Theory of small-scale self-focusing of spatially partially coherent beams and its implications for high-power laser systems

Based on the paraxial wave equation, this study extends the theory of small-scale self-focusing (SSSF) from coherent beams to spatially partially coherent beams (PCBs) and derives a general theoretical equation that reveals the underlying physics of the reduction in the B-integral of spatially PCBs. From the analysis of the simulations, the formula for the modulational instability (MI) gain coefficient of the SSSF of spatially PCBs is obtained by introducing a decrease factor into the formula of the MI gain coefficient of the SSSF of coherent beams. This decrease can be equated to a drop in the injected light intensity or an increase in the critical power. According to this formula, the reference value of the spatial coherence of spatially PCBs is given, offering guidance to overcome the output power limitation of the high-power laser driver due to SSSF.