Abstract
We developed a method for simulating the birefringence of an annealed ingot of CaF_2 single crystal caused by the residual stress after annealing process. The method comprises the heat conduction analysis that provides the temperature distribution in the ingot during annealing, the elastic thermal stress analysis using the assumption of the stress-free temperature that provides the residual stress after annealing, and the analysis of the birefringence of an annealed ingot induced by the residual stress. The finite element method was applied to the heat conduction analysis and the elastic thermal stress analysis. In these analyses, the temperature dependence of material properties and the crystal anisotropy were taken into account. In the birefringence analysis, the photo-elastic effect gives the change of refractive indices, from which the optical path difference is calculated using the Jones matrix. The distribution of the optical path difference in the annealed ingot obtained from the present calculation agrees well with that of the experiment. Its calculated value also agrees reasonably well with that of the experiment, when the stress-free temperature is adequately selected.
