Analytical solution for SH wave propagating through a graded plate of metamaterial

Abstract

A physical model for the shear horizontal (SH) wave propagating from left-handed material (LHM) through a graded or transition layer to right-handed material (RHM) has been proposed in this paper. After the comparison of the basic wave equations of the electromagnetic, longitudinal, and SH waves, it is found that they take similar differential form. The analytical solutions have been found for power law, hyperbolic, and polynomial profiles. Numerical waveforms of the amplitude and phase of the displacement are obtained for the corresponding profiles. It is found that the waveforms are symmetric for the power law and hyperbolic profiles, and that the waveform for the polynomial profile is shifted and non-symmetric. The shift along with the anti-symmetric profile may provide a way to monitor the wave behavior of the metamaterials.