Effect of spectrum broadening on photon-counting fiber Bragg grating sensing

In a photon-counting fiber Bragg grating (FBG) sensing system, a shorter probe pulse width reaches a higher spatial resolution, which inevitably causes a spectrum broadening according to the Fourier transform theory, thus affecting the sensitivity of the sensing system. In this work, we investigate the effect of spectrum broadening on a photon-counting FBG sensing system with a dual-wavelength differential detection method. A theoretical model is developed, and a proof-of-principle experimental demonstration is realized. Our results give a numerical relationship between the sensitivity and spatial resolution at the different spectral widths of FBG. In our experiment, for a commercial FBG with a spectral width of 0.6 nm, an optimal spatial resolution of 3 mm and a corresponding sensitivity of 2.03 nm^-1 can be achieved.