Topological transition of the iso-frequency contour (IFC) from a closed ellipsoid to an open hyperboloid provides unique capabilities for controlling the propagation of light. However, the ability to actively tune these effects remains elusive, and the related experimental observations are highly desirable. Here, a tunable electric IFC in a periodic structure composed of graphene/dielectric multilayers is investigated by tuning the chemical potential of the graphene layer. Specially, we present the actively controlled transportation in two kinds of anisotropic zero-index media containing perfect electric conductor/perfect magnetic conductor impurities. Finally, by adding variable capacitance diodes into a two-dimensional transmission-line system, we present an experimental demonstration of the actively controlled magnetic topological transition of dispersion based on electrically controllable metamaterials. With the increase in voltage, we measure the different emission patterns from a point source inside the structure and observe the phase-transition process of IFCs. The realization of an actively tuned topological transition will open up a new avenue in the dynamical control of metamaterials.
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