In this paper, using the Richards-Wolf formalism, we investigate the helicity of hybrid vector vortex beams, which represent beams with various combinations of topological charges (vortex orders) and polarization orders. It is shown that the helicity in such beams is centrally asymmetric. It was shown that when focusing an optical vortex with hybrid polarization, both the intensity and the helicity density do not exhibit radial symmetry, but have central symmetry. Unlike non-vortex beams with hybrid polarization, an asymmetry in the zones with negative and positive helicity density values is observed. For example, for a beam with a unit polarization order and a unit topological charge, the maximum positive helicity density values are approximately half the absolute value of the minimum negative values. Such an asymmetry in the helicity density zones has not been previously observed in beams.
This paper is devoted to the study of the classification of parameters of Laguerre-Gaussian optical vortices with an increased dark region using convolutional neural networks. A significant part of the work is dedicated to the analysis of the obtained classification results. The ResNet architecture was shown to be more suitable for this task than the alternatives, achieving high classification accuracy of 99.35
By employing the Richards–Wolf formalism, analytical expressions for the orbital angular momentum spectrum (OAM-spectrum) in the focus of an elliptically polarized optical vortex are derived. It is found that the OAM-spectrum remains independent of the phase of the focused light beam. Polarization of the incident field influences solely the asymmetry of the spectrum, leaving unchanged the energy partitioning into the side and main components. In contrast, the radial amplitude of the focused light beam does not alter the spectral asymmetry. However, it governs the energy fractions carried by the side and the main spectral components. Quadratic inequalities are obtained, which enable one to assess the feasibility of generating a prescribed OAM-spectrum when the incident beam is confined by a ring diaphragm.
In this paper, we consider deep learning methods based on the ResNet50 architecture for automatic identification of both single wave aberrations of optical systems and superposition of two types of aberration. The use of residual connections provides a high level of accuracy in classification of aberration types (defocusing, 1st and 2nd order astigmatism, coma, trefoil, quatrefoil and spherical) and their magnitudes from intensity distributions with several diffraction orders obtained using multichannel DOEs. Numerical experiments demonstrate the effectiveness of the proposed approach in automated recognition, which makes it promising for real-time use in adaptive optics and ophthalmology. Based on network training over 20 epochs, it was found that on the validation sample, the average absolute error of aberration recognition does not exceed 0.0056.
It was theoretically and numerically demonstrated that in a nonparaxial light field containing a line of zero intensity in its cross-section, longitudinal optical vortices are formed in the longitudinal cross-section containing the optical axis at isolated points of zero intensity. Energy circulates around these vortices. Moreover, along a segment of this energy circulation path, the energy propagates opposite to the main direction of propagation. The diameter of the region where energy circulates around the intensity zero is approximately 0.2λ. Longitudinal optical vortices appear in pairs. Optical vortices on the one side of the optical axis have the same topological charge (+1 or –1). Optical vortices on the opposite side of the optical axis have topological charges (TC) of opposite signs. If a vortex with a TC of –1 is located to the left of the optical axis (when viewed along the direction of propagation), and a vortex with a TC of +1 is to the right, then light does not pass in the forward direction between these optical vortices. Conversely, if the left optical vortex has TС of +1, and the right vortex has TС of –1, then light does propagate forward between these optical vortices.
