For a fiber Bragg grating (FBG) surface-bonded to a substrate subjected to tension, the FBG reflective wavelength spectrum measured using an optical spectrum analyzer is different in either the location of the center wavelength or the spectral shape from that calculated using the transfer matrix (T-matrix) method. We show that the difference in the two wavelength spectra is caused by the adhesive layer used to bond the FBG to the substrate and a birefringence effect within the strained FBG. In the former case, the adhesive reduces the strain transferred from the substrate to the FBG and, therefore, causes the T-matrix method to overestimate the shift in the center wavelength. In the latter case, a birefringence effect is induced within the FBG because only the lower part of the FBG is bonded to the stressed substrate. As a result, both the peak power and the full width at half-maximum of the experimental spectrum differ from that predicted by the T-matrix method, in which the effects of birefringence are ignored. However, it is shown that when the strain transmission loss and birefringence effect are compensated using a strain transmission correction factor and a modified T-matrix formulation based on a discretized value of the refractive index, respectively, a good agreement is obtained between the calculated spectrum and that measured experimentally.
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