Accurate Measurement of THz Dielectric Constant Using Metamaterials on a Quartz Substrate

We present dielectric constant measurements of thin films using THz metamaterials fabricated on a quartz substrate. The resonance shifts of the metamaterials exhibit saturation behavior with increasing film thickness. The saturation frequency shift varies with the real part of the dielectric constant, from which the numerical expression for the particular metamaterial design was extracted. We first performed finite-difference time-domain simulations to find an explicit relationship between the saturated frequency shift and the dielectric constant of a thin film, which was confirmed by the experimental results from conventional techniques. In particular, the quartz substrate enables us to determine their values more accurately, because of its low substrate index. As a result, we extracted the dielectric constants of various films whose values have not been addressed previously without precise control of the film thickness.