Due to the unique physical properties of hollow beams, such as cylindrical intensity distribution, small dark spot size, no heating effect, propagation invariance, as well as spin and orbital angular momentum, hollow beams exhibit broad application prospects in fields such as excitation fields, field information processing, particle waveguides, isotope separation, microelectronics and materials science, biotechnology, medicine, and atomic and molecular science. This study proposed a new hollow beam model and adopted Collins formula theory to derive analytical expressions of diffraction propagation field of the new beam in free space and a spherical aberration aperture lens system.

Taking the typical parameters of hollow beams as examples, this study conducted detailed numerical simulations on the spatial distribution characteristics of this new type of hollow beam in free space. The numerical results revealed that the characteristic parameters (m, n) of the beam had different effects on the spatial distribution of the new type of hollow beam, and the influence degree and influence pattern varied. As the value of n increased, the hollow width of the new type of hollow beam increased, and the sharpness of the hollow edge of the light field improved. As the value of m increased, the variation pattern of the hollow width of the light field was not obvious. An increase in the value of m could produce a convergence effect on the energy of the light field, with the energy concentration around the hollow surface higher than that of traditional models. When the new type of hollow beams with different values of m propagated in free space, the spatial distribution of field intensity exhibited a polygonal ring shape of the hollow beam, indicating that the new type of hollow beam possessed diffraction propagation characteristics with an unchanged surface shape during free-space propagation, which was consistent with the propagation invariance property of hollow beams. In contrast, when the new type of hollow beam propagated in free space, its spatial distribution of field intensity had its unique spatial characteristics compared to the surface shape of traditional hollow beams. The center of the light field exhibited a well-uniform hollow distribution, and the edge light intensity presented regular N-sided polygonal edge distribution as the beam characteristic parameters (m, n) changed. The number of polygon sides was equal to the value of m, and the field intensity on each side followed a Gaussian-like spatial distribution, which was arranged at equal intervals along the beam edge. Compared to traditional hollow beams, the uniformity of field intensity in the hollow region of the new type of hollow beam was superior.

Secondly, this study numerically simulated the spatial distribution characteristics of diffraction field after the new hollow beam passed through spherical aberration lens. The results indicated that the spherical aberration coefficient exerted a significant impact on the spatial distribution of the light intensity of the new hollow beam. As the spherical aberration coefficient increased, the area of the hollow region in the new hollow beam expanded, and the sharpness of the field intensity boundary became better. Compared with the mentioned research results, it was found that the spherical aberration lens system had a weakening effect on the polygonal characteristics of the spatial distribution of the new hollow beam. The Gaussian profile at the field-intensity edge became significantly weakened, and the polygonal trace was significantly reduced. Compared with the free space, the uniformity of the field intensity in the hollow region and the edge light intensity was better. As the spherical aberration coefficient increased, the lateral length of the hollow region of the hollow beam increased sequentially, and the sharpness of the field intensity boundary in the hollow region kept improving. This characteristic compensated for the use error of the lens system and had practical application significance.

The proposed new type of hollow beam model will provide a new theoretical basis and description for the experimental design and generation of hollow beams.