Analysis for long period fiber gratings using thermal kernel function

To analyze the various LPFGs with thermal changes, we present how makes the kernel function to translate the information of thermal change into the coupling coefficient and detuning factor changed by temperature. We propose the extended fundamental matrix model with the proposed kernel function. To verify the validity of the proposed model experimentally, we have manufactured the LPFG structures with the thermal changes using the divided coil heater. We have observed that the transmission spectra calculated using the proposed model are close to the corresponding measured spectra in the wavelength band of interest.