In this paper, we have proposed a dispersive formulation of scalar-based meshless method for time-domain analysis of electromagnetic wave propagation through left-handed (LH) materials. Moreover, we have incorporated Berenger's perfectly matched layer (PML) absorbing boundary condition (ABC) into the dispersive formulation to truncate open-domain structures. In general, the LH medium as a kind of dispersive media can be described by frequency-dependent constitutive parameters. The most appropriate numerical techniques for analysis of LH media are dispersive formulations of conventional numerical methods. In comparison to the conventional grid-based numerical methods, it is proved that meshless methods not only are strong tools for accurate approximation of derivatives in Maxwell's equations but also can provide more flexibility in modeling the spatial domain of problems. However, we have not seen any reports on using dispersive forms of meshless methods for simulation of wave propagation in metamaterials and applying any PML ABCs to dispersive formulation of meshless method. The proposed formulation in this paper enables us to take advantage of meshless methods in analysis of LH media. For modeling the frequency behavior of the medium in the proposed dispersive formulation, we have used auxiliary differential equation (ADE) method based on the relations between electromagnetic fields intensities and current densities. Effectiveness of the proposed formulation is verified by a numerical example; also, some basic factors which affect the accuracy and computational cost of the simulations are studied.
