Mechanical foundations of birefringence of photo-elastoplastic media

Abstract

General birefringent formulae for an optically elastoplastic medium are theoretically deduced from the mechanical point of view. A hypothetical photo-elastoplastic medium is defined, i.e. the index tensor is a function of the elastic strain tensor and the plastic strain tensor. According to the principle of isotropy of space, the index tensor is explicitly expressed by the elastic strain tensor and the plastic strain tensor, or by the stress tensor and the total strain tensor. The directions of polarization for a given wave-vector are parallel to the secondary principal axes of the diametral conic section of the pseudo-strain quadric, cut by a plane parallel to the wave-front. The birefringent effect is the product of the secondary principal pseudo-strain difference and a scalar function of the invariants of the elastic strain and the plastic strain. Two special deformation states are investigated. Polynomial approximations are presented. In first-order approximation, the birefringent effect is expressed by a linear combination of stress and strain, which is the formula proposed by several investigators [1, 2, 3, 4, and 6].