We show that the axial component of the magnetic permeability tensor is resonant for a wire medium consisting of high-index epsilon-positive nanowires, and its real part changes the sign at a certain frequency. At this frequency the medium experiences the topological transition from the hyperbolic to the elliptic type of dispersion. We show that the transition regime is characterized by extremely strong dependence of the permeability on the wave vector. This implies very high density of electromagnetic states that results in the filamentary pattern and noticeable Purcell factor for a transversely oriented magnetic dipole.
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