Generation of Multiple Focal Hole Segments Using Double-Ring Shaped Azimuthally Polarized Beam

We investigated the focusing properties of a double-ring-shaped azimuthally polarized beam tightly focused with a high NA lens and a binary phase filter. We observe that by using 3 belts and 5 belts binary phase filters novel focal patterns including splitting of focal rings and multiring focus are obtained. We also found that a suitably designed phase structure can shift the focal rings along optical axis. The author expects such investigation is worthwhile for optical manipulation and material processing technologies. 1. Introduction Growing interest in the generation of three-dimensional (3D) optical beams that are dark regions in space surrounded by light is driven by wide ranging applications including dark optical traps for atoms [1], manipulation, guiding and binding of microparticles and biological cells [2], and erase beams for super-resolution fluorescence microscopy [3]. Such beams are also known as twice-closed tubular optical structure (TCTOS) [4], optical bubbles [5], and hollow dark spherical spots [6]. Optical beams with oscillating on-axis intensity due to interference resulting in 3D intensity voids and 3D optical chains were proposed recently for trapping of multiple particles along the beam propagation and for controllable particle delivery [7]. Over the past years, a variety of techniques have been proposed for generating such optical bottle beams for applications in optical tweezers and atom traps [8–15]. Recently, a subwavelength focal hole (~0.5 ) with a quite long depth of focus (~48 ) is achieved near the focus by tight focusing of double-ring-shaped azimuthally polarized beam with high NA lens axicon [16]. In this paper we investigate the focal properties of the tightly focused azimuthally polarized double-ring-shaped beam using 3 belts and 5 belts binary phase filters. We observed that by properly designing the binary phase filters one can achieve many novel focal patterns including splitting of focal rings and generation of multiring structures. 2. Theoretical Work A schematic diagram of the suggested method is shown in Figure 1. The analysis was performed on the basis of Richards and Wolf’s vectorial diffraction method [17] widely used for high-NA focusing systems at arbitrary incident polarization. In the case of the azimuthally incident polarization, adopting the cylindrical coordinates and and the notations of [18], the electric field in the vicinity of the focal region can be written as Here is relative amplitude, = arcsin ( ) is the maximum aperture angle with ( ) is the numerical aperture, and is the index of