Soliton percolation in random optical lattices
Optics Express, Vol. 15, Issue 19, pp. 12409-12417 (2007)
http://dx.doi.org/10.1364/OE.15.012409
Acrobat PDF (1028 KB)
Abstract
We introduce soliton percolation phenomena in the nonlinear transport of light packets in suitable optical lattices with random properties. Specifically, we address lattices with a gradient of the refractive index in the transverse plane, featuring stochastic phase or amplitude fluctuations, and we discover the existence of a disorder-induced transition between soliton-insulator and soliton-conductor regimes. The soliton current is found to reach its maximal value at intermediate disorder levels and to drastically decrease in both, almost regular and strongly disordered lattices.
© 2007 Optical Society of America
15. Y. S. Kivshar, S. A. Gredeskul, A. Sanchez, and L. Vazquez, “Localization decay induced by strong nonlinearity in disordered systems,” Phys. Rev. Lett. 64, 1693 (1990). [CrossRef] [PubMed]
16. V. A. Hopkins, J. Keat, G. D. Meegan, T. M. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996). [CrossRef] [PubMed]
17. V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous discrete nonlinear Schrödinger system,” Phys. Rev. E 53, 6476 (1996). [CrossRef]
19. T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004). [CrossRef] [PubMed]
20. R. Knapp, “Transmission of solitons through random-media,” Physica D 85, 496 (1995). [CrossRef]
23. J. Garnier, “Propagation of solitons in a randomly perturbed Ablowitz-Ladik chain,” Phys. Rev. E 62, 026608 (2001). [CrossRef]
27. Y. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555 (1999). [CrossRef]
28. A. P. Vinogradov and A. M. Merzlikin, “Band theory of light localization in one-dimensional disordered systems,” Phys. Rev. E 70, 026610 (2004). [CrossRef]
29. Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E 72, 026606 (2005). [CrossRef]
30. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007). [CrossRef]
31. A. A. Sukhorukov, “Enhanced soliton transport in quasiperiodic lattices with introduced aperiodicity,” Phys. Rev. Lett. 96, 113902 (2006). [CrossRef] [PubMed]
35. D. Clement, A. F. Varon, J. A. Retter, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle,” New J. Phys. 8, 165 (2006). [CrossRef]
38. S. Das Sarma, M. P. Lilly, E. H. Hwang, L. N. Pfeiffer, K. W. West, and J. L. Reno, “Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system,” Phys. Rev. Lett. 94, 136401 (2005). [CrossRef] [PubMed]
39. Y. J. Yun, I. C. Baek, and M. Y. Choi, “Phase transition and critical dynamics in site-diluted Josephson-junction arrays,” Phys. Rev. Lett. 97, 215701 (2006). [CrossRef] [PubMed]
40. G. Allison, E. A. Galaktionov, A. K. Savchenko, S. S. Safonov, M. M. Fogler, M. Y. Simmons, and D. A. Ritchie, “Thermodynamic density of states of two-dimensional GaAs systems near the apparent metal-insulator transition,” Phys. Rev. Lett. 96, 216407 (2006). [CrossRef] [PubMed]
41. V. I. Kozub, A. A. Zyuzin, Y. M. Galperin, and V. Vinokur, “Charge transfer between a superconductor and a hopping insulator,” Phys. Rev. Lett. 96, 107004 (2006). [CrossRef] [PubMed]
30. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007). [CrossRef]
43. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Oscillations of two-dimensional solitons in harmonic and Bessel optical lattices,” Phys. Rev. E 71, 036621 (2005). [CrossRef]
46. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton control in chirped photonic lattices,” J. Opt. Soc. Am. B 22, 1356 (2005). [CrossRef]
5. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999). [CrossRef]
7. H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Brauer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006). [CrossRef] [PubMed]
