  We describe a micro-fabrication method to create concave features with
ultra-low surface roughness in silica, either on the end facets of optical
fibers or on flat substrates. The machining uses a single focused CO2 laser
pulse. Parameters are chosen such that material is removed by thermal
evaporation while simultaneously producing excellent surface quality by surface
tension-induced movement in a low-viscosity melt layer. A surface roughness
{\sigma}~0.2nm is regularly obtained. The concave depressions are
near-spherical close to the center with radii of curvature between 20 and
2000{\mu}m. The method allows the fabrication of low-scatter micro-optical
devices such as mirror substrates for high-finesse cavities or negative lenses
on the tip of optical fibers, extending the range of micro-optical components.
