Self-focusing of high-intensity beams with grid structures

Laser beams with high optical power propagating in a Kerr medium can undergo self-focusing when their power exceeds a critical power determined by the optical properties of the medium. The highly concentrated energy close to the in the region of the self-focus can lead to other nonlinear phenomena and cause significant irreversible damage to the material. We propose a transverse grid beam structure that effectively suppresses self-focusing even in the absence of other competing effects through the redistribution of optical power by inter-beamlet nonlinear interaction. We find that a beam with a $N \times N$ grid structure with optimized lattice spacing undergoes a dimension-dependent multi-stage self-focusing. We also identify specific grid layouts that can increase the total transmitted power beyond that permitted by the critical level of self-focusing for each beamlet. Lastly, we derive a general numerical relation between the optimal grid lattice spacing and the size of beamlets. Our results could potentially inform the use of beam shaping to prevent damage to optical components in high-powered and directed-energy applications.