Singular skeleton of a Laguerre–Gaussian beam transformed by the double-phase-ramp converter

Abstract

We analyze transformations of circular Laguerre-Gaussian beams with zero radial index after passage through the double-phase-ramp (DPR) converter and study the behavior of optical vortices in the propagating transformed beam. Direct and inverse DPR converters are considered, and informative features of the complete set of optical vortices are revealed. For the input beam with even azimuthal index, such a reaction may cause the sign reversal of the axial optical vortex. The results can be used for creation of light beams with prescribed singular skeleton, for the beam diagnostics, and in high-resolution metrology.

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

“…In the moving coordinate frame associated with this combined (V 2 + V') vortex line (in which the longitudinal axis coincides with the tangent straight line), the energy circulation direction is constant [2,4] but in the laboratory frame the retrograde segment looks as if the topological charge of V' is opposite. The similar features of the 3D patterns are typical to other cases of the OV-beam diffraction discussed earlier [20,31,32].…”

“…(here the relations (20) of [29] are adapted to an LG beam with the waist at the screen plane z = 0). Finally, after substitution of (A4) -(A6) into (A1) and equating the result to zero, the polar coordinates of the OV core can be found as  …”

“…(cf. equations ( 21) and ( 22) of [29] and (19), (20) of [31]). In view of the near-axis approximation (A4), equations (A7) -(A9) describe only the "central" OV V 1 (see section 3), and are valid approximately for the initial segments (a > 1) of the V 1 -trajectories in figures 3a, 3b, 4a, 4b, 6 and 7.…”

Phase Singularities to Polarization Singularities

“…Intracavity generation by introducing a spot defect in one of the resonator mirrors is also demonstrated [266][267][268]. Mirrors bent in the shape of a ramp [213,269,270] and digital micromirror device [192] can also be used for phase singularity generation. ere are also reports [271][272][273][274][275][276][277][278][279] on the generation of vortices in optical fibers.…”

Decision support methods in optical research

“…Задача симетрійна -тобто утворені сингулярності знаходяться поза центром пучка. Це означає, що при необхідності досліджувати ефекти в світловому полі, що спостерігаються на осі пучка, у зв'язку з розпадом темних плям та їх розташуванню навколо осі, ми не зможемо отримати ці осьові ефекти [11] Якщо головним для використання зображення є профіль інтенсивності та наявність нулів амплітуди, наприклад для захоплення мікрочастинок світлом у рідині [12], та такий розподіл відповідає вимогам і має бути прийнятим.…”