Map of spatial-dispersion induced birefringence losses in single-crystal silicon

We report measurements of the birefringence-induced losses in silicon single crystals for [001] and [111] crystallographic orientation and for different doping levels. These results are compatible with the so-called spatial-dispersion-induced birefringence in cubic crystals. These angular maps have been used to fix some tolerances for the next generation of optics in the Virgo gravitational-wave detector