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Dispersion features of a graphene-coated semiconductor nanowire operating in the terahertz frequency band are consistently studied in the framework of a special theory of complex waves. Detailed classification of the waveguide modes was carried out based on the analysis of characteristics of the phase and attenuation constants obtained from the complex roots of characteristic equation. With such a treatment, the waves are attributed to the group of either 'proper' or 'improper' waves, wherein their type is determined as the trapped surface waves, fast and slow leaky waves, and surface plasmons. The dispersion curves of axially symmetric TM 0n and TE 0n modes, as well as nonsymmetric hybrid EH 1n and HE 1n modes were plotted and analyzed in details, and both radiative regime of leaky waves and guided regime of trapped surface waves are identified. Peculiarities of propagation of the TM modes of surface plasmons were revealed. Two subregions of existence of surface plasmons were found out where they appear as propagating and reactive waves. The cut-off conditions for higher order modes were correctly determined.

The topology of isofrequency surfaces of a magnetic-semiconductor superlattice influenced by an external static magnetic field is studied. In particular, in the given structure, topology transitions from standard closed forms of spheres and ellipsoids to open ones of Type I and Type II hyperboloids as well as bi-hyperboloids were revealed and analyzed. In the latter case, it is found out that a complex of an ellipsoid and bi-hyperboloid in isofrequency surfaces appears as a simultaneous effect of both the ratio between magnetic and semiconductor filling factors and magnetic field influence. It is proposed to consider the obtained bi-hyperbolic isofrequency surface as a new topology class of the wave dispersion.A topology of photonic systems is related to global behaviors of a wave function accounting constitutive and structural parameters in the entire dispersion band [1]. It means that in the phase space of a propagating electromagnetic wave at a constant frequency the topology appears in the form of an isofrequency surface (also known as Fresnel wave surface or surface of wave vectors), which governs the wave propagation conditions along an arbitrary direction inside the corresponding optical material (in fact it expresses the relationships between the directions of the wave vector and the vector of group or phase velocity of the wave; for the first reading on construction of isofrequency surfaces according to the laws of geometrical optics we refer to methodological notes in [2]). By definition, each isofrequency surface belongs to a class of quadrics [3], from a large variety of which three particular nondegenerated forms are well known in optics-sphere, ellipsoid and hyperboloid.Thus, in an isotropic medium isofrequency surfaces appear in the closed form of a sphere, whereas in a uniaxial optical crystal they transit to a complex of a sphere and spheroid, which characterize propagation conditions of ordinary and extraordinary waves, respectively [4]. These isofrequency surfaces can intersect each other in some sections at certain singular points. In a biaxial crystal the complex consists of a sphere and ellipsoid. In other natural anisotropic media including acoustic crystals, plasmas and magnetically ordered (gyrotropic) media isofrequency surfaces can acquire both closed and open forms. In the latter case they resemble the form of a hyperboloid (see Fig. 8.3.2 in [5] for a taxonomy of isofrequency surfaces in anisotropic media). In this way, different forms of topology of the wave dispersion express the kind of anisotropy, namely the relations be- * volodymyr.i.fesenko@gmail.com tween components of permittivity and/or permeability tensors characterizing the medium.Indeed, in an anisotropic crystal when all principal values of its permittivity tensor are positive (i.e., ε > 0 and ε ⊥ > 0), the isofrequency surfaces have closed forms [ Fig. 1(a)]. Contrariwise, when one or two corresponding tensor's components are negative (i.e., the medium is "extremely" anisotropic), the topology appears in the open form ...