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In this paper, a numerical three-dimensional (3D) model of electromagnetic left- handed metamaterials (LH MTM) is applied for the modelling of composite right-left handed (RH/LH) structures with a graded refractive index profile commonly named GRIN MTM. The core of this model is Transmission Line Matrix (TLM) Z-transform method that incorporates the Drude function to account for dispersive LH MTM properties in the time-domain. Lossy GRIN slabs with abrupt, hyperbolic tangent, cosine, and linear refractive index profiles have been considered. The accuracy, efficiency and stability of the proposed approach are verified using analytical solution.

TLM Z-transform method modelling of Lossy Grin MTM with different refractive index profiles