Using density-functional perturbation theory with a scissor correction, we
compute the entire photoelastic tensor of alpha -quartz. Its components, wh
ose absolute values range between 0.047 and 0.29 are all described within 0
.04. We also compute the Born effective charge tensor and present its varia
tion with respect to strain, as well as the relative deformation potentials
and the structural rearrangement caused by strain. Then, we discuss briefl
y the mechanisms involved in the photoelasticity of quartz.