84, 053857 (2011).
[CrossRef]

V. Folli and C. Conti, “Self-induced transparency and the Anderson localization of light,” Opt. Lett. 36, 2830–2832 (2011).
[CrossRef]

2010 (2)

D. V. Novitsky, “Pulse trapping inside a one-dimensional photonic crystal with relaxing cubic nonlinearity,” Phys. Rev. A 81, 053814 (2010).
[CrossRef]

I. V. Shadrivov, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and Yu. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef]

2009 (2)

M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef]

S. Flach, D. O. Krimer, and C. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
[CrossRef]

2008 (3)

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef]

A. S. Pikovsky and D. L. Shepelyansky, “Destruction of Anderson localization by a weak nonlinearity,” Phys. Rev. Lett. 100, 094101 (2008).
[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

2007 (2)

C. Conti, L. Angelani, and G. Ruocco, “Light diffusion and localization in three-dimensional nonlinear disordered media,” Phys. Rev. A 75, 033812 (2007).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[CrossRef]

2006 (2)

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef]

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

2003 (2)

S. E. Skipetrov, “Instability of speckle patterns in random media with noninstantaneous Kerr nonlinearity,” Opt. Lett. 28, 646–648 (2003).
[CrossRef]

B. Liu, A. Yamilov, Y. Ling, J. Y. Xu, and H. Cao, “Dynamic nonlinear effect on lasing in a random medium,” Phys. Rev. Lett. 91, 063903 (2003).
[CrossRef]

2000 (1)

S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
[CrossRef]

1999 (1)

Yu. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).
[CrossRef]

1997 (1)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[CrossRef]

1987 (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

1986 (1)

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

1977 (1)

Aegerter, C. M.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).

Akkermans, E.

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

Angelani, L.

C. Conti, L. Angelani, and G. Ruocco, “Light diffusion and localization in three-dimensional nonlinear disordered media,” Phys. Rev. A 75, 033812 (2007).
[CrossRef]

Asatryan, A. A.

S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
[CrossRef]

Aubry, S.

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef]

Avidan, A.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[CrossRef]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[CrossRef]

Belic, M. R.

D. M. Jović, Yu. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Bertolotti, J.

M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108, 110604 (2012).
[CrossRef]

Bliokh, K. Y.

S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
[CrossRef]

I. V. Shadrivov, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and Yu. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef]

Bliokh, Yu. P.

S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
[CrossRef]

I. V. Shadrivov, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and Yu. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef]

Bodyfelt, J. T.

T. V. Laptyeva, J. T. Bodyfelt, and S. Flach, “Subdiffusion of nonlinear waves in two-dimensional disordered lattices,” Europhys. Lett. 98, 60002 (2012).
[CrossRef]

Bruno-Alfonso, A.

E. Reyes-Gomes, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices,” Phys. Rev. B 85, 195110 (2012).
[CrossRef]

Burresi, M.

M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108, 110604 (2012).
[CrossRef]

Cao, H.

B. Liu, A. Yamilov, Y. Ling, J. Y. Xu, and H. Cao, “Dynamic nonlinear effect on lasing in a random medium,” Phys. Rev. Lett. 91, 063903 (2003).
[CrossRef]

Cavalcanti, S. B.

E. Reyes-Gomes, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices,” Phys. Rev. B 85, 195110 (2012).
[CrossRef]

Centurion, M.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).

Christodoulides, D. N.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Combrie, S.

M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef]

Conti, C.

V. Folli and C. Conti, “Anderson localization in nonlocal nonlinear media,” Opt. Lett. 37, 332–334 (2012).
[CrossRef]

C. Conti, “Solitonization of the Anderson localization,” Phys. Rev. A 86, 061801 (2012).
[CrossRef]

V. Folli and C. Conti, “Self-induced transparency and the Anderson localization of light,” Opt. Lett. 36, 2830–2832 (2011).
[CrossRef]

C. Conti, L. Angelani, and G. Ruocco, “Light diffusion and localization in three-dimensional nonlinear disordered media,” Phys. Rev. A 75, 033812 (2007).
[CrossRef]

De Rossi, A.

M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef]

Denz, C.

D. M. Jović, Yu. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Fishman, S.

Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Super-diffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[CrossRef]

Flach, S.

T. V. Laptyeva, J. T. Bodyfelt, and S. Flach, “Subdiffusion of nonlinear waves in two-dimensional disordered lattices,” Europhys. Lett. 98, 60002 (2012).
[CrossRef]

S. Flach, D. O. Krimer, and C. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
[CrossRef]

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef]

Folli, V.

Freilikher, V. D.

