Controlling nonlinear rogue-wave formation using the coherence length of phase noise

Weak phase noise present on an optical field can be amplified by a self-focusing nonlinearity (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>n</a:mi><a:mn>2</a:mn></a:msub><a:mo>></a:mo><a:mn>0</a:mn></a:mrow></a:math>) 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 than the beam diameter, the likelihood is minimally affected by a 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.