We extend the concept of spiral zone plates along the optical axis and define a specific single optical element, termed as single-focus spiral zone plates (SFSZPs), for the generation of a single-focus vortex beam. The key idea is to make the transmittance of the spiral zone plates sinusoidal in the azimuthal direction. Furthermore, a two-parameter modified sinusoidal apodization window is introduced to modulate the transmittance function. Theoretical analysis reveals that the third-order diffraction light intensity of the SFSZPs could be reduced by more than three orders of magnitude compared to a conventional spiral zone plate. The experimental results are also presented, confirming the desired single-focus characteristics. The unique single-focus phase singularity properties imply that SFSZPs may find a wide range of imaging and microscopy applications, as well as fundamental studies of vortex beams.
We present composited holograms to realize the azimuthal interference of cylindrical optical lattices (COLs) and the flower modes (FMs) of Fourier transform-truncated Bessel beams (FT-TBB). Three types of binarization operations are evaluated for the composited holograms generated by two FT-TBB with independent topological charges l and l and the same radial index p=1. Both the numerical solutions and experimental results demonstrate that the four types of COLs and FMs, namely, the conventional COL, interleaved COL, flower-core FM, and polygon-core FM, can be produced by the Fourier transformation of the composited holograms with the same radial index p=1 and topological combinations ||l|-|l||<2, ||l|-|l||=2, ||l|-|l||=3, and ||l|-|l||=4, respectively. Moreover, a modified hologram with a scalar factor is introduced for further tailoring of these multi-ring azimuthal distribution profiles. The evolutions of the intensity profiles for various values of the scale factor are presented. Our results indicate that the modified hologram is capable of an in-depth exploration of the desired intensity profile of COLs and FMs, providing a flexible platform for a light potential probe and microscopy.
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