S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
[CrossRef]

I. V. Shadrivov, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and Yu. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef]

Gabet, R.

M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef]

Gligoric, G.

Gredeskul, S. A.

S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
[CrossRef]

Gross, P.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef]

Hong, C.-S.

Hughes, S.

M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef]

Jaouën, Y.

M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Jovic, D. M.

D. M. Jović, Yu. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Kaliteevski, M. A.

Yu. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).
[CrossRef]

Kevrekidis, P. G.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

Kivshar, Yu. S.

S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
[CrossRef]

D. M. Jović, Yu. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

I. V. Shadrivov, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and Yu. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef]

Komineas, S.

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef]

Kopidakis, G.

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef]

Krimer, D. O.

S. Flach, D. O. Krimer, and C. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
[CrossRef]

Krivolapov, Y.

Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Super-diffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
[CrossRef]

Lagendijk, A.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[CrossRef]

Lahini, Y.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Laptyeva, T. V.

T. V. Laptyeva, J. T. Bodyfelt, and S. Flach, “Subdiffusion of nonlinear waves in two-dimensional disordered lattices,” Europhys. Lett. 98, 60002 (2012).
[CrossRef]

Levi, L.

Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Super-diffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
[CrossRef]

Ling, Y.

B. Liu, A. Yamilov, Y. Ling, J. Y. Xu, and H. Cao, “Dynamic nonlinear effect on lasing in a random medium,” Phys. Rev. Lett. 91, 063903 (2003).
[CrossRef]

Liu, B.

B. Liu, A. Yamilov, Y. Ling, J. Y. Xu, and H. Cao, “Dynamic nonlinear effect on lasing in a random medium,” Phys. Rev. Lett. 91, 063903 (2003).
[CrossRef]

Maluckov, A.

Maret, G.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef]

Maynard, R.

S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
[CrossRef]

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

S. E. Skipetrov and R. Maynard, “Diffuse waves in nonlinear disordered media,” in Wave Scattering in Complex Media: From Theory to Applications (Springer, 2003).

Milovic, D.

Morandotti, R.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Nikolaev, V. V.

Yu. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).
[CrossRef]

Novitsky, D. V.

D. V. Novitsky, “Effects of pulse collisions in a multilayer system with noninstantaneous cubic nonlinearity,” J. Opt. 15, 035206 (2013).
[CrossRef]

D. V. Novitsky, “Search for the optimal parameters of relaxing nonlinearity to obtain self-trapping of an ultrashort pulse in a photonic crystal,” J. Nonlinear Opt. Phys. Mater. 21, 1250010 (2012).

D. V. Novitsky, “Asymmetric light transmission through a photonic crystal with relaxing Kerr nonlinearity,” Europhys. Lett. 99, 44001 (2012).
[CrossRef]

D. V. Novitsky, “Spectral transformations in the regime of pulse self-trapping in a nonlinear photonic crystal,” Phys. Rev. A 84, 053857 (2011).
[CrossRef]

D. V. Novitsky, “Pulse trapping inside a one-dimensional photonic crystal with relaxing cubic nonlinearity,” Phys. Rev. A 81, 053814 (2010).
[CrossRef]

Oliveira, L. E.

E. Reyes-Gomes, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices,” Phys. Rev. B 85, 195110 (2012).
[CrossRef]

Patterson, M.

M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef]

Pikovsky, A. S.

A. S. Pikovsky and D. L. Shepelyansky, “Destruction of Anderson localization by a weak nonlinearity,” Phys. Rev. Lett. 100, 094101 (2008).
[CrossRef]

Porter, M. A.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

Pozzi, F.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Psaltis, D.

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

Quynh Tran, N.-V.

M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef]

Radhalakshmi, V.

M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108, 110604 (2012).
[CrossRef]

Radosavljevic, A.

Reyes-Gomes, E.

E. Reyes-Gomes, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices,” Phys. Rev. B 85, 195110 (2012).
[CrossRef]

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[CrossRef]

Ruocco, G.

C. Conti, L. Angelani, and G. Ruocco, “Light diffusion and localization in three-dimensional nonlinear disordered media,” Phys. Rev. A 75, 033812 (2007).
[CrossRef]

Savo, R.

M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108, 110604 (2012).
[CrossRef]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[CrossRef]

Segev, M.

Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Super-diffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[CrossRef]

Shadrivov, I. V.

S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
[CrossRef]

I. V. Shadrivov, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and Yu. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef]

Shepelyansky, D. L.

A. S. Pikovsky and D. L. Shepelyansky, “Destruction of Anderson localization by a weak nonlinearity,” Phys. Rev. Lett. 100, 094101 (2008).
[CrossRef]

Silberberg, Y.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Skipetrov, S. E.

