The Design Formulas of Substrate Integrated Multilayer Tensor Metasurfaces

Metasurfaces are able to effectively manipulate electromagnetic wave propagations. A metasurface can be characterized by surface electric impedance and surface magnetic impedance. Conventionally, the realization of surface magnetic impedance requires non-planar structures, such as metallic loops, which are not easy to fabricate, especially at optical frequencies. Recently, we have shown that effective surface magnetic and electric impedances can be realized using multilayer electric impedance surfaces only. In this article, we use the network theory to derive the ABCD matrix of substrate integrated multilayer tensor metasurfaces with arbitrary incident angles. The formulas are general, and thus can handle a wide range of analysis and synthesis problems of multilayer tensor metasurfaces.