  The self-accelerating beams such as the Airy beam show great potentials in
many applications including optical manipulation, imaging and communication.
However, their superior features during linear propagation could be easily
corrupted by optical nonlinearity or spatial incoherence individually. Here we
investigate how the interaction of spatial incoherence and nonlinear
propagation affect the beam quality of Airy beam, and find that the two
destroying factors can in fact balance each other. Our results show that the
influence of coherence and nonlinearity on the propagation of partially
incoherent Airy beams (PIABs) can be formulated as two exponential functions
that have factors of opposite signs. With appropriate spatial coherence length,
the PIABs not only resist the corruption of beam profile caused by
self-focusing nonlinearity, but also exhibits less anomalous diffraction caused
by the self-defocusing nonlinearity. Our work provides deep insight into how to
maintain the beam quality of self-accelerating Airy beams by exploiting the
interaction between partially incoherence and optical nonlinearity. Our results
may bring about new possibilities for optimizing partially incoherent
structured field and developing related applications such as optical
communication, incoherent imaging and optical manipulations.
