In this paper, we report on analytical results of terahertz (THz)-wave response of frame structures that support a thin film where metamaterial elements exist. Since the transmittance spectra of the metamaterial including the support frames differ from those of the metamaterial elements excluding the frames, investigation of influences of the frames on the measured spectra is important. A preliminary analysis revealed that the spectra of the metamaterial elements are partially recovered by compensating the measured spectra using time-domain transmittance waves of a bulk silicon-on-insulator wafer, from which the support frames are made. We experimentally demonstrate that the spectra of the support frames depend on the width, but not on the pitch, of the frames. Moreover, we show that a slab-type waveguide model can explain the interference between the support frames and the incident THz waves. The physical mechanism of THz response of support frames, which are clarified in this article, will be helpful to design thin-film type metamaterials.
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