Fractal Light Vortices

Abstract

Vortex lenses produce special wavefronts with zero-axial intensity, and helical phase structure. The variations of the phase and amplitude of the vortex produce a circular flow of energy that allows transmitting orbital angular momentum. This property is especially in optical trapping, because due to the orbital angular momentum of light, they have the ability to set the trapped particles into rotation. Vortex lenses engraved in diffractive optical elements have been proposed in the last few years. These lenses can be described mathematically as a two-dimensional (2D) function, which expressed in polar coordinates are the product of two different separable one-dimensional (1D) functions: One, depends only on the square of radial coordinate, and the other one depends linearly on the azimuthal coordinate and includes the topological charge. The 1D function that depends on the radial coordinate is known as a zone plate. Here, vortex lenses, constructed using different aperiodic zone plates, are reviewed. Their optical properties are studied numerically by computing the intensity distribution along the optical axis and the transverse diffraction patterns along the propagation direction. It is shown that these elements are able to create a chain of optical traps with a tunable separation, strength and transverse section.

Digital Sorting of Optical Vortices in Perturbed Singular Beams

“…At the same time, the speckle structure is formed by the skeleton of optical vortex array [13][14][15]. In turn, the analysis of such a complex vortex structure is conveniently carried out on the basis of vortex fractal techniques [16] (see also [17] and references therein). There are a variety of approaches for the fractal vortex models of laser beams scattered by biological tissues [18,19] based on the light scattering by nonspherical particles [20] that involves the representation of the wave field in terms of Legendre polynomials.…”

Diffractive Corneal Inlays: A New Concept for Correction of Presbyopia

“…In this chapter we describe a new concept of CI developed by our research group that is based on the concept of diffraction. It consists of a variation of an amplitude Fresnel zone plate [15] in which micro-holes conform the clear zones of the zone plate in a similar way as was proposed to construct the so-called photon sieves [16]. Photon sieves were conceived for its use in X-ray microscopy but were also found to have numerous applications in various scientific and technological areas [17][18][19].…”

Composite Spiral Zone Plate

“…The spiral phase plates were combined with fractal zone plates to produce a sequence of focused vortices along the propagation direction [23]. Fibonacci lenses and Thue-Morse lenses were also proposed to produce twin-focused-vortices beams [24], [25]. Recently, fractal spiral zone plates have been proposed to generate a series of focused vortices along the optic axis [26].…”