Abstract
In this paper, we consider the comparative formation of perfect optical vortices in the non-paraxial mode using various optical elements: non-paraxial and parabolic toroidal vortex lenses, as well as a vortex axicon in combination with a parabolic lens. The theoretical analysis of the action of these optical elements, as well as the calculation of caustic surfaces, is carried out using a hybrid geometrical-optical and wave approach. Numerical analysis performed on the basis of the expansion in conical waves qualitatively confirms the results obtained and makes it possible to reveal more details associated with diffraction effects. Equations of 3D-caustic surfaces are obtained and the conditions of the ring radius dependence on the order of the vortex phase singularity are analyzed. In the non-paraxial mode, when small light rings (several tens of wavelengths) are formed, a linear dependence of the ring radius on the vortex order is shown. The revealed features should be taken into account when using the considered optical elements forming the POV in various applications.
Highlights
Caustics of Non-Paraxial PerfectRecently, the attention of researchers has been attracted by the “perfect” optical vortices (POVs) having a ring radius independent of its vortex number [1,2,3,4]
In this paper, we consider the comparative formation of perfect optical vortices in the non-paraxial mode using various optical elements: non-paraxial and parabolic toroidal vortex lenses, as well as a vortex axicon in combination with a parabolic lens
The attention of researchers has been attracted by the “perfect” optical vortices (POVs) having a ring radius independent of its vortex number [1,2,3,4]
Summary
The attention of researchers has been attracted by the “perfect” optical vortices (POVs) having a ring radius independent of its vortex number [1,2,3,4]. In Reference [49], a comparison of POV generation by means of different elements was investigated as follows: using a combination of a lens with an amplitude-phase element with a transmission function proportional to a Bessel function, an optimal phase element with a transmission equal to the sign function of a Bessel function, and a spiral axicon These elements are similar, since the axicon is Optical Vortices Generated by Toroidal Vortex Lenses. The vortex toroidal lens, as well as the vortex axicon combined with a classic lens, allows for the formation of POVs. Note, if the ring formed in the focal plane has a small radius, at large orders of the optical vortex, the POV ceases to be “perfect”. The obtained results can be useful in various applications using non-paraxial POVs, such as optical trapping and manipulation, vortex-based multiplexing, and laser structuring
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