We analyze thickness-shear vibrations of an at-cut quartz plate with elliptical electrodes. The electrodes are essentially optimal in the sense of Mindlin in that they approximately satisfy the criterion for the Bechmann number in every direction. The scalar differential equation derived by Tiersten and Smythe is used which allows us to obtain the overtone modes in addition to the fundamental modes.
The super energy flows generated and transmitted have been investigated in a parallel-plate waveguide, which is filled with air and the anisotropic left-handed materials. Theoretical analysis and numerical simulations show that the propagation modes of the anisotropic super waveguide are consistent with those of the isotropic waveguides [1–3]. They also show that the loss of electromagnetic parameters size of waveguide will influence the amplitude of time-average power flows.
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