Objective Optical systems (OSs) that produce bottle beams (BBs) are increasingly diversifying in the literature, according to recent studies. However, the practicability of most OSs is relatively limited, and it has been difficult to meet the increasingly flexible application requirements. Therefore, under the premise of satisfying the properties of the bottle light field, it is necessary to design a controllable OS to obtain a multifunctional BB. In the traditional axicon-lens OS, the incident light that produces the BB is generally a circular Gaussian beam (GB). With the diversification of BB systems and applications, the initial beam with a special shape has important research significance for the regulation of BBs. Therefore, in this study, we design an OS for BBs and use the polygonal aperture to control the light field and analyze its characteristics. The circular GB was modulated by the polygonal aperture into a polygonal beam with a special shape. The BB produced after passing through the axicon-lens OS carries multiple notches. This has potential application value for multiparticle capture and precise capture and is of great significance for the multifunctional application of BBs.

Methods In this study, the axicon-lens structure was an OS, and polygonal apertures were placed before the axicon, so the BB with multiple notches was generated after the focusing lens. Polygonal apertures, including regular triangles, regular quadrilaterals, and regular hexagonal, were taken as the research objects. First, we theoretically analyzed and derived their transmission aperture functions, and used the Collins formula to calculate the light field distribution formula after the BB passes through the axicon-lens. Then, we used MATLAB software to analyze the theoretical formula and obtain the diffraction spot pattern after the axicon-lens via simulation and studied the relationship between the polygonal aperture shape and central diffraction spot. Finally, an experimental device of the OS was developed by replacing the polygonal aperture and using the charge-coupled device camera to observe the BB with multiple notches behind the focusing lens. Further, the influence of the number and position of the sides of the polygonal aperture on the notch of the bottle optical trap was studied.

Results and Discussions First, compared with the circular GB, the special shape beam could be adjusted by the polygonal aperture to form a BB with multiple notches (Fig. 2). The number of sides of the polygonal aperture was the same as that of the BB. In addition, the spot image obtained in the experiment showed that the notch position of the BB corresponded to the polygonal aperture. When the side number of the polygonal aperture was odd, the notch position of the BB was complementary to the side position, the angular position was the same. When the number of sides of the polygonal aperture was even, the notch position of the BB was the same as the side position, complementary to the angular position. Therefore, we could qualitatively analyze the notch position of the BB generated according to the odd and even number of apertures (Fig. 5). Finally, we found that as the number of sides of the polygonal aperture increased, the notch size of the BB gradually decreased. It has important research significance of the capture of particles with different sizes.

Conclusions A circular GB was regulated by the polygonal aperture (regular triangle, regular quadrilateral, and regular hexagon), and the diffracted beam and BB formed by the axicon system were studied. In the research process, to ensure the generation of the BB, the focusing lens was placed at 46, 78, and 63 mm, respectively, and the formed BBs carried multiple notches. After the research, we found that the number of the notches of the formed BBs corresponded to the number of sides of the polygonal aperture. The notch position of the BB generated by the even-numbered side aperture was the same as the position of the side, whereas that of the BB generated by the odd-numbered side aperture was complementary to the position of the side, and the local area could be analyzed according to the number of sides of the aperture. In addition, the analysis showed that the notch size of the BBs decreased with the increase in the number of sides of the polygonal aperture. The notch of the BB of different sizes was the key to high-quality capture and stable trapped particles. The radius of the largest focal plane hollow spot of the BB was 0.41 mm. The hollow spot size of the bottle optical trap was in the order of hundreds of microns, which was more suitable for capturing and manipulating large-sized particles.