Transformation of the singular skeleton in optical-vortex beams diffracted by a rectilinear phase step

Abstract

Based on the Kirchhoff-Fresnel approximation, we numerically analyze spatial characteristics of the light field formed after a circular Laguerre-Gaussian beam with a single-charged optical vortex (OV) passes the transparent screen with a rectilinear phase step. The main attention is paid to the localization and interactions of the OVs, which form the singular skeleton of the transformed field. The phase-step influence depends on its value and position with respect to the beam axis. Upon "weak perturbation" (low phase step) the main effect is that the OV is shifted from the initial axial position and describes a closed loop when the phase step is monotonously translated across the beam. The "strong perturbation" (the phase step is close to ) induces topological reactions with emergence and annihilation of additional singularities in the near-axial region of the diffracted beam cross section. These features are interpreted based on the 3D OV trajectories that show an intricate behavior with kinks and "retrograde" segments. The details of the OV migration and singular skeleton transformations reveal the fundamental helical nature and transverse energy circulation in the OV beams. The numerical results obtained in this paper show possibilities for the purposeful control of the singular skeleton characteristics within the transformed beam, and can be useful for the OV diagnostics, OV metrology and micromanipulation techniques.

Opto-Electronics Review

“…Finally, there is a very interesting and meaningful group of phenomena in which the "intrinsic" rotational properties of light (normally "hidden" in circular-vortex beams or non-singular beams with circular polarization) "come to light" due to breaking the beam symmetry [142]. An important special case is represented by the edge or slit diffraction of OV beams [196][197][198][199][200]: here, even a small violation of the circular symmetry leads to a singularity shift from the initial axial position, and, with further propagation, the singularity (or multiple singularities, if the incident OV was multicharged) describe the spiral-like 3D trajectories, brightly illustrating the helical nature of the OV beams [196].…”

Untitled

“…Note that the integrals of Eqs. ( 9) and ( 10) can be deduced into analytical expressions that are pretty complicated [32] , and numerical methods such as the fast Fourier transform (FFT) algorithm used in this paper are more convenient to simulate and analyze the evolution of the partially blocked OV beams.…”

“…A phase step is formed between the perturbed and 'survived' segments of the vortex beam and exhibits strong perturbation when the phase step value approaches π or d = 4 in Fig. 3(b) [32] . In this case, the two segments of the vortex beam interfere to the maximum extent.…”

Controllable singular skeleton formation by means of the Kummer optical-vortex diffraction at a rectilinear phase step

“…Among multiple fascinating physical effects associated with optical vortices (OVs) [1][2][3][4], the most impressive ones accompany the usual edge-diffraction phenomena [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Many aspects of the diffracted beam behavior expressively demonstrate the inherent OV properties, in particular, its helical nature and the transverse energy circulation, due to which the diffracted beam intensity profile effectively 'rotates' during the post-screen propagation [4,9,11,12].…”

“…Even a 'weak diffraction perturbation' (when the diffraction screen is placed at the far periphery of the beam cross section and the doughnut-shaped intensity distribution of the incident OV-beam visually preserves) induces the singularity displacement from its initial (axial) position; in the propagating diffracted beam, the singularity evolves along a spiral-like 3D 'trajectory' spectacularly demonstrating the OV rotational nature [13][14][15] (z-dependent evolution [16]). An incident circular OV with non-unity topological charge [1][2][3] m is decomposed into a set of |m| single-charged 'secondary' singularities which form an intricate 'singular skeleton' [3,16,18] of the diffracted beam. The secondary OVs evolve separately along complex spiral-like 3D trajectories which contain additional oscillations, pulsations and sometimes 'backward' segments [16,18]; when the beam structure is observed in a given cross section, such 'bendings' of the OV trajectory look as topological reactions [3,[15][16][17][18] with generation of 'new' OVs and annihilation of 'old' ones.…”