Truncated-Bloch-wave solitons in optical lattices

We study self-trapped localized nonlinear states in the form of truncated Bloch waves in one-dimensional optical lattices, which appear in the gaps of the linear bandgap spectrum. We demonstrate the existence of families of such localized states which differ by the number of intensity peaks. These families do not bifurcate from the band edge, and their power curves exhibit double branches. Linear stability analysis demonstrates that in deep lattice potentials the states corresponding to the lower branches are stable, whereas those corresponding to the upper branches are unstable, independently of the number of peaks.