The Propagation Properties of a Lorentz–Gauss Vortex Beam in a Gradient-Index Medium

Abstract

Based on the Huygens–Fresnel integral and ABCD matrix, the propagation equation for the Lorentz–Gauss vortex beam (LGVB) in a gradient-index medium (GRIN) is rederived. The evolution of the intensity and phase distributions of an LGVB through a GRIN medium are numerically calculated as a function of the gradient-index parameter with changes in the incident beam parameters. The results showed that the propagation path and intensity distributions changed periodically with increasing propagation distance. In contrast, phase distributions change at multiples of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>π</a:mi><a:mo>/</a:mo><a:mi>β</a:mi></a:math> or <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"><c:mn>2</c:mn><c:mi>π</c:mi><c:mo>/</c:mo><c:mi>β</c:mi></c:math> , depending on whether the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"><e:mi>M</e:mi></e:math> values are odd or even, respectively. At the same time, the parameters of the gradient index determine the periodic values of the Lorentz–Gauss vortex beams during propagation, and as <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M4"><g:mi>β</g:mi></g:math> increased, the period of evolution decreased. The Lorentz–Gauss vortex beam propagating through the gradient index will develop from a square beam to a Gaussian vortex beam more quickly with an increase of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M5"><i:msub><i:mrow><i:mi>w</i:mi></i:mrow><i:mrow><i:mn>0</i:mn><i:mi>x</i:mi></i:mrow></i:msub><i:mo>=</i:mo><i:msub><i:mrow><i:mi>w</i:mi></i:mrow><i:mrow><i:mn>0</i:mn><i:mi>y</i:mi></i:mrow></i:msub></i:math> . In addition, the topological charge affects the size of the dark spot at the center of the beam and the size of the beam, causing the phase distributions to change periodically in the medium. This study is beneficial for laser optics and optical communications.

Topics & Concepts