Plasmon-polaritons along the asymmetric hyperbolic metamaterial

Background and Objectives: Plasmon-polaritons along a surface of bulk hyperbolic metamaterial and along a slab of such metamaterial with an arbitrary orientation of the crystallographic axis are considered (the axis in the polarization plane is an arbitrary angle with the direction of propagation). We use the rigorous approach based on Maxwell's equations. The parameters of the hyperbolic metamaterial in the form of the effective dielectric constant tensor are determined by homogenization. The dielectric permittivity of metal layers is determined by the Drude-Lorentz model. The axis change is made using the rotation matrix of the coordinate system, and the effective permittivity tensor is transformed accordingly. The possibility of using graphene layers with the conductivity of a graphene sheet based on the Kubo model is considered. The conditions of existence of fast, slow, flowing, forward and backward plasmon-polaritons are found. Backward plasmon-polaritons correspond to a wave in which the phase velocity is opposite to the energy transfer velocity. Classification of waves is made both on the basis of calculation of Pointing vector, and by the solution of the dispersion equation and definition of signs of real and imaginary parts of a constant of propagation. The Fresnel formulas are also derived for the diffraction of a plane wave of arbitrary polarization on such a structure. Methods of analytical and numerical solution of dispersion equations are applied. Partial analytical solutions of dispersion equations are obtained. A new type of backward inverse plasmon-polaritons propagating along the flat boundary of a massive sample of a hyperbolic metamaterial with a vacuum, which does not exist for a solid metal sample, is found. The possibility of dispersion control by applying an external magnetic field is considered, as well as the possibility of plasmon-polariton amplification in waveguides from metamaterials with optically pumped graphene sheets, as well as in diffraction on plane-layered structures. Methods: We use the Maxwell equation, mode matching technique, the homogenization for hyperbolic metamaterials without spatial dispersion and construct the complex dispersion equation. We consider the asymmetric hyperbolic metamaterial with a rotated optical axis. The dispersion equation was solved analytically and numerically by the iterative method.