Simplified algorithms of computational holograms: II – for generation of the optical beams and vortices

Beam in optics refers to a monochromatic solution of the wave equation that has transverse field concentration. The optical beam that is described by a superposition of plane waves arises from the need to be able to confine and transport light through free space without suffering the effects of diffraction, remaining invariable during propagation. The most common type of optical beam is the Gaussian beam, whose transverse pattern is described by a Gaussian function, which is subject to diffraction effects. There are other types of beams called non-diffractive or diffractive-resistant beams that do not present diffraction effects and their intensity profile is constant along the propagation direction. Non-diffractive beams include, for example, Bessel beams, Mathieu beams, Parabolic beams, Airy beams and superpositions of these beams. The purpose of this work is to present and make available to the academic, scientific and other areas of knowledge our studies and algorithms (routines) for holographic generation of optical beams in an accessible and didactic way. Specifically, in this second article, we intend to study theoretically and computationally the properties of optical beams: Gaussian, Bessel, Airy, Laguerre-Gauss and Hankel-Bessel optical vortices; as well as the techniques for generating amplitude and phase computational holograms of these beams using MATLAB. These present interesting possibilities of experimental realization through their optical reconstruction (reproduction) using SLMs devices, as has been experimentally validated in numerous published works and in numerous applications in optics and photonics.

Keywords:
Holography; Computer generated holograms; Optical beams; Vortices; Structured Light; MATLAB