Abstract
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.
Highlights
The development of physics related to artificial composite material has been brought into a new finding, namely a negative refractive index material (NIM) or so-called lefthanded materials (LHM)
In below are the graphs of permeability (Fig. 1.a) and permittivity (Fig.1.b) vary according to the material thickness y where the interface between right-handed materials (RHM) and LHM is located at y = 0
Wave propagation of electric field E(y,z) which is expressed in Fig. 3 give explanation that in a graded interface between left-handed and right-handed material using hyperbolic sinus plus tangent function has the symmetry propagation with y=0 is the interface point
Summary
The development of physics related to artificial composite material has been brought into a new finding, namely a negative refractive index material (NIM) or so-called lefthanded materials (LHM). The first time, in 1968, Vaselago reviewing theoretically what if a material is based on the negative electric permittivity and negative magnetic permeability.[3] in orde to bring the concept of metamaterial into the experiment takes a long time, which is preceded by Pendry et al in 1996 related to research of wire with a negative permittivity.[4] followed in 1999 regarding the material with negative permeability.[5] A year later, Pendry conducts experiments on negative refraction index material that could be used to manufacture the perfect lens.[6] In the same year, Smith et al.[7] doing research for verification if possible negative value electric permittivity and magnetic permeability simultaneously to a material under test Some of these studies become the basis for the development of metamaterial studies by many researchers today.
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