Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics

The discovery of a significant spatial-dispersion-induced birefringence (intrinsic birefringence) in $CaF2$ at ultraviolet wavelengths has had a major impact on the design of 157 nm lithography systems, requiring complete redesign of the optics to take account of the imaging aberrations resulting from the birefringence and the accompanying index anisotropy. This intrinsic birefringence phenomena results from a symmetry-breaking effect of the finite wave vector of the photon on the symmetry of the light-matter interaction in fluorite-structure cubic crystals. As a follow-up to our original concise report of measurements and theory of the effect in $CaF2$ and $BaF2,$ we present here a more detailed analysis of the theory, focusing on the symmetry and its consequences. We also provide the full directional dependence of the effect in useful closed forms. We analyze the implications for precision optical design with $CaF2$ optical elements, and discuss qualitatively the approaches being considered to compensate for it. © 2002 Society of Photo-Optical Instrumentation Engineers.