Birefringence simulations of single crystals

Abstract

Fluoride single crystals such as calcium fluoride (CaF₂) belonging to the cubic crystal system and magnesium fluoride (MgF₂) belonging to the tetragonal crystal system are utilized as optical elements in high power lithography systems. In such uses of the single crystals, birefringence is an important phenomenon that affects optical performance. Based on the papers published by the present authors, we review the birefringence of CaF₂ and MgF₂ single crystals. Intrinsic birefringence is dealt with in addition to stress birefringence. First of all calculation methods for stress birefringence are presented. They are the Jones calculus, an exact method, and the average stress method, an approximate method, and the relation between the two methods is given. In the stress birefringence simulations after annealing of CaF₂ single crystal, the importance of time-dependent nonlinear deformation behavior of a material called creep is pointed out in calculating residual stress that induces stress birefringence. When the wavelength of light becomes down to the vacuum ultraviolet region, CaF₂ single crystal shows intrinsic birefringence in addition to stress birefringence. Birefringence simulations of a CaF₂ single crystal chamber window of an ArF excimer laser light source are performed by considering both stress birefringence and intrinsic birefringence to evaluate the optical performance and to obtain the optimum condition of CaF₂ single crystal window. MgF₂ single crystal shows intrinsic birefringence even for visible light because of its strong crystal anisotropy. The results of birefringence analyses are shown for MgF₂ single crystal as an example of combining stress birefringence with intrinsic birefringence under a visible light condition.