Transversely stable soliton trains in photonic lattices

Abstract

We report the existence of transversely stable soliton trains in optics. These stable soliton trains are found in two-dimensional square photonic lattices when they bifurcate from $X$-symmetry points with saddle-shaped diffraction inside the first Bloch band and their amplitudes are above a certain threshold. We also show that soliton trains with low amplitudes or bifurcated from edges of the first Bloch band ($\ensuremath{\Gamma}$ and $M$ points) still suffer transverse instability. These results are obtained in the continuous lattice model and are further corroborated by the discrete model.