This paper brings together two phenomena that can each produce surprising optical focusing effects - partial coherence and the Kerr effect - and explores their interaction.  Nonlinear materials exhibiting the Kerr effect have a refractive index that changes as a function of the intensity of the propagating light, and can induce either a "self-focusing" or "self-defocusing" effect.  Partially coherent beams lie in the space between fully coherent fields (e.g., those produced by a single-mode laser) and highly incoherent fields (such as the light emitted by a fluorescent bulb).  In many cases, converging or diverging partially coherent beams can be conveniently described by the Gaussian-Schell model (GSM).  The mathematical rigor offered by the GSM allows quantitative exploration of partial coherence effects.  For example, Gbur and Wolf showed how partially coherent beams may propagate more robustly in a turbulent atmosphere.

In this paper, Hu and coworkers relate GSM beams, Kerr media, and the common ABCD method for beam propagation. The techniques are presented clearly and in the context of previous work in the field.  The authors also helpfully describe how their model reduces to established relationships in cases where the Kerr parameter goes to zero (linear propagation) or the degree of coherence becomes infinite (fully coherent beam).  These new tools are applied to the case where the ABCD model is used to represent a lens, resulting in useful focusing metrics.  Discussion of these metrics illustrates the interplay of material nonlinearity, beam intensity, beam coherence and the focal properties of the lens; and suggests how this new understanding can be used to control partially coherent propagation in nonlinear media. 

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