44. A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Transition radiation by matter-wave solitons in optical lattices,” Phys. Rev. Lett. 91, 260402 (2003). [CrossRef]
45. Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, “Spatial soliton switching in quasi-continuous optical arrays,” Opt. Lett. 29, 766 (2004). [CrossRef] [PubMed]
30. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007). [CrossRef]
Acknowledgments
References and links
1. | E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed] |
2. | S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987). [CrossRef] [PubMed] |
3. | E. Yablonovitch, “Photonic crystals: Semiconductors of light,” Scientific American 285, 47 (2001). [CrossRef] |
4. | J. D. Joannopoulos, “Photonic-bandgap microcavities in optical waveguides,” Nature 386, 143 (1997). [CrossRef] |
5. | T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83, 4752 (1999). [CrossRef] |
6. | H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903 (2006). [CrossRef] [PubMed] |
7. | H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Brauer, and U. Peschel, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006). [CrossRef] [PubMed] |
8. | R. Scharf and A. R. Bishop, “Properties of the nonlinear Schrödinger equation on a lattice,” Phys. Rev. A 43, 6535 (1991). [CrossRef] [PubMed] |
9. | V. V. Konotop, O. A. Chubykalo, and L. Vazquez, “Dynamics and interaction of solitons on an integrable inhomogeneous lattice,” Phys. Rev. E 48, 563 (1993). [CrossRef] |
10. | J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90, 023902 (2003). [CrossRef] [PubMed] |
11. | J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature 422, 147 (2003). [CrossRef] [PubMed] |
12. | D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, “Spatial solitons in optically induced gratings,” Opt. Lett. 28, 710 (2003). [CrossRef] [PubMed] |
13. | H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, “Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices” Phys. Rev. Lett. 92, 123902 (2004). [CrossRef] [PubMed] |
14. | Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express 12, 2831 (2004). [CrossRef] [PubMed] |
15. | Y. S. Kivshar, S. A. Gredeskul, A. Sanchez, and L. Vazquez, “Localization decay induced by strong nonlinearity in disordered systems,” Phys. Rev. Lett. 64, 1693 (1990). [CrossRef] [PubMed] |
16. | V. A. Hopkins, J. Keat, G. D. Meegan, T. M. Zhang, and J. D. Maynard, “Observation of the predicted behavior of nonlinear pulse propagation in disordered media,” Phys. Rev. Lett. 76, 1102 (1996). [CrossRef] [PubMed] |
17. | V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous discrete nonlinear Schrödinger system,” Phys. Rev. E 53, 6476 (1996). [CrossRef] |
18. | P G. Kevrekidis, Y. S. Kivshar, and A. S. Kovalev, “Instabilities and bifurcations of nonlinear impurity modes,” Phys. Rev. E 67, 046604 (2003). [CrossRef] |
19. | T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, “Nonlinearity and disorder in fiber arrays,” Phys. Rev. Lett. 93, 053901 (2004). [CrossRef] [PubMed] |
20. | R. Knapp, “Transmission of solitons through random-media,” Physica D 85, 496 (1995). [CrossRef] |
21. | P. L. Christiansen, Y. B. Gaididei, M. Johansson, K. O. Rasmussen, D. Usero, and L. Vazquez, “Stabilization of nonlinear excitations by disorder,” Phys. Rev. B 56, 14407 (1997). [CrossRef] |
22. | Y. B. Gaididei, D. Hendriksen, P. L. Christiansen, and K. O. Rasmussen, “Stationary states of the two-dimensional nonlinear Schrodinger model with disorder,” Phys. Rev. B 58, 3075 (1998). [CrossRef] |
23. | J. Garnier, “Propagation of solitons in a randomly perturbed Ablowitz-Ladik chain,” Phys. Rev. E 62, 026608 (2001). [CrossRef] |
24. | Fluctuation Phenomena: Disorder and Nonlinearity, Ed. by A. R. Bishop, S. Jimenez, and L. Vazquez (World Scientific, Singapore, 1995). |
