Abstract
Metasurfaces are metamaterials with two-dimensional (2D) or planar structures. Compared to traditional metamaterials, metasurfaces have the advantage of being lightweight, easy to control and simple to design. This paper outlines the phase matching principle and constitutive parameter theory of electromagnetic (EM) metasurfaces, as well as the constitutive parameter analysis and model equations for metasurface cloaks. Due to the singularity of the metasurface cloak, an Adaptive Edge Finite Element Method (AEFEM) is developed in this paper. In addition, the convergence theory of the AEFEM for the time-harmonic Maxwell's equations with one sign-changing coefficient is established under the T-coercivity assumption. Numerical simulations of the arc-shaped metasurface cloak have confirmed the accuracy of our model and numerical theory. Furthermore, we have used our numerical method to design a triangular-shaped metasurface cloak with fewer singularities.
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