Analysis of FBG reflection spectra under anti-symmetrical strain distributions using the approximated transfer matrix model

In this paper, we used the efficient formulation of the approximated transfer matrix model (ATMM) for the analysis of fibre Bragg grating (FBG) sensors' response under anti-symmetrical strain fields. Exploiting the flexible representation of the transfer matrices in this new model, we will analytically prove that any sort of anti-symmetrical strain distribution over the length of a uniformFBG sensor will result in symmetrical reflected spectra. This phenomenon had been already observed in the literature, but proving it using the classical transfer matrix model was laborious and impractical. The same discussion will be extended to the grating distribution of the FBG sensors as well. A special case of an anti-symmetrical grating distribution could be the linearly chirped FBG sensor (LCFBG), in which the grating distribution is linearly increasing over the length of the FBG. Using computer simulations, it can be seen that such a grating distribution will result in perfectly symmetrical reflected spectra. Therefore, we expect that a well-produced LCFBG, should also have a close to symmetrical reflected spectra, and deviation from this symmetry could possibly indicate undesirable birefringence effects.