Estimation of the nonlinear dependence of the indications of a fiber Bragg grating on temperature and strain from experimental data

The readings of the Bragg grating are determined based on the optical radiation reflected from it. A quantitative characteristic of this radiation is the wavelength at which the maximum power of the optical signal is achieved. This characteristic is called the central wavelength of the grating. The central wavelength shift depends on temperature and strain. As a rule, a linear approximation of this dependence is used. However, from the available literature it is known that, the grating wavelength shift demonstrates a strong nonlinear dependence on temperature at 5<T<200K and a weak quadratic dependence close to room temperature. Thus far, the authors have not found studies that consider all terms in the quadratic expansion of the central wavelength of the Bragg grating as a function of temperature and strain at near-room temperatures. Our work is intended to fill this gap. The article describes an experiment in which an optical fiber with Bragg grating was subjected to loading using three different weights. A step-wise temperature change from 5 to 100 0С was realized for each weight. Based on these data, all terms of the quadratic expansion of the desired function are determined. The contribution of each term is estimated.