25. | Nonlinearity with Disorder, Ed. by F. Kh. Abdullaev, A. R. Bishop, S. Pnevmatikos, and E. N. Economou (Springer, Berlin, 1992). [CrossRef] |
26. | F. Abdullaev, Theory of Solitons in Inhomogeneous Media (Wiley, New York, 1994). |
27. | Y. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555 (1999). [CrossRef] |
28. | A. P. Vinogradov and A. M. Merzlikin, “Band theory of light localization in one-dimensional disordered systems,” Phys. Rev. E 70, 026610 (2004). [CrossRef] |
29. | Y. V. Kartashov and V. A. Vysloukh, “Anderson localization of solitons in optical lattices with random frequency modulation,” Phys. Rev. E 72, 026606 (2005). [CrossRef] |
30. | T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature (London) 446, 52 (2007). [CrossRef] |
31. | A. A. Sukhorukov, “Enhanced soliton transport in quasiperiodic lattices with introduced aperiodicity,” Phys. Rev. Lett. 96, 113902 (2006). [CrossRef] [PubMed] |
32. | R. C. Kuhn, C. Miniatura, D. Delande, O. Sigwarth, and C. A. Muller, “Localization of matter waves in twodimensional disordered optical potentials,” Phys. Rev. Lett. 95, 250403 (2005). [CrossRef] [PubMed] |
33. | T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, “Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices,” Phys. Rev. Lett. 95, 170411 (2005). [CrossRef] [PubMed] |
34. | U. Gavish and Y. Castin, “Matter-wave localization in disordered cold atom lattices,” Phys. Rev. Lett. 95, 020401 (2005). [CrossRef] [PubMed] |
35. | D. Clement, A. F. Varon, J. A. Retter, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, “Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle,” New J. Phys. 8, 165 (2006). [CrossRef] |
36. | G. R. Grimmett, Percolation (Springer, Berlin, 1999). |
37. | B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors, Springer Series in Solid-State Sciences (Springer, Berlin, 1984). |
38. | S. Das Sarma, M. P. Lilly, E. H. Hwang, L. N. Pfeiffer, K. W. West, and J. L. Reno, “Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system,” Phys. Rev. Lett. 94, 136401 (2005). [CrossRef] [PubMed] |
39. | Y. J. Yun, I. C. Baek, and M. Y. Choi, “Phase transition and critical dynamics in site-diluted Josephson-junction arrays,” Phys. Rev. Lett. 97, 215701 (2006). [CrossRef] [PubMed] |
40. | G. Allison, E. A. Galaktionov, A. K. Savchenko, S. S. Safonov, M. M. Fogler, M. Y. Simmons, and D. A. Ritchie, “Thermodynamic density of states of two-dimensional GaAs systems near the apparent metal-insulator transition,” Phys. Rev. Lett. 96, 216407 (2006). [CrossRef] [PubMed] |
41. | V. I. Kozub, A. A. Zyuzin, Y. M. Galperin, and V. Vinokur, “Charge transfer between a superconductor and a hopping insulator,” Phys. Rev. Lett. 96, 107004 (2006). [CrossRef] [PubMed] |
42. | Y. S. Kivshar and D. K. Campbell, “Peierls-Nabarro potential barrier for highly localized nonlinear modes,” Phys. Rev. E 48, 3077 (1993). [CrossRef] |
43. | Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Oscillations of two-dimensional solitons in harmonic and Bessel optical lattices,” Phys. Rev. E 71, 036621 (2005). [CrossRef] |
44. | A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Transition radiation by matter-wave solitons in optical lattices,” Phys. Rev. Lett. 91, 260402 (2003). [CrossRef] |
45. | Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, “Spatial soliton switching in quasi-continuous optical arrays,” Opt. Lett. 29, 766 (2004). [CrossRef] [PubMed] |
46. | Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton control in chirped photonic lattices,” J. Opt. Soc. Am. B 22, 1356 (2005). [CrossRef] |
OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.6135) Nonlinear optics : Spatial solitons
ToC Category:
Nonlinear Optics
History
Original Manuscript: June 26, 2007
Revised Manuscript: September 10, 2007
Manuscript Accepted: September 11, 2007
Published: September 14, 2007
Citation
