Analytical solution of four-mode coupling in shear strain loaded fiber Bragg grating sensors

The polarization-dependent reflection spectra of fiber Bragg grating (FBG) sensors in polarization-maintaining fibers are influenced by shear strain. This influence can be evaluated from a tensorial coupled-mode theory approach. Yet, this approach requires the numerical integration of the four coupled-mode equations. We present an easy to handle, completely analytical treatment of the polarization-dependent reflection spectra of FBGs. We derive the required equations and compare the results to the numerical integration of the four tensorial coupled mode equations.