Spatial solitons and Anderson localization

Abstract

Stochastic (Anderson) localization is the spatial localization of the wave-function of quantum particles in random media. We show, that a corresponding phenomenon can stabilize spatial solitons in optical resonators: spatial solitons in resonators with randomly distorted mirrors are more stable than in perfect mirror resonators. We demonstrate the phenomenon numerically, by investigating solitons in lasers with saturable absorber, and analytically by deriving and analyzing coupled equations of spatially coherent and incoherent field components.

Frustrated Brownian Motion of Nonlocal Solitary Waves

“…In recent years, widespread investigations dealt with the interplay between randomness and nonlinearity, with emphasis on Anderson localization and SW [23][24][25][26][27][28][29]. Understanding the interplay between nonlocality and randomness is hence a fundamental subject in the theory of self-trapped waves.…”

Transverse dynamics in cavity nonlinear optics (2000–2003)

“…By investigating solitons in lasers with a saturable absorber, it is shown that stochastic (Anderson) localization can stabilize dissipative spatial solitons: spatial solitons in resonators with randomly distorted mirrors are more stable than those in perfect mirror resonators [133]. The interaction of two weakly overlapping localized structures has been analysed [134].…”

Solitonization of the Anderson localization

“…However, on closer inspection, they have some similarities: They are exponentially localized, they correspond to appropriately defined negative eigenvalues, and they may be located in any position in space. Various recent investigations reported on the theoretical, numerical, and experimental analyses of localized states in the presence of disorder and nonlinearity [5][6][7][8][9][10][11][12][13][14][15][16][17], specifically in optics [18][19][20], in Bose-Eistein condensation (BEC) [21][22][23][24], and more recently for random lasers [25]. In the presence of nonlinearity, disorder-induced localizations are expected to have eigenvalue and localization length dependent on power (or number of atoms for BEC and pump energy for lasers).…”