Tight focusing of a radially polarized Laguerre–Bessel–Gaussian beam and its application to manipulation of two types of particles

• The tightly focusing of radially polarized LBG beams is examined.
• The focusing performances of LBG beams are preferable over that of LG and BG modes.
• A bright spot and an optical cage can be formed by special phase modulation.
• These special focusing patterns can stably manipulate two types of particles.

The intensity distributions near the focus for radially polarized Laguerre–Bessel–Gaussian beams by a high numerical aperture objective in the immersion liquid are computed based on the vector diffraction theory. We compare the focusing properties of the radially polarized Laguerre–Bessel–Gaussian beams with those of Laguerre–Gaussian and Bessel–Gaussian modes. Furthermore, the effects of the optimally designed concentric three-zone phase filters on the intensity profiles in the focal region are examined. We further analyze the radiation forces on Rayleigh particles produced by the highly focused radially polarized Laguerre–Bessel–Gaussian beams using the specially engineered three-zone phase filters.