Thermo-optical modeling of an intrinsically heated polymer fiber Bragg grating

A fully concatenated thermo-optical model is presented to predict the thermo-optical behavior of an intrinsically heated polymer fiber Bragg grating (PFBG). Coupled-mode theory and heat-conduction theory are first used to determine the axial heat generation and temperature distribution of a PFBG and the transfer matrix method (TMM) is subsequently employed to predict its thermo-optical behavior. The validity of the TMM is corroborated experimentally using an externally heated glass fiber Bragg grating (FBG) with an axially decaying temperature field. The verified model is utilized to investigate the thermo-optical behavior of a poly(methyl methacrylate) (PMMA) FBG. The counteracting thermally driven changes in the refractive index and the grating pitch, respectively, are found to be of comparable magnitude and to result in very modest net shifts in the Bragg wavelengths despite the considerable temperature changes induced by the absorption of the incident light.