Thermal effects on the transmission spectra of long-period fiber gratings

A detailed theoretical and experimental analysis of the thermal effects on the transmission spectra of long-period fiber gratings is presented. We show that the temperature sensitivity of the resonance wavelength of the grating is proportional to a modal dispersion factor of the fiber and the difference of the thermo-optic coefficients of the core and the cladding of the fiber. To facilitate our study, we derive a simple, accurate analytical formula for the calculation of the modal dispersion factor. Our formula shows explicitly that the temperature sensitivity of the resonance wavelength can be greatly enhanced by maximizing this factor with a suitable cladding mode. We also show explicitly that the temperature sensitivity of the strength of the grating is mainly determined by the coupling coefficient of the grating and the temperature sensitivity of the resonance wavelength. A good agreement between our theoretical and experimental results is obtained. Our results are useful for the design and the packaging of devices and sensors based on long-period fiber gratings.