Tangential Network Transmission Theory of Reflective Metasurface with Obliquely Incident Plane Waves

In this paper, a tangential network transmission theory is established for the reflective metasurface composed of periodic subwavelength metallic elements and a perfect electrical conductor (PEC)-backed substrate. The theory is divided into two parts. The first part shows that the oblique incidence can be handled the same way as a normal incidence for a PEC-backed substrate in terms of tangential components of electric fields and a normal wave vector. Therefore, the network transmission theory is extended from the PEC-backed substrate to the reflective metasurface, whose total tangential reflection matrix depends on the induction matrix of the metallic elements in the air-substrate interface. The second part deals with the conversion of the induction matrices of different metallic elements into equivalent circuits, whose electrical parameters can be theoretically calculated or extracted from numerical simulations. Based on the obtained electrical parameters, the theory can be used to analyze or design reflective metasurfaces. Finally, the theory is verified by a metasurface, which is composed of periodic double-L shaped elements. The analytical results agree with the simulated ones for arbitrary substrate and incidence angle. The measured results further validate the proposed theory.