Model of a four-petal Lorentz-Gauss beam and its paraxial propagation

The concept of a four-petal Lorentz-Gauss beam was first introduced, which is consisted by Lorentz part and Gaussian part. Based on the Collins integral formula, the equation of a four-petal Lorentz-Gauss beam propagating in ABCD optical system was derived. The propagation properties of a four-petal Lorentz-Gauss bean in free space was illustrated and analyzed using numerical examples. The intensity distributions of four-petal Lorentz-Gauss beam can be modulated by the beam waist of Lorentz part, and the beam will evolve into a larger Gaussian-like beam in the center around by smaller beamlets in the far field.