Fig. 1. Optical system of rectangular aperture with different aspect ratios

Fig. 2. Simulated light spot maps behind axial pyramid and on focal plane behind focuing lens after the light is regulated by rectangular apertures with length-width ratio of 0.9，0.6, and 0.3, respectively. (a)(c)(e) Simulated light spot maps behind axial pyramid; (b)(d)(f) simulated light spot maps on focal plane behind focuing lens

Fig. 3. Relationship among R, Δz, and z₀

Fig. 4. Simulated process from beginning to closing of three-dimensional closed region of a localized hollow beam formed by rectangular apertures with different length-width ratios

Fig. 5. Experimental process from beginning to closing of three-dimensional closed region of a localized hollow beam formed by rectangular apertures with different length-width ratios

Fig. 6. Interaction between light and particle. (a) The center of localized hollow beam is above the center of particle; (b) the center of localized hollow beam is below the center of particle

Fig. 7. Longitudinal gradient force and scattering force in localized hollow beam at σ＝0.9. (a)-(c) Longitudinal gradient force; (d)-(f) scattering force

Fig. 8. Comparison diagrams of transverse gradient force (F_grad-x) and gravity plus Brownian force (G＋F_B) on a gold particle with radium of 150 nm in localized hollow beam when length-width ratio is 0.9, 0.6, and 0.3, respectively