Linear-crossing metamaterials mimicked by multi-layers with two kinds of single negative materials

The topological transition of an iso-frequency contour will provide a powerful control for the interaction between light and matter. For example the transition of iso-frequency contour from an elliptical dispersion to a hyperbolic dispersion can result in many interesting optical phenomena including super-resolution, optical switching and collimation. In recently published literature, it has been shown that another transition from the metal-type hyperbolic dispersion to dielectric-type hyperbolic dispersion can be realized in the microwave circuit-based metamaterials. Particularly, the transition point corresponds to a new class of metamaterials with two intersecting linear dispersions, which can be called linear-crossing metamaterials (LCMMs). Because of the linear dispersion, LCMMs have been demonstrated to possess many unusual properties such as directional propagation and slab-focusing with a partial cloaking effect. In this perspective, we will demonstrate that the multilayered structure composed of ε -negative material and μ -negative material can mimic the LCMM in the optical regime. Based on this effective LCMM, we study the slab-imaging with a partial cloaking effect. In addition, we reveal that with the aid of LCMM, the Bessel beam with self-healing can be realized by a point source. The results show that LCMMs would be very useful in a variety of applications such as 50/50 beam splitters, focusing and non-diffraction beams.