Extending optical filaments of annular beams via square root spatial phase modulation

Abstract

The femtosecond annular Gaussian beam with square root spatial phase modulation propagation in air is investigated. The numerical simulations show that the filament length can be extended about two times, in contrast to the linear spatial phase modulated annular Gaussian beam Although the onset distance of the filamentation is not the same as the linear spatial phase modulation under the same conditions, the problem can be addressed by adding a Gaussian core to the beam. The results of the paper may inspire potential applications in a lot of fields, such as laser-guided electric discharge and remote sensing.