Time-domain modelling of graded refractive index metamaterials by using 3D TLM Z-transform method

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