Multiple linear-crossing metamaterials for directional refraction

Recently, linear-crossing metamaterials (LCMMs) in the hyperbolic topological transition of iso-frequency contour, have attracted people's great attention. Due to the novel linear dispersion, LCMM provides a new platform to control and enhance the light-matter interactions, such as all-angle negative refraction, filters, super-lens, etc. However, the narrow-band working frequency is currently the major limitation in LCMMs. In this work, we propose two methods to realize multiple linear-crossing metamaterials (MLCMMs), including a basic Drude-Lorenz model and an actual step-like multilayer structure. Especially, in order to identify the designed two kinds of MLCMMs, we numerically demonstrate the unique beam splitting and directional refraction of MLCMM at different frequencies. Our findings may not only provide a new platform for the fundamental study of LCMM, but also facilitate some broadband applications.