  A Si/Si3N4 high contrast grating mirror has been designed for a VCSEL
integration in mid-infrared ({\lambda} = 2.65 $\mu$m). The use of an
optimization algorithm which maximizes a VCSEL mirror quality factor allowed
the adjustment of the grating parameters while keeping large and shallow
grating pattern. The robustness with respect to fabrication error has been
enhanced thanks to a precise study of the grating dimension tolerances. The
final mirror exhibits large high reflectivity bandwidth with a polarization
selectivity and several percent of tolerance on the grating dimensions.
