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We present a highly sensitive technique for determining the complex permittivity of nanoliter liquid samples in the terahertz band based on a photonic crystal resonator and microcapillary. Liquids are characterized by using a capillary tube to introduce a ∼4 nl liquid sample into the electromagnetic field of a resonant mode confined by an L3 resonant cavity in a high-resistivity silicon photonic crystal slab. Monitoring the perturbation of the resonant frequency and unloaded Q-factor of the resonant mode at 100 GHz and ∼5800, respectively, allows a sample's permittivity to be calculated. An analytical model describing the system response based on perturbation theory and quasi-static analysis of the electric field within the capillary is also presented and found to agree well with FEM simulations and experimental measurements of ethanol-water mixtures of various concentrations for low to moderate loss tangents of the liquid samples. We demonstrate the utility of this approach by measuring the complex permittivity of several bioliquids, including suspensions of red and white blood cells. These results represent a step towards a lab-on-a-chip device for the analysis of extremely small quantities of biological, toxic, explosive, and other liquid types at terahertz frequencies.


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