Two-dimensional disordered lattice solitons.

We investigate families of optical solitons supported by two-dimensional disordered lattices. The linear modes of the system are identified, and their eigenvalues are arranged in a band structure. Introducing Kerr nonlinearity, we find that families of solitons originate from linear modes. Such solutions, depending on the eigenvalue of the supporting linear mode, as the power increases may become less localized/delocalized via resonant interactions with the modes of the linearized lattice. In addition, families of highly confined solitons exist in every waveguide of the lattice and for both signs of the nonlinearity.