Optical surface modes in the presence of nonlinearity and disorder

Abstract

We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson - nonlinear Schrödinger equation, the propagation of the mode amplitudes up to some finite distance is monitored. The analysis is based on the calculated localization length and the participation number, two standard measures for the statistical description of Anderson localization. For relatively weak disorder and nonlinearity, a higher disorder strength is required to achieve the same degree of localization at the edge than in the interior of the array, in agreement with recent experimental observations in the linear regime. However, for relatively strong disorder and/or nonlinearity, this behavior is reversed and it is now easier to localize an excitation at the edge than in the interior.

5 double-column pages, 7 figures, submitted for publication

References in corpus (9)

• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Anderson localization and nonlinearity in one dimensional disordered photonic lattices
• Destruction of Anderson localization by a weak nonlinearity
• Universal spreading of wavepackets in disordered nonlinear systems
• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays
• Wave localization at the boundary of disordered photonic lattices
• $q$-Breathers in finite lattices: nonlinearity and weak disorder

Cited by in corpus (7)

• Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices
• Direct measurement of superdiffusive and subdiffusive energy transport in disordered granular chains
• Anderson localization of light with topological dislocations
• Transverse localization in nonlinear photonic lattices with second-order coupling
• Anderson localization in Bragg-guiding arrays with negative defects
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems
• Chaotic behaviour of disordered nonlinear lattices