Mirror and Circular Symmetry of Autofocusing Beams

This article demonstrates the crucial importance of the symmetrization method for the formation of autofocusing beams. It is possible to impart autofocusing properties to rather arbitrary distributions, for example, truncated and inverted classical modes (such as Hermite–Gaussian, Laguerre–Gaussian, and Bessel modes) or shift the fundamental Gaussian beam by inserting mirror or circular symmetry. The most convenient for controlling autofocusing characteristics is the truncated sinus function with a power-law argument dependence. In this case, superlinear chirp beams (with power q > 2) exhibit sudden and more abrupt autofocusing than sublinear chirp beams (with power 1 < q < 2). Comparison of the different beams’ propagation is performed using fractional Fourier transform, which allows obtaining the field distribution in any paraxial region (both in the Fresnel and Fraunhofer diffraction regions). The obtained results expand the capabilities of structured beams in various applications in optics and photonics.

Minimal Focal Spot Size Measured Based on Intensity and Power Flow

It is shown, theoretically and numerically, that the distributions of the longitudinal energy flow for tightly focused light with circular and linear polarization are the same, and that the spot has circular symmetry. It is also shown that the longitudinal energy flows are equal for optical vortices with unit topological charge and with radial or azimuthal polarization. The focal spot has a minimum diameter (all other characteristics being equal), which is measured based on the intensity of an optical vortex with azimuthal polarization. The diameter of the focal spot calculated from the energy flow for light with circular or linear polarization is slightly larger (by a fraction of a percentage). The magnitude of the diameter based on the intensity plays a role in the interaction of light with matter, and the magnitude of the diameter based on the energy flux affects the resolution in optical microscopy which is crucial in sensorial applications.

Thin-shell wormholes in $$(2+1)$$-dimensional F(R) theories

We construct a broad family of thin-shell wormholes with circular symmetry in $$(2+1)$$ ( 2 + 1 ) -dimensional F(R) theories of gravity, with constant scalar curvature R. We study the stability of the static configurations under perturbations preserving the symmetry. We present examples of charged thin-shell wormholes which are asymptotically anti-de Sitter at both sides of the throat. We show that stable solutions are possible when suitable values of the parameters are taken.

Measurements of periodically perturbed dewetting force fields and their consequences on the symmetry of the resulting patterns

We studied the origin of breaking the symmetry for moving circular contact lines of dewetting polymer films suspended on a periodic array of pillars. There, dewetting force fields driving polymer flow were perturbed by elastic micro-pillars arranged in a regular square pattern. Elastic restoring forces of deformed pillars locally balance driving capillary forces and broke the circular symmetry of expanding dewetting holes. The observed envelope of the dewetting holes reflected the symmetry of the underlying pattern, even at sizes much larger than the characteristic period of the pillar array, demonstrating that periodic perturbations in a driving force field can establish a well-defined pattern of lower symmetry. For the presented system, we succeeded in squaring the circle.

ON ONE APPROACH TO DETERMINING THE VORTEX SOUND SOURCE

The work consists of five sections and a bibliographic list. The first section provides answers to questions about the relevance, the applied value of the study, as well as the need to develop new approaches that allow modeling vortex structures in engineering practice. In the second section, some mathematical models and approaches used to solve problems of vortex dynamics are considered. The third section is devoted to solving the problem of determining the main parameters of the flow in the core of a vortex ring for given geometric dimensions. It is shown that a turbulent vortex ring is obtained as a result of the interaction of two vortex columns. The fourth section is devoted to methods for characterizing a concentrated vortex as a source of acoustic vibrations. As an object of research, the flow in the core of a turbulent vortex ring is considered. It is assumed that the core of the vortex ring has the shape of a torus. An approach is proposed that makes it possible to establish a strict link between the main flow parameters and the shape of the vortex ring. The aim of this work is to obtain the flow parameters in the core of a vortex ring with their subsequent substitution into the acoustic-vortex equation to analyze the source of acoustic oscillations. It is also necessary to show the presence of a structure in the vortex ring corresponding to some point symmetry and, thus, to abandon the concept of the circular symmetry of the core of the vortex ring. The proposed approach is based on the assertion that a vortex ring can be represented as a set formed according to a “rule” that determines a spatial geometric shape. As a result, an approach was proposed for analyzing the vortex ring as a source of acoustic oscillations, and it was also formulated and theoretically substantiated that the core of a turbulent vortex ring having the shape of a torus can be considered as a result of the interaction of two vortex columns.

Laser Printing of Chiral Silicon Nanoprotrusions by Asymmetric Donut-Shaped Femtosecond Pulses

Here, we showed formation of chiral nanoprotrusions upon direct laser ablation of bulk crystalline silicon (c-Si) wafer with single femtosecond (fs) pulses having asymmetric donut-shaped intensity profile. Breaking circular symmetry of the irradiating donut-shaped fs-pulse beam was demonstrated to switch the geometry of formed surface nanoprotrusions from regular to chiral, while the chirality of the obtained Si nanostructures was found to promote with a degree of asymmetry of the laser beam. The obtained experimental results explain, for the first time, the formation of previously reported chiral c-Si nanostructures produced via donut-shaped beam ablation in terms of uneven helical flow of laser-melted Si material caused by asymmetry of initial intensity and temperature pattern on laser-irradiated Si surface. Our findings open a pathway towards easy-to-implement inexpensive fabrication of chiral all-dielectric nanostructures for advanced nanophotonic applications.