Divergence and self-healing of a discrete vortex formed by phase-locked lasers

Abstract

Optical beams carrying orbital angular momentum (optical vortices) are sought for various applications, such as optical communications, optical trapping and manipulation, and material processing. Many of these applications involve the propagation of such beams; therefore, the knowledge of various aspects such as beam size and beam divergence, as well as the effect of beam obstruction, is required. In this paper, we present a numerical study on the generation of high-power discrete vortices by phase locking a 1D ring array of lasers in a degenerate cavity that involves spatial Fourier filtering with a specifically designed amplitude mask. Further, we show that, for a given system size (number of lasers) and fixed distance between the nearest-neighbor lasers, the size of a discrete vortex and its divergence upon propagation do not depend on the orbital angular momentum (topological charge), as opposed to a continuous vortex (Laguerre–Gaussian/Bessel–Gauss beams). We also investigate the self-healing of a discrete vortex by obstructing it at the waist plane ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>z</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:math> ) as well as propagation plane ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>z</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:math> ), and we show that a discrete vortex possesses good self-healing abilities. The propagation of a truncated discrete vortex has enabled us to identify an unknown topological charge and the rotation dynamics of intensity in a discrete vortex.