The generation of near-IR surface plasmon resonance in gold-coated tilted fiber Bragg gratings is strongly dependent on both the polarization state of the transmission light and the property of confining materials (including the coating materials and surrounding media). These dependencies can be advantageously used to demodulate the amplitude spectrum and retrieve the surrounding refractive index. In this paper, we present an automated demodulation technique that measures the surrounding refractive index by comparing the differential amplitude of resonance peaks near the plasmon attenuation for two orthogonal amplitude spectra recorded in the same operating conditions. A mean sensitivity of more than 500 nm per refractive index unit is reported. This new refractive index measurement method is shown to be accurate to 5×10(-5) over a full range of 0.01 in water solutions.