Controlling high-power autofocusing waves with periodic lattices

We show numerically that by using radial symmetric lattices, the focal spot characteristics and filament peak intensity of high-power autofocusing waves can be controlled. The lattice induced diffraction is able to isolate the main on-axis peak and control the focus position. In addition, at higher power the lattice can control and stabilize the peak intensity of the filament over an extended distance.