Guided Modes in a Slab Waveguide of Anisotropic dispersive Metamaterial

We derive the guidance conditions of a slab waveguide of uniaxially anisotropic dispersive material with not all of the components in the permittivity and permeability tensor the same sign. Taking the lossless dispersive left-handed media model for example, in terms of the operating angular frequency omega_o of the metamaterial, the even mode properties for guided TE waves are discussed in three classes. When omega² _mpz < omega² _o < omega² _mpperp there are infinite guided modes. In addition, it is also found that there may be multiple solutions of the propagating mode with wave number when imaginary transverse wave number omega² _em < omega² _o < omega² _mpz.