Conditions for repulsive Casimir forces between identical birefringent materials

Repulsive Casimir-Lifshitz forces are known to exist between two dissimilar materials if a third material, whose dielectric response is intermediate, separates them. However, the force between two identical materials is almost always attractive. Here we show that the force between two identical, semi-infinite birefringent slabs can be repulsive for particular orientations and compare the conditions for repulsion in this system to those of isotropic materials. We examine the dependence of the Casimir-Lifshitz force on retardation and relative orientation in this system and discuss situations in which the force can be changed from attractive to repulsive as a function of both distance and rotation angle.