Gap soliton formation in a nonlinear anti-directional coupler

We consider propagation of electromagnetic solitary waves in two tunnel-coupled waveguides. It is assumed that one of the waveguides is made of a positive-index dielectric, having a Kerr nonlinearity. The other waveguide is made of a linear optical metamaterial characterised by the so-called negative refraction. The gap soliton formation in such a system, which, as shown, has a threshold character, is studied numerically.