Mathematical Modeling of π-Phase-Shifted Fiber Bragg Grating and its Application for Strain Measurement in Epoxy Resin Cantilever Beam

The Z domain model of π-phase-shifted fiber Bragg grating (PS-FBG) is developed. The developed mathematical model is used for the evaluation of spectral response. The transmission response of PS-FBG of length 10 mm is determined and the spectral characteristic is found to be in very close agreement with previously published result. The transmission characteristics are examined when the position of phase-shift is not exactly at the center of the grating. The transmission response of a grating with multiple phase shifts is also investigated using the Z domain analysis. Measurement of strain with the help of single phase-shift grating sensors in a cantilever beam composed of epoxy resin is proposed. Strain developed at different positions across the beam can be measured simultaneously from the Bragg wavelength shifts of the array of in-fiber phase shifted gratings bonded to the beam. The PS-FBG sensors offer a much higher resolution and detection in measurement of strain perturbations compared to the FBG sensors. The superior detection is due to the extremely narrow reflection notch of 22.83 pm of PS-FBG sensor which is reduced by a factor of around 19.52 compared to the bandwidth of the reflected light from a FBG of same length.