Dark localized structures in a cavity filled with a left-handed material

We consider a nonlinear passive optical cavity filled with left-handed and right-handed materials and driven by a coherent injected beam. We assume that both left-handed and right-handed materials possess a Kerr focusing type of nonlinearity. We show that close to the zero-diffraction regime, high-order diffraction allows us to stabilize dark localized structures in this device. These structures consist of dips in the transverse profile of the intracavity field and do not exist without high-order diffraction. We analyze the snaking bifurcation diagram associated with these structures. Finally, a realistic estimation of the model parameters is provided.