Complete Analytical Expression of Lorentz-Hermite-Gauss Laser Beams
G-Q. Zhou, Z-Y. Ji and G-Y. Ru
When the Lorentzian distribution is modulated by the Hermite-Gaussian function the outcome is just the Lorentz-Hermite-Gaussian (LHG) laser beam. Analytical expression of the LHG laser beams passing through an ABCD paraxial optical system is derived. Analytical expressions of the second-order and the fourth-order light moments of the LHG laser beams are presented in the source plane, respectively. Based on the second-order and the fourth-order light moments, the beam propagation factor, the beam half width, and the kurtosis parameter of the LHG laser beam passing through an ABCD paraxial optical system can be obtained. As a numerical example, the propagation characteristics of the LHG laser beam are demonstrated in free space. Moreover, the comparison with the corresponding standard Hermite-Gaussian (SHG) laser beam is also performed. When the LHG laser beam propagates from the source plane to the near field, the LHG laser beam changes its profile. When the LHG laser beam propagates from the near field to the far field, the LHG laser beam keeps stable. When the width parameters of the Lorentzian part in the transverse directions is smaller than the waist of the Gaussian part, the evolutionary process of the LHG laser beam is varied. Due to the varied evolutionary process, the LHG laser beams can be used to describe specially distributed laser beams that cannot be characterized by the existing SHG laser beam model; therefore, the LHG laser beam model enriches and supplements the existing laser beam model.
Keywords: Lorentz-Hermite-Gaussian (LHG) laser beam, standard Hermite- Gaussian (SHG) laser beam, beam propagation factor, beam half width, kurtosis parameter