  Light beams carrying orbital angular momentum (OAM) have led to stunning
applications in various fields from quantum information to microscopy. In this
letter, we examine OAM from the recently discovered high-harmonic generation
(HHG) in semiconductor crystals. HHG from solids could be a valuable approach
for integrated high-flux short-wavelength coherent light sources. The solid
state nature of the generation medium allows the possibility to tailor directly
the radiation at the source of the emission and offers a substantial degree of
freedom for spatial beam shaping. First, we verify the fundamental principle of
the transfer and conservation of the OAM from the generation laser to the
harmonics. Second, we create OAM beams by etching a spiral zone structure
directly at the surface of a zinc oxide crystal. Such diffractive optics act on
the generated harmonics and produces focused optical vortices with nanometer
scale sizes that may have potential applications in nanoscale optical trapping
and quantum manipulation.
