Localized plateau beam resulting from strong nonlocal coupling in a cavity filled by metamaterials and liquid-crystal cells

We investigate the formation of a localized plateau beam in the transverse section of a nonlinear optical ring cavity filled with a metamaterial and a nonlocal medium such as a nematic liquid crystal. We show that, far from the modulational instability regime, localized structures with a varying width may be stable in one and two-dimensional settings. The mechanism of stabilization is related with strong nonlocal coupling mediated by a Lorentzian type of kernel. We show that there exists stable bright and dark localized structures. A reduction of Lugiato-Lefever equation in the regime close to the nascent bistability allows us to analytically derive a simple formula for the width of localized structures in one-dimensional systems. Direct numerical simulations of the dynamical model agree with the analytical predictions.