S. E. Skipetrov, “Instability of speckle patterns in random media with noninstantaneous Kerr nonlinearity,” Opt. Lett. 28, 646–648 (2003).
[CrossRef]

S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
[CrossRef]

S. E. Skipetrov and R. Maynard, “Diffuse waves in nonlinear disordered media,” in Wave Scattering in Complex Media: From Theory to Applications (Springer, 2003).

Skokos, C.

S. Flach, D. O. Krimer, and C. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
[CrossRef]

Sorel, M.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Stepic, M.

Störzer, M.

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef]

Vlasov, Yu. A.

Yu. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).
[CrossRef]

Vynck, K.

M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108, 110604 (2012).
[CrossRef]

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).

Wiersma, D. S.

M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108, 110604 (2012).
[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[CrossRef]

Wilkinson, M.

Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Super-diffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
[CrossRef]

Wolf, P. E.

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

Xu, J. Y.

B. Liu, A. Yamilov, Y. Ling, J. Y. Xu, and H. Cao, “Dynamic nonlinear effect on lasing in a random medium,” Phys. Rev. Lett. 91, 063903 (2003).
[CrossRef]

Yamilov, A.

B. Liu, A. Yamilov, Y. Ling, J. Y. Xu, and H. Cao, “Dynamic nonlinear effect on lasing in a random medium,” Phys. Rev. Lett. 91, 063903 (2003).
[CrossRef]

Yariv, A.

Yeh, P.

Europhys. Lett. (2)

T. V. Laptyeva, J. T. Bodyfelt, and S. Flach, “Subdiffusion of nonlinear waves in two-dimensional disordered lattices,” Europhys. Lett. 98, 60002 (2012).
[CrossRef]

D. V. Novitsky, “Asymmetric light transmission through a photonic crystal with relaxing Kerr nonlinearity,” Europhys. Lett. 99, 44001 (2012).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

D. V. Novitsky, “Search for the optimal parameters of relaxing nonlinearity to obtain self-trapping of an ultrashort pulse in a photonic crystal,” J. Nonlinear Opt. Phys. Mater. 21, 1250010 (2012).

J. Opt. (1)

D. V. Novitsky, “Effects of pulse collisions in a multilayer system with noninstantaneous cubic nonlinearity,” J. Opt. 15, 035206 (2013).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (1)

Low Temp. Phys. (1)

S. A. Gredeskul, Yu. S. Kivshar, A. A. Asatryan, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and I. V. Shadrivov, “Anderson localization in metamaterials and other complex media,” Low Temp. Phys. 38, 570–602 (2012).
[CrossRef]

Nature (2)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[CrossRef]

New J. Phys. (1)

Y. Krivolapov, L. Levi, S. Fishman, M. Segev, and M. Wilkinson, “Super-diffusion in optical realizations of Anderson localization,” New J. Phys. 14, 043047 (2012).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (5)

C. Conti, “Solitonization of the Anderson localization,” Phys. Rev. A 86, 061801 (2012).
[CrossRef]

D. V. Novitsky, “Spectral transformations in the regime of pulse self-trapping in a nonlinear photonic crystal,” Phys. Rev. A 84, 053857 (2011).
[CrossRef]

C. Conti, L. Angelani, and G. Ruocco, “Light diffusion and localization in three-dimensional nonlinear disordered media,” Phys. Rev. A 75, 033812 (2007).
[CrossRef]

D. M. Jović, Yu. S. Kivshar, C. Denz, and M. R. Belić, “Anderson localization of light near boundaries of disordered photonic lattices,” Phys. Rev. A 83, 033813 (2011).
[CrossRef]

D. V. Novitsky, “Pulse trapping inside a one-dimensional photonic crystal with relaxing cubic nonlinearity,” Phys. Rev. A 81, 053814 (2010).
[CrossRef]

Phys. Rev. B (2)

Yu. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).
[CrossRef]

E. Reyes-Gomes, A. Bruno-Alfonso, S. B. Cavalcanti, and L. E. Oliveira, “Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices,” Phys. Rev. B 85, 195110 (2012).
[CrossRef]

Phys. Rev. Lett. (13)

M. Patterson, S. Hughes, S. Combrie, N.-V. Quynh Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

M. Störzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).
[CrossRef]

E. Akkermans, P. E. Wolf, and R. Maynard, “Coherent backscattering of light by disordered media: analysis of the peak line shape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef]

M. Burresi, V. Radhalakshmi, R. Savo, J. Bertolotti, K. Vynck, and D. S. Wiersma, “Weak localization of light in superdiffusive random systems,” Phys. Rev. Lett. 108, 110604 (2012).
[CrossRef]

