k-space topology. (a) Spherical isofrequency surface for an isotropic dielectric. Inset shows an energy versus momentum relationship with the red dot indicating the operating frequency for the derived isofrequency surface. (b) Hyperboloid isofrequency surface for a uniaxial medium with an extremely anistropic dielectric response (Type I HMM: εzz < 0; εxx; εyy > 0) (c) Hyperboloid isofrequency surface for an extremely anistropic uniaxial medium with two negative components of the dielectric tensor (Type II HMM: εxx; εyy < 0; εzz > 0). The (b) Type I and (c) Type II metamaterials can support waves with infinitely large wavevectors in the effective medium limit. Such waves are evanescent and decay away exponentially in vacuum.