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Wave propagation for transverse electric (TE) mode in a graded interface between left-handed and right-handed material has been investigated by using asymptotic iteration method. By using hyperbolic functions for negative permittivity and negative permeability, we obtained the graded graphs of permittivity and permeability as a function of material thickness. Maxwell equation for the dielectric with the hyperbolic function in permittivity and permeability has been reduced to second orde differential equation. The second orde differential equation has been solved by using asymptotic iteration method with the eigen functions in complementary error functions. The eigen functions explained about the wave propagation in a graded interface of material. The distribution of the electric field and the wave vector were given in approximate solution

Wave Propagation Solution for Transverse Electric Mode in a Graded Interface between Left-Handed and Right-Handed Material