In the design and construction of ultra-high-peak-power laser systems, it is necessary to control the accumulated B-integral of the laser pulse, but currently there are no reasonable B-integral control standards for picosecond and femtosecond lasers. We systematically evaluate the influence of the B-integral on the output capability of picosecond and femtosecond laser systems for the first time, to our knowledge, taking Nd:glass lasers and Ti:sapphire lasers as examples. For picosecond lasers, the temporal domain compressibility and the small-scale self-focusing effect restrict the B-integral to 1.7 and 1.9, respectively. For femtosecond lasers, the B-integral is mainly restricted by the small-scale self-focusing effect and the far-field focusability, which limit the B-integral to 1.5 and 1.7, respectively. The restriction made by far-field focusability can be largely relaxed by inserting a deformable mirror. The study of the factors restricting the B-integral will provide guidance for the design of ultra-high-peak-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.

It was shown experimentally that for a 65-fs 17-J pulse, the effect of filamentation instability, also known as small-scale self-focusing, is much weaker than that predicted by stationary and nonstationary theoretical models for high B-integral values. Although this discrepancy has been left unexplained at the moment, in practice no signs of filamentation may allow a breakthrough in nonlinear pulse post-compression at high laser energy.