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A fiber-optic refractive index (RI) sensor based on a π-phase-shifted fiber-Bragg-grating (πFBG) inscribed on a side-hole fiber is presented. The reflection spectrum of the πFBG features two narrow notches associated with the two polarization modes and the spectral spacing of the notches is used for high-sensitivity RI sensing with little temperature cross-sensitivity. The side-hole fiber maintains its outer diameter and mechanical strength. The side-hole fiber is also naturally integrated into a microfluidic system for convenient sample delivery and reduced sample amount. A novel demodulation method based on laser frequency modulation to enhance the sensor dynamic range is proposed and demonstrated.