  Hyperbolic Meta-Materials~(HMMs) are anisotropic materials with permittivity
tensor that has both positive and negative eigenvalues. Here we report that by
using a type II HMM as cladding material, a waveguide which only supports
higher order modes can be achieved, while the lower order modes become leaky
and are absorbed in the HMM cladding. This counter intuitive property can lead
to novel application in optical communication and photonic integrated circuit.
The loss in our HMM-Insulator-HMM~(HIH) waveguide is smaller than that of
similar guided mode in a Metal-Insulator-Metal~(MIM) waveguide.
