Optical vortices in focal regions

We show that imaging a non-diverging Bessel beam by a spherical lens leads to the generation of a diverging Bessel beam. Expressions for the projections of the Umov-Poynting vector for a two-dimensional TE-polarized Bessel beam and a three-dimensional paraxial linearly polarized Bessel beam are derived. A fifth-order Bessel beam is produced using a single optical element-a 16-level phase-only diffractive helical axicon fabricated using electron beam lithography. This beam was successfully used to trap and rotate 5-10 μm diameter yeast particles and polystyrene beads of diameter 5 μm.

Rotation of microparticles with Bessel beams generated by diffractive elements

Nondiffracting stationary electromagnetic field

Evolution of focused Hankel waves and Bessel beams

The focusing evolution of apertured propagation invariant optical fields (PIOFs) with arbitrary transverse intensity distribution is analysed in detail. A decomposition of the PIOF into its constituent plane waves is applied to find a simple expression of the normalized intensity along the propagation axis which is valid for any PIOF. It is shown that the presence of an apparent focus close to the focal plane is a general property of any focused PIOF and that it is not related to the focal shift due to apertures. By selecting appropriate parameters it is possible to generate a second intense peak beyond the focal plane. Additionally, we define the conditions under which the original PIOF can be reconstructed beyond the focal plane with a desired magnification.

Focusing evolution of generalized propagation invariant optical fields

The nondiffractive propagation of the ideal zero-order Bessel beam is explained in terms of both the geometrical imaging and the interference of spherical waves emitted from the ring source. The source shift with respect to the focal plane of the imaging system is simply related to the divergence of the produced beam. The intensity distribution of the ideal Bessel beam in the focal region is examined for an aberration-free lens of finite aperture. Both the resolution gain at the focal plane and the position of the axial intensity maximum are investigated in dependence on the truncation of the input Bessel beam.

Marek Olivik

Papers

Bessel beams in the focal region