Substrate Effects on Terahertz Metamaterial Resonances for Various Metal Thicknesses

We demonstrate dielectric substrate effects on the resonance shift of terahertz metamaterials with various metal thicknesses by using finite-difference time-domain simulations. We found a small red shift in the metamaterial resonance with increasing metal thickness for the free-standing case. Conversely, when the metamaterial pattern was supported by a substrate with a high dielectric constant, the resonant frequency exhibited a large blue shift because the relative contribution of the substrate's refractive index to the resonant frequency decreased drastically as we increased the metal thickness. We determined the substrate's refractive index, 1.26, at which the metamaterial resonance was independent of the metal thickness. We extracted the effective refractive index as a function of the substrate's refractive index explicitly, which was noticeably different for different film thicknesses.