Analytical coherency matrix treatment of shear strained fiber Bragg gratings

Reconstruction of the strain tensor at the position of an embedded fiber Bragg grating sensor has been the goal of recent research. However, ambiguities in the measurand--the polarization resolved reflected intensity spectrum--upon occurrence of shear strain hinder its achievement due to lack of an invertible model. In this work, we derive such a model using coherency matrix properties of unpolarized light. We deduce simplified sensor parameters for the ambiguous shear strain loading case, which possibly lead to a practical inversion of the problem.