We investigate the effect of substrate etching on terahertz frequency range metamaterials using finite-element method simulations. A blue shift was found in the metamaterial resonance with increasing substrate etch depth, caused by a decrease in the effective refractive index. The relative contribution of the substrate’s refractive index to the effective refractive index was obtained as a function of the etch depth, finding that the decay length of the electric field magnitude below the gap is larger for the etched metamaterials due to their lower effective refractive index. We suggest designs for a terahertz metamaterial liquid sensor utilizing substrate etching which shows a significant enhancement in sensitivity compared to unetched sensors using ethanol as an example analyte. The sensitivity of the liquid sensor was enhanced by up to ~6.7-fold, from 76.4 to 514.5 GHz/RIU, for an ethanol liquid layer with a thickness of 60 μm by the incorporation of a substrate etch depth of 30 µm. Since the region of space close to the metamaterial is the most sensitive, however, we find that for small liquid thicknesses, larger etch depths can act to sensitivity, and provide quantitative estimates of this effect.
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