Theory of the Photoelastic Interaction

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Abstract
We apply our recent theory of nonlinear electrodynamics of elastic anisotropic dielectrics to the photoelastic interaction and derive for the first time from a fundamental point of view the form of the photoelastic susceptibility for materials of arbitrary symmetry. An indirect photoelastic effect is shown to exist in piezoelectric crystals. Its susceptibility cannot be represented as an ordinary tensor; it possesses different symmetry than the normal or direct photoelastic susceptibility, and it can be comparable in size to the latter. The direct photoelastic susceptibility can be represented by a fourth-rank tensor, but it lacks the traditionally assumed symmetry upon interchange of the last two (elastic) indices. The independent elastic variable relevant to the photoelastic interaction is the displacement gradient, not the strain as believed since 1841. This arises because rotations can play as significant a role as strains do in photoelasticity of strongly birefringent crystals in the presence of shear distortions. The form of the derived photoelastic tensor gives information about the various origins of the effect and can predict the frequency dispersion of the effect. Though the nonlinear polarization derived here is equally applicable to Brillouin scattering, specific application is made in this paper to acousto-optic scattering, and the form of the phase-matched output wave is derived for waves having an arbitrary orientation to an anisotropic medium.