When a circularly-symmetric light beam with optical vortex (OV) diffracts at an opaque screen with the sharp edge, the OV core is displaced from the beam axis and, in case of the mcharged incident OV, decomposed into |m| single-charged ones. By means of numerical simulations and based on examples of incident beams with topological charges |m| =1, 2, 3 we show that, while the screen edge monotonously advances towards the beam axis, the OVs in the diffracted beam cross section move away from the incident beam axis along spiral-like trajectories. The trajectories contain fine structure details that reflect the nature and peculiar spatial configuration of the diffracting beam. For the Kummer beams' diffraction, the trajectories contain self-crossings and regions of "backward" rotation (loops); in case of Laguerre-Gaussian beams, the trajectories are smoother. The numerical results are supported by analytical approximations and conform with experiment The general shape of the trajectories and their local behavior show high sensitivity to the diffraction conditions (spatial structure of the diffracting beam, its disposition with respect to the screen edge, etc.), which can be used in diverse metrological applications. Besides the rich and impressive physical contents, including the phase singularities, internal energy circulation, specific features of the linear and angular momentum distributions [4][5][6], such beams offer a wide range of perspective applications in the micromanipulation techniques [7][8][9][10], information transfer and processing [11,12], sensitivity and resolution enhancement in optical observations and measurements [13][14][15][16][17][18][19].Among diverse manifestations of the specific "circulational" properties of optical vortices, an important place belongs to the edge diffraction phenomena [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. A series of experimental and theoretical researches has demonstrated that diffraction "reveals" the internal energy circulation, normally "hidden" in circular OV beams, and induces the essential transformation of their phase profile. In particular, even at weak screening (when the opaque obstacle covers only a far periphery of the beam cross section and induces no visible deformation of the intensity profile), the axial OV of the incident beam changes its position and, if its absolute topological charge |m| > 1, splits into a set of |m| single-charged "secondary" vortices. As a result, a complicated pattern of singular points ("singular skeleton") is formed in the diffracted beam cross section that is highly sensitive to the diffraction conditions, especially to the screen edge position with respect to the incident beam axis.

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Edge diffraction of a circular optical vortex (OV) beam transforms its singular structure: a multicharged axial OV splits into a set of single-charged ones that form the 'singular skeleton' of the diffracted beam. The OV positions in the beam cross section depend on the propagation distance as well as on the edge position with respect to the incident beam axis, and the OV cores describe regular trajectories when one or both change. The trajectories are not always continuous and may be accompanied with topological reactions, including emergence of new singularities, their interaction and annihilation. Based on the Kirchhoff-Fresnel integral, we consider the singular skeleton behavior in diffracted Kummer beams and Laguerre-Gaussian beams with topological charges 2 and 3. We reveal the nature of the trajectories' discontinuities and other topological events in the singular skeleton evolution that appear to be highly sensitive to the incident beam properties and diffraction geometry. Conditions for the OV trajectory discontinuities and mechanisms of their realization are discussed. Conclusions based on the numerical calculations are supported by the asymptotic analytical model of the OV beam diffraction. The results can be useful in the OV metrology and for the OV beam's diagnostics.

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

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.