Dielectric substrate effect on the metamaterial resonances in terahertz frequency range

•Frequency shifts of various metamaterial resonances due to substrate effect.•Resonant frequencies are determined by an effective refractive index.•Effective index is given as a linear combination of substrate and air indices.•Relative contribution of substrate index is twice that of air.

We report on the effect of dielectric substrate on the resonance shift of metallic metamaterials operating in the terahertz frequency region. The resonance frequencies for various metamaterials obtained by time-domain spectroscopy agree well with calculations based on the finite-difference time-domain method. The dependencies of the resonance frequency to substrate index are studied, and are systematically determined by introducing an effective substrate index. The relative contributions of the substrate index for various metamaterials are obtained by fitting the numerically obtained effective refractive indices as a function of substrate index, which is found to be ∼0.63 regardless of the metamaterial geometry.