Effect of thermal expansion mismatch in grating material and host specimen on thermal sensitivity of FBG sensor

Authors have studied thermal sensitivity characteristics of FBG temperature sensor attached to the surface of targeted host specimen (Lee and Lee in J Korean Phys Soc 59(5):3188–3191, 2011; Yu-Lung and Han-Sheng in Meas Sci Technol 9:1543–1547, 1998; Reddy et al. in Opt Appl 40(3):685–692, 2010). In their mathematical analysis, the coefficient of thermal expansion of grating material is ignored due to its contribution to the shift in the wavelength is small as compared to shift because of CTE of host specimen. However, we find that the Bragg’s wavelength shift used for measuring temperature in FBG sensor is dependent on difference in thermal expansions of grating and targeted host specimen materials. We have investigated the effect of the expansion in the material of the grating as well as that of host material and have found that at low temperature the difference in the shift in wavelength is indeed very small of the order of 0.67 pm at \(26\,{^\circ }\hbox {C}\), but the difference in the shift in the wavelength at higher temperature say 350–\(400\,{^\circ }\hbox {C}\) is quite large of the order of 250 pm and cannot be neglected as it will result in error reading of the temperature for higher ranges.