Topological Hyperbolic and Dirac Plasmons

In this chapter, criteria for existence of propagating optical modes which are transversely bound at the interface of two materials are studied. In particular, quite general cases are considered, where the materials involved are assumed to be anisotropic, but also demonstrating magneto-electric effects. Moreover, surface states of two-dimensional materials like topological insulators and graphene are also modeled via consideration of a conductivity sheet existing at the interface. A characteristic equation for obtaining the propagation constant of generalized interface modes is presented. Furthermore, optical modes sustained by a thin film of anisotropic materials with magneto-electric effect and topological surface states are also investigated. It is shown that interface modes supported by such a system are hybrid in nature, and can be further decomposed into the well-known classes of transverse magnetic and electric modes, only at the absence of magneto-electric effect. Although the formulations driven here are mathematically abstract, they can be used to investigate polaritons in van der Waal materials, hyperbolic materials, and topological insulators.