Pseudo-nondiffracting beams generated by radial harmonic functions

Abstract

A Fourier hologram with the distribution of a radial harmonic function creates a nondiverging beam in the far field. The properties of this beam are analyzed and the beam is demonstrated. We also give a set of theorems that describe the relations between the hologram and the longitudinal distribution of the beam.

Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verifications

“…The analogous case to this phenomenon from diffraction theory can be found in Ref. 19. Thus the tilt and the effect of the noncentered zone-plate-like source together can explain the phenomenon that the first order is a peak above all the rest, which we observed in our experiments.…”

Rotation of microparticles with Bessel beams generated by diffractive elements

“…Earlier, the propagation of the BB through the optical system was studied in [33][34][35]. In [33] using the ABCD-matrix transform it was shown that, being imaged, the BB changes in scale, i.e.…”

“…It has been demonstrated that the diverging BB imaged by a spherical lens is also a diverging BB (see equation (21) in [34]). In [35] pseudo non-diffracting light beams were studied, the BB beams being a particular case. It was shown that a hologram of transmittance given by a radial angular harmonic (see equation (5) in [35]) is able to form a converging BB in the neighbourhood of the spherical lens' focal plane (see equation (12) in [35]).…”

“…In [35] pseudo non-diffracting light beams were studied, the BB beams being a particular case. It was shown that a hologram of transmittance given by a radial angular harmonic (see equation (5) in [35]) is able to form a converging BB in the neighbourhood of the spherical lens' focal plane (see equation (12) in [35]). However, it can be seen that in [33][34][35] the problem of imaging the diffraction-free BB was not considered and no conclusion was made as to the BB divergence in the region of imaging.…”

Nondiffracting images under coherent illumination

“…4,7 The second is the design of the phase and amplitude distributions at the image plane so that the diffracted field yields a desired transverse intensity pattern over an extended distance (focal depth). This has been attempted for continuous-phase masks 8 and proven successful only for very simple transverse images.…”