  We present a metamaterial-based terahertz (THz) sensor for thickness
measurements of subwavelength-thin materials and refractometry of liquids and
liquid mixtures. The sensor operates in reflection geometry and exploits the
frequency shift of a sharp Fano resonance minimum in the presence of dielectric
materials. We obtained a minimum thickness resolution of 12.5 nm (1/16000 times
the wavelength of the THz radiation) and a refractive index sensitivity of 0.43
THz per refractive index unit. We support the experimental results by an
analytical model that describes the dependence of the resonance frequency on
the sample material thickness and the refractive index.
