  Weak phase noise present on an optical field can be amplified by a
self-focusing nonlinearity and form intense "rogue wave" features. Here, we
study the effect of the coherence length (or grain size) of this phase noise on
the likelihood of rogue wave formation in the presence of a self-focusing
nonlinearity. We show that while the likelihood of rogue wave formation
increases with laser power when the coherence length is only slightly smaller
that the beam diameter, the likelihood is minimally affected by change in laser
power when the coherence length is significantly smaller than the beam
diameter. Our study provides insight into the interaction of nonlinearity with
phase instabilities on a field, and could be useful in applications such as
reducing the effect of turbulence-induced breakup of intense laser beams, and
developing radiance limiters to reduce the focusable power in a beam.
