An all-dielectric composite route is proposed for the construction of a left-handed material at THz frequency. It is shown that the interaction between the crystal lattice vibration of the polaritonic dielectric and the electromagnetic wave could induce a negative permittivity. By combining the electric inclusion of polaritonic dielectric with the magnetic inclusion based on Mie resonance, the dielectric composite exhibits simultaneously negative permittivity and negative permeability, hence a negative refractive index. Additionally, the simulation results of the electromagnetic coupling between the electric and magnetic inclusions indicate that the behavior of the negative refractive index is closely related to the distance between the two inclusions.
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