Transformation equation in three-dimensional photoelasticity.

Optical phenomena that occur when polarized light passes through an inhomogeneous birefringent medium are complicated, especially when the principal directions of the dielectric tensor rotate on the light ray. This case is typical in three-dimensional photoelasticity, in particular in integrated photoelasticity by stress analysis on the basis of measured polarization transformations. Analysis of polarization transformations in integrated photoelasticity has been based primarily on a system of two first-order differential equations. Using a transformed coordinate in the direction of light propagation, we have derived a single fourth-order differential equation of three-dimensional photoelasticity. For the case of uniform rotation of the principal directions we have obtained an analytical solution.