Transfer Matrix Approach to Four Mode Coupling in Fiber Bragg Gratings

Shear strain effects within fiber Bragg grating sensors have been neglected in the theoretical treatment of these devices. Shear strains do however occur in everyday applications and additionally shear strains do change the spectral response of these sensors. This may lead to a nonlinear behavior or measurement errors. We develop a transfer matrix method using coupled mode theory, that is capable of modeling the encountered effects. The effects include intra grating polarization mode coupling and changes of the spectral response. We show how the transfer matrix is derived and construct a test case for checking the correctness of its results. We compute different load cases and compare the obtained solutions to the numerically integrated coupled mode equations.