Yaroslav V. Kartashov, Victor A. Vysloukh, and Lluis Torner, "Soliton percolation in random optical lattices," Opt. Express 15, 12409-12417 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-19-12409
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References
- E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059 (1987). [CrossRef] [PubMed]
- S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486 (1987). [CrossRef] [PubMed]
- E. Yablonovitch, "Photonic crystals: Semiconductors of light," Scientific American 285, 47 (2001). [CrossRef]
- J. D. Joannopoulos, "Photonic-bandgap microcavities in optical waveguides," Nature 386, 143 (1997). [CrossRef]
- T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752 (1999). [CrossRef]
- H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," Phys. Rev. Lett. 96, 053903 (2006). [CrossRef] [PubMed]
- H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Brauer, and U. Peschel, "Visual observation of Zener tunneling," Phys. Rev. Lett. 96, 023901 (2006). [CrossRef] [PubMed]
- R. Scharf and A. R. Bishop, "Properties of the nonlinear Schrödinger equation on a lattice," Phys. Rev. A 43, 6535 (1991). [CrossRef] [PubMed]
- V. V. Konotop, O. A. Chubykalo, and L. Vazquez, "Dynamics and interaction of solitons on an integrable inhomogeneous lattice," Phys. Rev. E 48, 563 (1993). [CrossRef]
- J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003). [CrossRef] [PubMed]
- J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003). [CrossRef] [PubMed]
- D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003). [CrossRef] [PubMed]
- H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced disloca-tions in partially coherent photonic lattices" Phys. Rev. Lett. 92, 123902 (2004). [CrossRef] [PubMed]
- Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton trains in photonic lattices," Opt. Express 12, 2831 (2004). [CrossRef] [PubMed]
- Y. S. Kivshar, S. A. Gredeskul, A. Sanchez, and L. Vazquez, "Localization decay induced by strong nonlinearity in disordered systems," Phys. Rev. Lett. 64, 1693 (1990). [CrossRef] [PubMed]
- V. A. Hopkins, J. Keat, G. D. Meegan, T. M. Zhang, and J. D. Maynard, "Observation of the predicted behavior of nonlinear pulse propagation in disordered media," Phys. Rev. Lett. 76, 1102 (1996). [CrossRef] [PubMed]
- V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. Grønbech-Jensen, "Interaction of a soliton with point impurities in an inhomogeneous discrete nonlinear Schrödinger system," Phys. Rev. E 53, 6476 (1996). [CrossRef]
- P G. Kevrekidis, Y. S. Kivshar, and A. S. Kovalev, "Instabilities and bifurcations of nonlinear impurity modes," Phys. Rev. E 67, 046604 (2003). [CrossRef]
- T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, "Nonlinea-rity and disorder in fiber arrays," Phys. Rev. Lett. 93, 053901 (2004). [CrossRef] [PubMed]
- R. Knapp, "Transmission of solitons through random-media," Physica D 85, 496 (1995). [CrossRef]
- P. L. Christiansen, Y. B. Gaididei, M. Johansson, K. O. Rasmussen, D. Usero, and L. Vazquez, "Stabilization of nonlinear excitations by disorder," Phys. Rev. B 56, 14407 (1997). [CrossRef]
- Y. B. Gaididei, D. Hendriksen, P. L. Christiansen, and K. O. Rasmussen, "Stationary states of the two-dimensio-nal nonlinear Schrodinger model with disorder," Phys. Rev. B 58, 3075 (1998). [CrossRef]
- J. Garnier, "Propagation of solitons in a randomly perturbed Ablowitz-Ladik chain," Phys. Rev. E 62, 026608 (2001). [CrossRef]
- Fluctuation Phenomena: Disorder and Nonlinearity, Ed. by A. R. Bishop, S. Jimenez, and L. Vazquez (World Scientific, Singapore, 1995).
- Nonlinearity with Disorder, Ed. by F. Kh. Abdullaev, A. R. Bishop, S. Pnevmatikos, and E. N. Economou (Springer, Berlin, 1992). [CrossRef]
- F. Abdullaev, Theory of Solitons in Inhomogeneous Media (Wiley, New York, 1994).
