In this paper, we theoretically and numerically consider the sharp focusing of a laser beam whose polarization pattern in the initial plane is a superposition of a cylindrical vector beam of order m and a homogeneous linear polarization. At the focal spot of such a beam, for odd m, there will be areas with elliptical or circular polarization with alternating directions of rotation. For even m at the focal spot, the field is linearly polarized at every point and has no transverse energy flux. These beams can be used to create a micromachine in which two microparticles in the form of gears are captured in the focal spot of the beam into neighboring local areas in which the energy flux twists in various directions, and therefore, these gears will also twist in various directions.
Hybridly polarized beams have attracted increasing attention in recent years. Due to the features of spatial polarization and phase singularity, they can be used in STED microscopy, as optical tweezers, in nanoprocessing, to excite surface plasmon polaritons, in nonlinear optics, in quantum optics, and in telecommunication technologies. In this work, using the FDTD method, we simulated the passage of laser radiation through a binary spiral zone plate with a fractional order m=0.5 and a focal length of 0.532 μm. Quartz glass n=1.5 was assumed as the material for the relief of the zone plate. The zone plate radius was 4 μm. A TE polarized Gaussian beam with a wavelength of 0.532 μm was fed to the input. In this work, the intensity distribution and the Poynting vector in focus were studied. The possibility of forming an optical vortex with a fractional order was demonstrated.
By simulating sharp focusing of vector beams with azimuthal polarization of fractional order 0 < m <1 (m = 1 is azimuthal polarization, m = 0 is linear polarization), it was shown that the shape of the intensity distribution in the focal spot changes from annular (m = 1) to round (m = 0.5) and then to elliptical ring (m = 0). The opposite changes we can see for the shape of the distribution of the longitudinal component of the Poynting vector (energy flux) in the focal spot: from annular (m = 1) to elliptical (m = 0.5) and then to circular ring (m = 0). The diameter of the focal spot at full width at half maximum for a beam with azimuthal polarization (m = 1) with an optical vortex of the first order for a numerical aperture NA = 0.95 is 0.46 of the wavelength, and the diameter of the axial energy flux for linearly polarized light (m = 0) is 0.45 of the wavelength. Because of this, the answers to the questions: Whether the focal spot is round or elliptical and whether the focal spot is minimal: with azimuthal polarization with a vortex or with linear polarization without a vortex, depend on whether we are considering the intensity at the focus or the energy flow.
By simulating tight focusing of vector beams with azimuthal polarization of fractional order, the effect of the deviation of the beam order from m = 2 (i.e., the case when the backflow is observed at the center of the focal spot) was investigated. It was shown that the reverse flow is retained in the center of the spot even with a significant deviation of the beam order from m = 2 - it is retained up to m = 1.55.
Using simplified two-dimensional finite element method (FEM) modeling we study such structures where the triangular dielectric prism is used for producing nano-jets. The soda-lime glass (n=1.46), polystyrene (n=1.56), polyester (n=1.59), barium titanate (n=1.8) is considered as material of the prism. The width of the triangular prism base is fixed at 60 um while the height is varied to obtain optimal focal spot parameters such as maximum intensity, full width and depth at half-maximum of intensity. The linear polarized Gaussian beam with a wavelength of 4 um and the waist width of 80 um is taken as the input radiation. All numerical simulations were carried out by COMSOL Multiphysics which used irregular grids with variable steps for FEM. The small step equal to 0.1 um was used in regions which are close to the interface between two media, while the other area is described by grids with steps of 0.2 um. Comparison of simulation results for dielectric triangular prism and simulation results for dielectric circular cylinder shows that prism can produce the narrower focal spot. It can be also noticed that there are resonance modes similar to the whispering gallery modes are formed inside the triangular dielectric prism. The influence of these modes on light focusing is also studied.
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