The linearized problem of magneto-photoelasticity
Inverse Problems and Applications
25 February 15:30 - 16:30
The idea of using the Faraday rotation in photoelasticity was proposed by Aben in 1970. He introduced the term "magneto-photoelasticity''. The mathematical nature of the problem is still not well understood. In the first part of our talk, we use the quasi-isotropic approximation of geometric optics for deriving the equations of magneto-photoelasticity in the case of a nonhomogeneous background medium and of a variable exterior magnetic field. In the case of a homogeneous background medium and of a constant exterior magnetic field our equations coincide with Aben's ones. We derive an explicit linearized formula for the solution to Aben's equations. Finally, we consider the inverse problem of recovering the medium anisotropy from the results of polarization measurements that are known for several values of the intensity of the exterior magnetic field. The linearized version of the problem turns out to be very easy in virtue of our explicit formula. Actually, if values of the intensity of the exterior magnetic field are chosen in an appropriate way, the measurements give us Fourier coefficients of sought functions.