Displacements and evolution of optical vortices in edge-diffracted Laguerre–Gaussian beams

Abstract

Based on the Kirchhoff-Fresnel approximation, we consider behavior of the optical vortices (OV) upon propagation of the diffracted Laguerre-Gaussian (LG) beams with topological charge |m| = 1, 2. Under conditions of weak diffraction perturbation (i.e. the diffraction obstacle covers only the far transverse periphery of the incident LG beam), the OVs describe almost perfect 3D spirals within the diffracted beam body, which is an impressive demonstration of the helical nature of an OV beam. The far-field OV positions within the diffracted beam cross section depend on the wavefront curvature of the incident OV beam so that the input wavefront curvature is transformed into the output azimuthal OV rotation. The results can be useful in the OV metrology and for the OV beam's diagnostics. IntroductionDuring the past decades, light beams with optical vortices (OV) attract close attention of the optical community [1][2][3][4]. These intriguing optical objects, closely associated with the topological phase singularities, spectacularly illustrate the deep and fruitful optical-mechanical analogies and universality of physical laws [1-6] as well as provide a lot of inspiring applications in precise metrology [7][8][9][10][11][12][13][14], information transfer and processing [15][16][17] and micromanipulation techniques [18][19][20]. In particular, the edge diffraction of OVs has been studied intensively [21][22][23][24][25][26][27][28][29][30][31][32][33] enabling visual manifestation of the unique OV properties associated with their helical nature. One of the most impressive evidences of the helical energy flow in OV beams is the recently revealed spirallike motion of the OV cores (amplitude zeros) within the diffracted beam cross section, that occurs when the screen edge performs a monotonous translation in the transverse direction towards or away from the beam axis [31][32][33].The similar rotational motion of the OV cores is expected when the screen edge rests but the longitudinal evolution of the propagating diffracted beam is observed behind the screen. Under such conditions, the evolution of phase singularities in propagating edge-diffracted beams was studied in many details [28][29][30]. In these works, the main attention was paid to severely screened OV beams, in which the diffracted beam structure is strongly perturbed by the obstacle, and its evolution is accompanied by multiple topological events: the OV disappearance and regeneration, emergence of new OVs, their interactions and topological reactions, etc. This performance is interesting and valuable for diverse metrological purposes but the presence of additional factors mask the expected

Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams

“…Generally, they show more regular and smooth behavior than in the case of Kummer beam, which is associated with the slower decay and oscillations of the Kummer beam intensity at r >> b [18,28]; remarkably, the analytical model of Eqs. (19), (20) give not only qualitative but also the fair quantitative characterization of the trajectory B even if a  b (see Fig. 4a where the trajectory obtained analytically from Eqs.…”

“…4a where the trajectory obtained analytically from Eqs. (19), (20) with M = 0 is presented as the thin dotted spiral; note that its final point corresponds to a = 1.2b). Upon calculations, the 'jumps' were identified as events at which the additional pair of OVs emerge.…”

“…However, this is not the case with structured light fields that have become a hot topic of modern optics during the past decades [3], especially, with light beams carrying optical vortices (OV) [4][5][6]. The edge diffraction of circular OV beams [7][8][9][10][11][12][13][14][15][16][17][18][19][20] shows many impressive non-trivial details associated with their special physical attributes: helical wavefront shape and transverse energy circulation. Even upon conditions of small diffraction perturbation (when the diffraction obstacle obscures just a far periphery of the beam cross section), the common and well studied diffraction effects (fringes, transverse diffusion of the light energy, etc.…”

“…It is well established, both theoretically and in experiment, that after diffraction of an incident circular OV beam, the singularity shifts from its initial axial position, and an m-charged OV is decomposed into a set of |m| secondary single-charged ones thus forming the 'singular skeleton' [6] of the diffracted beam. Upon the diffracted beam propagation, the OV cores move along intricate spiral-like trajectories [16,20] carrying distinct 'fingerprints' of the incident beam and its disposition with respect to the diffraction screen. The similar evolution of the singular skeleton can be observed in a fixed cross section of the diffracted beam when the screen edge performs a monotonous translation in the transverse direction towards or away from the beam axis [17][18][19].…”

Optical-vortex diagnostics via Fraunhofer slit diffraction with controllable wavefront curvature

“…1b). It can be solved based on the known fact [34]: If the beam with initial CA distribution   , a a u x y produces the diffracted field described by   , u x y (cf. Fig.…”