M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

I. V. Shadrivov, K. Y. Bliokh, Yu. P. Bliokh, V. D. Freilikher, and Yu. S. Kivshar, “Bistability of Anderson localized states in nonlinear random media,” Phys. Rev. Lett. 104, 123902 (2010).
[CrossRef]

S. E. Skipetrov and R. Maynard, “Instabilities of waves in nonlinear disordered media,” Phys. Rev. Lett. 85, 736–739 (2000).
[CrossRef]

A. S. Pikovsky and D. L. Shepelyansky, “Destruction of Anderson localization by a weak nonlinearity,” Phys. Rev. Lett. 100, 094101 (2008).
[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

S. Flach, D. O. Krimer, and C. Skokos, “Universal spreading of wave packets in disordered nonlinear systems,” Phys. Rev. Lett. 102, 024101 (2009).
[CrossRef]

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, “Absence of wave packet diffusion in disordered nonlinear systems,” Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef]

B. Liu, A. Yamilov, Y. Ling, J. Y. Xu, and H. Cao, “Dynamic nonlinear effect on lasing in a random medium,” Phys. Rev. Lett. 91, 063903 (2003).
[CrossRef]

Other (3)

S. E. Skipetrov and R. Maynard, “Diffuse waves in nonlinear disordered media,” in Wave Scattering in Complex Media: From Theory to Applications (Springer, 2003).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1994).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (AIP, 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1.
Fig. 1.

Transmission spectra of the photonic crystal with 10 periods for different values of disorder amplitude. Curves are averaged over 20 realizations.

Fig. 2.
Fig. 2.

Dynamics of transmitted intensity logarithm for the photonic crystal with 50 periods at the disorder amplitudes (a) Δd=0.05μm and (b) Δd=0.1μm. Curves are averaged over 25 realizations.

Fig. 3.
Fig. 3.

Dynamics of transmitted intensity logarithm for the photonic crystal with 50 periods at the nonlinearity coefficients (a) n2I0=0.01 and (b) n2I0=0.05. Curves are averaged over 25 realizations.

Fig. 4.
Fig. 4.

Tail intensity deviation from the linear ordered case as a function of disorder and nonlinearity strengths. This density plot is based on the data of Figs. 2 and 3.

Fig. 5.
Fig. 5.

Profiles of transmitted pulses for the photonic crystal with 50 periods at the nonlinearity coefficients (a) n2I0=0.01 and (b) n2I0=0.05. Curves are averaged over 25 realizations.

Fig. 6.
Fig. 6.

Dynamics of transmitted intensity logarithm for the photonic crystal with 50 periods at different relaxation times. The disorder amplitudes are (a) Δd=0.02μm, (b) Δd=0.05μm, and (c) Δd=0.1μm. The nonlinearity coefficient is n2I0=0.01. Curves are averaged over 25 realizations.

Fig. 7.
Fig. 7.

Same as in Fig. 6, but the nonlinearity coefficient is n2I0=0.05.

Fig. 8.
Fig. 8.

Profiles of the pulses transmitted through the photonic crystal with 50 periods at different relaxation times. Disorder amplitudes are (a) Δd=0.02μm and (b) Δd=0.1μm. Nonlinearity coefficient is n2I0=0.01. Curves are averaged over 25 realizations.

Fig. 9.
Fig. 9.

Same as in Fig. 8, but the nonlinearity coefficient is n2I0=0.05.

Fig. 10.
Fig. 10.

(a), (c), (d) Profiles of the transmitted and reflected radiation when the disorder amplitudes are Δd=0, 0.02, and 0.1 μm, respectively. (b) Distribution of light intensity inside the structure at the time instant t=100tp in the ordered case. The photonic crystal has 200 periods (length 128 μm); the nonlinearity coefficient is n2I0=0.01; and the relaxation time is tnl=10fs. Curves in panels (c) and (d) are averaged over 25 realizations.

Fig. 11.
Fig. 11.

Dependence of the output energy (as a part of the input one) on the disorder strength. Curves are the result of averaging over 25 realizations.

Fig. 12.
Fig. 12.

Four realizations of the distribution of light intensity inside the structure at the time instant t=100tp in the case Δd=0.02μm.

Fig. 13.
Fig. 13.

Same as in Fig. 12, but the disorder strength is Δd=0.1μm.

Equations (4)

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

2Ez21c22(n2E)t2=0,
n=n°(z)+δn(I,t,z),
tnldδndt+δn=n2I,
da,b=da,b°+Δd(ξ1/2),

Metrics