Modified Transfer Matrix Formulation for Bragg Grating Strain Sensors

This paper presents a formulation for the application of the transfer matrix method to Bragg grating strain sensors. A modified T-matrix representation is detailed for the sensor problem based on an effective period derived from the coupling coefficients. This modified T-matrix formulation is shown to converge to the coupled-mode equations solution for a large number of grating segments, even in the presence of significant strain gradients. Several numerical examples are presented to demonstrate the importance of inclusion of the strain gradient in the calculation. In addition, the current formulation is validated by application to previously published experimental data.