Tunable beam splitting and negative refraction in heterostructure with metamaterial

The dispersion characteristics of one-dimensional heterostructure with metamaterial is presented. We give a theoretical analysis and numerical simulations for tunable beam splitting and negative refraction. By adjusting the lattice constant of the heterostructure or the permeability of the metamaterial, the splitting angle can be tuned. Interestingly, if both the average permittivity and permeability are zero, the splitting angle will be 180 degrees. Moreover, when the permeability of metamaterial is small enough, the light cannot propagate in the heterostructure if the incident angle is less than the critical angle. And as soon as the incident angle is larger than the critical angle, negative refraction will occur. In addition, the negative refraction can also be tuned.