Localization of mode waves in a disordered multi-waveguide system

Localization properties of mode waves in a disordered multi-waveguide system composed of randomly different cores are presented. Coupled mode equations are transformed into a matrix eigenvalue problem and eigenvalues and eigenvectors are numerically obtained. The propagation constant of the modes propagating along isolated cores is a random variable. Amplitudes of localized modes decrease exponentially away from the center of localization. The average extent of the localized mode depends only on the single parameter delta beta/kappa where delta beta is the fluctuation of the propagation constants of modes and kappa is the mode coupling coefficient between neighboring cores. For a sufficiently large value of delta beta/kappa modes are strongly localized. The mode is localized at one core. The localized position depends on the propagation constant of the mode. (C) 1998 Elsevier Science B.V. All rights reserved.