A circular Lorentz–Gauss beam is introduced. The analytical optical field of the circular Lorentz–Gauss beam passing through a paraxial optical system is derived. Based on the second- and higher-order moments of the light intensity, the analytical beam propagation factor of a circular Lorentz–Gauss beam and the analytical kurtosis parameter of a circular Lorentz–Gauss beam passing through a paraxial optical system have also been derived. The properties of the circular Lorentz–Gauss beam propagating in free space are demonstrated. The normalized intensity distribution, the beam half width, the beam waist, the divergence, the beam propagation factor, and the kurtosis parameter of the circular Lorentz–Gauss beam are compared with those of the corresponding Lorentz–Gauss beam, respectively. The main difference between the circular Lorentz–Gauss and the Lorentz–Gauss beams is their different peripheries. The circular Lorentz–Gauss beam has better symmetry than the Lorentz–Gauss beam. The beam propagation factor of the circular Lorentz–Gauss beam is always slightly larger than that of the Lorentz–Gauss beam. Therefore, the circular Lorentz–Gauss beam is the enrichment and supplement of the existing Lorentz–Gauss beam.
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