Femtosecond laser filamentation with various orders of Mathieu beam in air

We have numerically studied the femtosecond laser filamentation with various orders of Mathieu beam in air. Simulations show that for the case of zero-order Mathieu beam, the on-axis filament together with two side filaments are formed, whereas the first-order and second-order Mathieu beams can generate the on-axis filaments twice due to the diffraction-free property. Moreover, zero-order Mathieu beam enhances the supercontinuum (SC) generation in the visible and ultraviolet spectrum due to the coherent superposition of MFs, while the other two Mathieu beams enhance the long-wavelength region owing to the steep gradient of the back part of the pulse during propagation.