The increasing interest in electromagnetic effects in the Left-Handed medium (LHM) requires the formulae capable of the full analysis of wave propagation in such materials. First, we develop a novel technique for discretization of the Lorentz medium model. In order to overcome the instability inherent in the standard perfectly matched layer (PML) absorbing boundary condition (ABC), we derive the modified PML ABC which can be extended to truncate the boundary of LHM. Then a convergent high-order accurate scheme based on triangle domains, discontinuous Galerkin method (DGM), is extended to the new DGM based on hybrid domains, triangle domains and quadrilateral domains. Finally, we adopt the new DGM and modified PML formulations to analysis the electromagnetic phenomena in the LHM. The simulation results show accuracy and stability of the proposed scheme.
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