  This article aims to propose a novel analytical model for anisotropic
multi-layer elliptical structures incorporating graphene layers. The
multi-layer structure is formed of various magnetic materials. An external
magnetic bias has been applied in the axial direction. A graphene layer, with
isotropic surface conductivity, has been sandwiched between two adjacent
anisotropic materials. A novel matrix representation has been derived to find
the propagation parameters of the multi-layer structure. Two exemplary
important cases of the proposed general structure, as waveguides, have been
investigated to show, first the validity of our proposed analytical model, and
second, the richness of the general structure. The analytical and simulation
results show an excellent agreement. A very large value of the figure of merit
(FOM), e.g. FOM=110, is achieved for the second structure for the chemical
potential and external magnetic bias of 0.9 ev and 1T, respectively. Our
general structure and its analytical model can be exploited to design
innovative THz devices such as absorbers, couplers, and cloaks.
