Hybrid topological evolution of multi-singularity vortex beams: generalized nature for helical-Ince–Gaussian and Hermite–Laguerre–Gaussian modes

Abstract

A generalized family of scalar structured Gaussian modes including helical-Ince-Gaussian (HIG) and Hermite-Laguerre-Gaussian (HLG) beams is presented with physical insight upon a hybrid topological evolution nature of multi-singularity vortex beams carrying orbital angular momentum (OAM). Considering the physical origins of intrinsic coordinates aberration and the Gouy phase shift, a closed-form expression is derived to characterize the general modes in astigmatic optical systems. Moreover, a graphical representation, Singularities Hybrid Evolution Nature (SHEN) sphere, is proposed to visualize the topological evolution of the multi-singularity beams, accommodating HLG, HIG and other typical subfamilies as characteristic curves on the sphere surface. The salient properties of SHEN sphere for describing the precise singularities splitting phenomena, exotic structured light fields, and Gouy phase shift are illustrated with adequate experimental verifications.

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

“…The special superposition of these modes can form a multi-singularity array with OAM, named the helical-IG (HIG) modes 80–82 :which carries multiple singularities with unit TC, having a total TC of v . Sharing the singularities hybrid evolution nature (SHEN) of the HIG and HLG modes, the SHEN mode is a very general family of structured Gaussian modes including the HG, LG, HLG, and HIG modes, the expression of which is 83 …”

“…(I) Intensity and (II) phase distributions of SU(2) vortex geometric modes for Ω = 1/4 ( d ) and Ω = 1/3 97 ( e ). SHEN spheres with orders of ( n , m ) = (3, 1) ( f ) and ( n , m ) = (0, 6) ( g ) along with represented mode (phase) fields at selected points 83 . b Reproduced from ref.…”

Structured Light from Lasers

“…Here, a ray‐based interpretation is used in conjunction with the Poincaré sphere analogy: the beam is represented by a two‐parameter family of rays, tracing out closed paths on a Poincaré‐like sphere for rays. The different classes of beams manifest as differing trajectories on this sphere, accounting for general propagation invariant beams, including ideal Bessel beams, airy beams, and generalized Gaussian beams, including Hermite–Laguerre–Gaussian beams, with the possibility to explore new classes of such structured light…”

Index-Tunable Structured-Light Beams from a Laser with an Intracavity Astigmatic Mode Converter

“…To generate a vortex beam, a classic and simple way is using cylindrical lens pair as astigmatic mode converter (AMC) to transform Hermite-Gaussian (HG) mode HG m,n into LG p, beam with index relationship of p = min(n, m) and = n − m [29][30][31]. With the AMC, the aim to generate a LG p, is equivalent to generate a HG m,n , while the required HG modes can be generated by using off-axis pumping in solid-state laser as an effective method [32][33][34].…”

“…With the AMC, the aim to generate a LG p, is equivalent to generate a HG m,n , while the required HG modes can be generated by using off-axis pumping in solid-state laser as an effective method [32][33][34]. However in this way, only HG modes with one-dimension tunable order can be generated directly from cavity, because symmetry in only one dimension could be broken along the off-axis displacement of pumping, in other words, leading to the converted LG beams with tunable OAM but untunable radial index (p = 0) [31,34]. By insert 2D artificial mask in cavity, a 2D high-order mode can be generated [35,36], but the fixed loss distribution prevents the mode indices from being freely tunable.…”