Numerical analysis of fiber Bragg grating and long period fiber grating undergoing linear and quadratic temperature change

The coupled-mode equations for fiber Bragg grating (FBG) and long period fiber grating (LPFG) undergoing linear and quadratic temperature change were given. The effects of temperature gradient and quadratic temperature change on the reflectivity spectrum of fiber Braggs grating and the transmission spectrum of long period fiber grating were investigated using the numerical simulation, and the dependence relationships of the central wavelength shift, the full-width-at-half-maximum, and the peak intensity upon temperature gradient were also obtained. These relationships may be used to design a novel fiber optical sensor which can simultaneously measure the temperature and temperature gradient.