  Dynamic phase-only beam shaping with a liquid crystal spatial light modulator
is a powerful technique for tailoring the beam's intensity profile or wave
front. While shaping and controlling the light field is a highly researched
topic, dynamic nonlinear beam shaping has hardly been explored so far. One
potential reason is that generating the second harmonic is a degenerate process
as it mixes two fields at the same frequency. To overcome this problem, we
propose the use of type II phase matching as a control mechanism to distinguish
the two involved fields. We experimentally demonstrate that arbitrary intensity
distributions can be shaped in the frequency-converted field at the same
quality as for linear beam shaping and with conversion efficiencies similar to
the case without beam shaping. We envision this technique as a milestone
towards beam shaping beyond the physical limits of liquid crystal displays,
i.e. facilitating dynamic phase-only beam shaping in the ultraviolet spectral
range.
