Analysis and synthesis of cascaded metasurfaces using wave matrices

Various matrix representations are used to analyze the propagation of electromagnetic waves through stratified (layered) media or cascaded circuit networks. These include ABCD matrices, scattering matrices, impedance matrices, and hybrid matrices. A less known network representation is the wave matrix. In this paper, a brief review of wave matrices is presented and their relation to other network representations derived. Wave matrices are found for common interfaces such as boundaries between dielectric media, dielectric slabs, as well as electric, magnetic, and magneto-electric sheet boundaries (generalized sheet transition conditions). These results are then used to develop an analytical synthesis approach for cascaded metasurfaces: metasurfaces consisting of a cascade of sheets separated by dielectric spacers. This is in contrast to earlier works which relied on numerical solvers or optimization methods to design such structures. A few design examples are presented to demonstrate the utility of the synthesis approach.