Abstract
Here, we deal with the nonlinear Schroedinger equation in the presence of structural disorder. The strength of disorder allows the formation of light localizations, the Anderson states. The effect of focusing and defocusing nonlinearities, present in the model equation, on Anderson localization in highly nonlocal media is theoretically and numerically investigated. A perturbative approach is developed to solve the nonlocal nonlinear Schroedinger equation in the presence of a random potential. We find closed form expressions showing that nonlocality stabilizes Anderson states. Numerical analysis validates the theoretical results. A regime in which multiple Anderson localizations are excited and compete by nonlocality is also outlined.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anderson PW (1958) Phys Rev 109:1492
Bang O, Krolikowski W, Wyller J, Rasmussen JJ (2002) Phys Rev E 66:046619
Rasmussen P, Bang O, Królikowski W (2005) Phys Rev E 72:066611
Maucher F, Krolikowski W, Skupin S (2010) ArXiv e-prints, pp 1008–1891
Conti C, Peccianti M, Assanto G (2003) Phys Rev Lett 91:073901
Snyder AW, Mitchell DJ (1997) Science 276:1538
Sheng P (ed) (1990) Scattering and localization of classical waves in random media. World Scientific, Singapore
Soukoulis CM (ed) (2001) Photonic crystals and light localization in the 21st century. Kluwer, Dordrecth
Wiersma DS, Bartolini P, Lagendijk A, Righini R (1997) Nature 390:671
John S (1987) Phys Rev Lett 58:2486
Conti C, Fratalocchi A (2008) Nat Phys 4:794
Shadrivov IV, Bliokh KY, Bliokh YP, Freilikher V, Kivshar YS (2010) Phys Rev Lett 104:123902
Kartashov YV, Vysloukh VA (2005) Phys Rev E 72:026606
Schwartz T, Bartal G, Fishman S, Segev M (2007) Nature 446:52
Billy J et al (2008) Nature 453:891
Roati G (2008) Nature 453:895
Modugno G (2010) Rep Prog Phys 73:102401
Folli V, Conti C (2010) Phys Rev Lett 104:193901
Batz S, Peschel U (2011) Phys Rev A 83:033826
Conti C, Schmidt M, Russell P, Biancalana F (2010) Arxiv preprint arXiv:1010.0331
Conti C, D’Asaro E, Stivala S, Busacca A, Assanto G (2010) Opt Lett 35:3760
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Folli, V. (2012). Disordered Nonlinear Schroedinger Equation. In: Nonlinear Optics and Laser Emission through Random Media. Springer Theses. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4513-1_4
Download citation
DOI: https://doi.org/10.1007/978-94-007-4513-1_4
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-4512-4
Online ISBN: 978-94-007-4513-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)