Abstract
The generation of subwavelength spots smaller than the Abbe diffraction limit has attracted great interest due to the various applications in many fields, such as high-density optical data storage and particle manipulation. Planar optics that can miniaturize conventional refractive optics have become increasingly attractive. In this work, we first formed a subwavelength bright spot and a three-dimensional optical trap under the illumination of an azimuthally polarized (AP) beam by only a single planar element, a spiral zone plate (SZP). Initially, the SZP was proposed as a computer-generated hologram to generate optical phase singularities. However, the SZP in this work was used to focus and modulate the incident AP beam with a vortex phase simultaneously. Therefore, no additional vortex phase modulating element was introduced in our method. The SZP has an ultra-long focal length of 250λ for a numerical aperture (NA) of 0.95 and an incident wavelength of 632.8 nm. The generated spot is purely transversely polarized with a lateral full width at half maximum (FWHM) of 0.43λ beyond the diffraction limit of 0.54λ. The generated focal field formed a stable optical trap for a Rayleigh dielectric particle in three dimensions.
Highlights
Subwavelength spots smaller than the Abbe diffraction limit have attracted great interest due to their wide applications in photolithography[1, 2], high-density optical data storage[3], super-resolution imaging[4, 5] and particle manipulation[6, 7]
A bright focal spot is achieved by the single planar element because the vortex 0–2π phase introduced by the spiral zone plate (SZP) converts the deconstructive interference between the transverse focal components to the constructive interference[18]
It is clear that the focal spots generated by the proposed method of azimuthally polarized (AP) + SZP are always the smallest and beyond the diffraction limit. These results demonstrate the proposed method of generating a subwavelength spot under the illumination of AP light beam by only a single planar element
Summary
When the topological charge p is 1, the SZP implements a vortex 0–2π phase modulation. The SZP can focus and encode the incident beam with a vortex phase simultaneously. The phase structure of the first-order SZP with Nmax = 24 is shown, and it is planar spiral and no longer circularly symmetrical. According to the vector diffraction theory, the electric field components near the focus of a first-order SZP illuminated by an AP beam can be written as[16, 25]. P(θ) is the amplitude of the incident field, and the Bessel-Gaussian beam is employed in this work, which is expressed as. According to the geometrical relationship between the Cartesian coordinates and the cylindrical coordinates, the radially and azimuthally polarized components of the focal electric field can be expressed as. The magnetic field components Hz, Hy and Hz can be calculated based on Maxwell’s equations by replacing [−sinφ, −cosφ, 0]′ on the right side of equation (3) with n1ε0c[−cosφcosθ, −sinφcosθ, sinθ]′. ε0 is the vacuum dielectric constant and c is the speed of light in vacuum
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