Vol. 6, Issue 2, Part C (2024)

Fiber Bragg Gratings (FBGs) have emerged as one of the most versatile and reliable optical fiber sensors, particularly for temperature and strain monitoring in aerospace, civil, and biomedical applications. The temperature sensitivity of FBGs originates from two intrinsic effects: the thermo-optic coefficient of silica and the thermal expansion of the fiber. In this study, the behavior of FBGs under varying temperatures is modeled using Coupled Mode Theory (CMT), which provides an analytical framework for the coupling of forward and backward propagating modes within a periodic refractive index structure. Theoretical equations are extended to incorporate temperature-dependent changes in both refractive index and grating period. Numerical simulations are performed using Scilab, focusing on uniform FBGs of lengths 5 mm, 10 mm, and 15 mm with a nominal Bragg wavelength of 1550 nm. Results demonstrate a linear red-shift of the Bragg wavelength with increasing temperature, consistent with experimental observations reported in literature. For a 10 mm FBG, a wavelength shift of approximately 10.2 pm/°C is observed, aligning well with known sensitivity ranges (8-12 pm/°C). Key plots include (i) reflection spectra showing progressive wavelength shift with temperature from 20 °C to 100 °C, (ii) linear Bragg wavelength shift versus temperature, and (iii) variation of sensitivity with grating length. The study establishes CMT as a robust theoretical tool for FBG sensor modeling and highlights Scilab as an effective open-source platform for photonic simulations.