  In this paper we reveal the physics behind the formation of tri- and
tetra-hyperbolic phases in anisotropic metamaterials without magnetoelectric
coupling and describe the anti-crossing splitting phenomenon in the hyperbolic
dispersion which arises due to the hybridization of the plasmonic and magnetic
Bloch high-k polaritons. This considerably deepens the understanding of the
high-k polaritons and the topology of the optical iso-frequency surfaces in
k-space and will find applications in optical nano-resolution imaging and
emission rate and directivity control. To accomplish this, we develop a range
of new techniques of theoretical optics for bianisotropic materials, including
the quadratic index of refraction operator method, suitable to study the high-k
polaritons with finite indices of refraction and the explicit expression for
the characteristic matrix in generic bianisotropic media. We introduce the
spatial stratification approach for the electric and magnetic responses of
anisotropic homogeneous media to analyze the underlying Bloch waves. We believe
that the formalisms developed here can be useful for the researchers in the
field of theoretical optics of anisotropic and bianisotropic media in the
future.
