Abstract
Theoretical and numerical analysis of the transmission function of the focusing system with high numerical aperture was conducted. The purpose of the study was to form a thin light tube in a focal area using the azimuthally polarized radiation. It was analytically shown that, due to destructive interference of two beams formed by two narrow rings, it is possible to overcome not only the full aperture diffraction limit but also the circular aperture limit. In this case, however, the intensity at the center of the focal plane is significantly reduced, which practically leads to the tube rupture. It was numerically shown that long thin one-piece tubes may be formed through the aperture apodization with diffractive axicon phase function or with complex transmission function of Laguerre-Gaussian or Airy-Gaussian beams.
Highlights
Introducing a narrow annular aperture to the tightly focused cylindrical beams with radial or azimuthal polarization, the blocking light in almost all central parts of the lens [1,2,3] is a simple but energetically expensive way of forming long narrow beams in the focal region
The formation of thin light tube by tightly focused azimuthally polarized light beams was investigated in the paper
It was theoretically shown that for the polar components the problem can be converted to a scalar one, and it can be solved by partitioning an aperture into narrow rings
Summary
Introducing a narrow annular aperture to the tightly focused cylindrical beams with radial or azimuthal polarization, the blocking light in almost all central parts of the lens [1,2,3] is a simple but energetically expensive way of forming long narrow beams in the focal region. The optimization procedures controlling the growth of the sidelobes lead to the inevitable broadening of the central spot size [12, 13] It was shown in [14] that the introduction of the radial phase jump on π radians for the midradius of the narrow annular aperture leads to a reduction of the central peak size to FWHM = 0.33λ for the radial polarization, which is less than a simple circular aperture result (FWHM = 0.36λ). This distribution is used in optical trapping and manipulation of solid microparticles and cold atoms [18, 19], in shadow microscopy, as well as in microscopy based on stimulated emission depletion: STED [20, 21]
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