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Advances in mid-IR lasers, detectors, and nanofabrication technology have enabled new device architectures to implement on-chip sensing applications. In particular, direct integration of plasmonic resonators with a dielectric waveguide can generate an ultra-compact device architecture for biochemical sensing via surface-enhanced infrared absorption (SEIRA) spectroscopy. A theoretical investigation of such a hybrid architecture is imperative for its optimization. In this work, we investigate the coupling mechanism between a plasmonic resonator array and a waveguide using temporal coupled-mode theory and numerical simulation. The results conclude that the waveguide transmission extinction ratio reaches maxima when the resonator-waveguide coupling rate is maximal. Moreover, after introducing a model analyte in the form of an oscillator coupled with the plasmonics-waveguide system, the transmission curve with analyte absorption can be fitted successfully. We conclude that the extracted sensing signal can be maximized when analyte absorption frequency is the same as the transmission minima, which is different from the plasmonic resonance frequency. This conclusion is in contrast to the dielectric resonator scenario and provides an important guideline for design optimization and sensitivity improvement of future devices.