Soliton mode beams with positive and negative group velocities in a thin left-handed film on a right-handed Kerr substrate

We consider propagation of stationary dark and bright spatial solitons and various pairs of incoherently coupled solitons in a planar waveguide consisting of a thin left-handed film on a Kerr substrate. It is shown that the solitons can be formed by waveguide modes with both positive and negative group velocities. Conditions are determined under which both bright and dark spatial solitons can propagate in the same waveguide, regardless of the sign of the nonlinear optical coefficient of the substrate.