Loss-induced topological transition of dispersion in metamaterials

Topological transition of dispersion in anisotropic metamaterials, in which isofrequency contour changes from a closed ellipsoid to an open hyperboloid, is usually realized by changing the sign of one component of permittivity (ε) or permeability (μ) from positive to negative. However, we show that topological transition of dispersion can occur by tuning the imaginary part of ε(μ) while fixing the real part of ε(μ). By adding different lumped resistors into two-dimensional transmission-line-based metamaterials, we just tune the imaginary part of μ at a fixed frequency. With the increase of loss, we measure the different emission patterns from a point source in the metamaterials to observe the changing process of isofrequency contours.