The evanescent wave enhancement of left-handed (LH) metamaterials (MTMs) have always been providing a great opportunity to establish useful refraction systems, which could be optimally utilized to a vast amount of engineering applications on the front burner. We proposed a specific MTM structure to realize and control the unusual properties of MTMs, which are aimed to be useful in the development process of conventional techniques governing certain applications. The simulation results are used to verify the credibility of the analysis, design, and theoretical construction methods. Besides, the study also includes a specific bending investigation for non-unity negative refractive index situation where the energy concentration, presented by a LH slab, begins to torn apart as a result of non-unity negative refractive index. The distance of the focus depends on how thick the slab is, the distance of the source, and two main compensator terms containing angle functions, which are disturbed in the case of non-unity negative refraction, are tried to be rehabilitated numerically/mathematically.