  We demonstrate that use of the field effect to tune the effective optical
parameters of a layered hyperbolic metamaterial leads to topological
transitions in its dispersion characteristics in the optical regime. Field
effect gating electrically modulates the permittivity in transparent conductive
oxides via changes in the carrier density. These permittivity changes lead to
active extreme modulation of ~200% of the effective electromagnetic parameters
along with active control of the anisotropic dispersion surface of hyperbolic
metamaterials and enable the opening and closing of photonic band gaps.
