We investigate in detail the guided modes in a two-layered planar waveguide where one layer is filled with an ordinary right-handed material (RHM) and the other is filled with a biaxially anisotropic metamaterial. We show that the mode properties are closely dependent on the spatial dispersion relation of the anisotropic medium. When the dispersion equation for the anisotropic medium becomes a two-sheet or a one-sheet hyperbola type, an infinite number of guided modes can be supported simultaneously in the waveguide, which is completely different from the cases of RHM and isotropic metamaterial. We also investigate the mode distributions of the planar waveguide in the lossy case, where we discover that the dominant mode in the waveguide is a forward wave while the higher-order modes are backward waves under the two-sheet hyperbolic dispersion. Numerical results validate our theoretical analysis.
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