- Y. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, "Different regimes of light localization in a disordered photonic crystal," Phys. Rev. B 60, 1555 (1999). [CrossRef]
- A. P. Vinogradov and A. M. Merzlikin, "Band theory of light localization in one-dimensional disordered systems," Phys. Rev. E 70, 026610 (2004). [CrossRef]
- Y. V. Kartashov and V. A. Vysloukh, "Anderson localization of solitons in optical lattices with random frequency modulation," Phys. Rev. E 72, 026606 (2005). [CrossRef]
- T. Schwartz, G. Bartal, S. Fishman and M. Segev, "Transport and Anderson localization in disordered two-dimensional photonic lattices," Nature (London) 446, 52 (2007). [CrossRef]
- A. A. Sukhorukov, "Enhanced soliton transport in quasiperiodic lattices with introduced aperiodicity," Phys. Rev. Lett. 96, 113902 (2006). [CrossRef] [PubMed]
- R. C. Kuhn, C. Miniatura, D. Delande, O. Sigwarth, and C. A. Muller, "Localization of matter waves in two-dimensional disordered optical potentials," Phys. Rev. Lett. 95, 250403 (2005). [CrossRef] [PubMed]
- T. Schulte, S. Drenkelforth, J. Kruse, W. Ertmer, J. Arlt, K. Sacha, J. Zakrzewski, and M. Lewenstein, "Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices," Phys. Rev. Lett. 95, 170411 (2005). [CrossRef] [PubMed]
- U. Gavish and Y. Castin, "Matter-wave localization in disordered cold atom lattices," Phys. Rev. Lett. 95, 020401 (2005). [CrossRef] [PubMed]
- D. Clement, A. F. Varon, J. A. Retter, L. Sanchez-Palencia, A. Aspect, and P. Bouyer, "Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle," New J. Phys. 8, 165 (2006). [CrossRef]
- G. R. Grimmett, Percolation (Springer, Berlin, 1999).
- B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors, Springer Series in Solid-State Sciences (Springer, Berlin, 1984).
- S. Das Sarma, M. P. Lilly, E. H. Hwang, L. N. Pfeiffer, K. W. West, and J. L. Reno, "Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system," Phys. Rev. Lett. 94, 136401 (2005). [CrossRef] [PubMed]
- Y. J. Yun, I. C. Baek, and M. Y. Choi, "Phase transition and critical dynamics in site-diluted Josephson-junction arrays," Phys. Rev. Lett. 97, 215701 (2006). [CrossRef] [PubMed]
- G. Allison, E. A. Galaktionov, A. K. Savchenko, S. S. Safonov, M. M. Fogler, M. Y. Simmons, and D. A. Ritchie, "Thermodynamic density of states of two-dimensional GaAs systems near the apparent metal-insulator transition," Phys. Rev. Lett. 96, 216407 (2006). [CrossRef] [PubMed]
- V. I. Kozub, A. A. Zyuzin, Y. M. Galperin, and V. Vinokur, "Charge transfer between a superconductor and a hopping insulator," Phys. Rev. Lett. 96, 107004 (2006). [CrossRef] [PubMed]
- Y. S. Kivshar and D. K. Campbell, "Peierls-Nabarro potential barrier for highly localized nonlinear modes," Phys. Rev. E 48, 3077 (1993). [CrossRef]
- Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Oscillations of two-dimensional solitons in harmonic and Bessel optical lattices," Phys. Rev. E 71, 036621 (2005). [CrossRef]
- A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, "Transition radiation by matter-wave solitons in optical lattices," Phys. Rev. Lett. 91, 260402 (2003). [CrossRef]
- Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, "Spatial soliton switching in quasi-continuous optical arrays," Opt. Lett. 29, 766 (2004). [CrossRef] [PubMed]
- Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton control in chirped photonic lattices," J. Opt. Soc. Am. B 22, 1356 (2005). [CrossRef]
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