Evolution of X-Gaussian-shaped beam with different frequency spectra

The propagation of X-Gaussian-shaped beam with different frequency spectra is studied. Results show that different X-shaped beams can be generated by using different frequency spectra. There are many differences among these X-shaped beams due to the change of the spectrum. Although the effect of the waist width of the Gaussian part of the X-shaped beam on the initial intensity distribution is very small, the effects of the waist width of the Gaussian part on the evolution of the X-Gaussian-shaped beam is very large.