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We propose a simple optical method and device design for the non-contact determination of small shift, thickness, refractive index, and tilt angle of thin films. The proposed sensor consists of a laser light source, a third- or two-order spiral amplitude zone plate with a high numerical aperture, and a CCD camera connected to a computer. It is shown that the third-order zone plate transforms the incident Gaussian beam into a three-petal rotating beam. By measuring the rotation angle of the three-petal intensity distribution, one can measure the following: a minimum shift along the optical axis of about 7 nm (the wavelength is 532 nm), a change in the plate thickness by 3 nm, a change in the tilt angle of the plate by 0.1 degrees, and a change in the refractive index by 0.01.

Using Richards-Wolf formulas, we show that an axisymmetric circularly polarized vortex-free field can be focused into a sharp subwavelength focal spot, around which there is a region where the light energy flow propagates along a spiral. This effect can be explained by the conversion of the spin angular momentum of the circularly polarized field into the orbital angular momentum near the focus, although the on-axis orbital angular momentum remains zero. It is also shown that a linearly polarized optical vortex with topological charge 2 forms near the focal plane an on-axis reverse energy flow (defined by the negative longitudinal component of the Poynting vector) whose amplitude is comparable with the direct energy flow.

In this paper, we numerically simulate the focusing of a second-order cylindrical vector beam with a gradient index Mikaelian lens. It is shown that the lens forms a region of the reverse energy flow near its output surface. If the lens has an on-axis micropit, the region of the direct energy flow can be confined within the lens material, whereas that of the reverse energy flow is put out in free space.

It is known that angular momentum (AM) is an important characteristic of light, which can be separated into the spin (SAM) and orbital parts (OAM). The dynamical properties of the spin and orbital angular momentums are determined by the polarization and spatial degrees of freedom of light. In addition to optical vortex beams possessing spatial polarization and phase singularities, optical fibers can be used to generate and propagate optical modes with the orbital and spin parts of the angular momentum. In this paper, using the example of hollow-core fibers, we demonstrate the fact that their leaky air core modes also have an orbital part of AM in the case of circular polarization arising from the spin–orbit interaction of the air core modes. The reason for the appearance of AM is the leakage of the air core mode energy.

The optical properties of solid-core micro-structured optical fibers (SC MOFs) have been studied for a long time. The process of the energy outflow of the core modes has always been associated with the process of constructive interference of the core modes fields under reflection from the photonic crystal cladding. In this paper, we want to offer a new look at the light localization in the core of SC MOFs related to the behavior of spin and orbital parts of the Poynting vector of these core modes and singularities arising in it. Such an approach can help in forming a better understanding of the process of the core modes energy leakage and also in the creation of SC MOFs with a simplified design and low losses.

We investigated an optical microsensor of the polarization state of a laser light based on a metalens. In contrast to known polarization sensors based on metasurfaces that deflect different polarization types using various angles to the optical axis, the studied polarization sensor generated different patterns in the metalens focus to realize varied polarization states: left circular polarization generated a light ring in the focus, right circular polarization generated a circular focal spot, and linear polarization generated an elliptic spot with two sidelobes. Moreover, the tilt angle of the linear polarization matched the tilt angle of the elliptic focal spot. The simulation results were consistent with the theoretical predictions. A metalens with a diameter of several tens of microns was designed and fabricated in a thin amorphous silicon film with a thickness of 120 μm and a low aspect ratio, high numerical aperture, and short focal distance equal to a wavelength of 633 nm.

It was theoretically shown that in the interference pattern of four plane waves with specially selected directions of linear polarization it is formed a reverse flow of energy. The areas of direct and reverse flow alternate in a staggered order in the cross section of the interference pattern. The absolute value of the reverse flow directly depends on the angle of convergence of the plane waves (on the angle between the wave vector and the optical axis) and reach the maximum at an angle of convergence close to 90 degrees. The right-handed triples of the vectors of four plane waves (the wave vector with positive values of projection to optical axis and the vector of electric and magnetic fields) when added in certain areas of the interference pattern form an electromagnetic field described by the left-handed triple of vectors; however, the projection of wave vector to optical axis has negative values. In these areas, the light propagates in the opposite direction. A similar explanation of the mechanism of the formation of a reverse flow can be applied to the case of a sharp focusing of a laser beam with a second-order polarization singularity. It is also shown that if a spherical dielectric Rayleigh nanoparticle is placed in the backflow region, then a force directed in the opposite direction will act on it (the scattering force will be more than the gradient force).

Using the Richards-Wolf formalism, we obtain general expressions for all components of the electric and magnetic strength vectors near the sharp focus of an optical vortex with the topological charge m and nth-order azimuthal polarization. From these equations, simple consequences are derived for different values of m and n. If m=n>1, there is a non-zero intensity on the optical axis, like the one observed when focusing a vortex-free circularly polarized light field. If n=m+2, there is a reverse flux of light energy near the optical axis in the focal plane. The derived expressions can be used both for simulating the sharp focusing of optical fields with the double singularity (phase and polarization) and for a theoretical analysis of focal distributions of the intensity and the Poynting vector, allowing one to reveal the presence of rotational symmetry or the on-axis reverse energy flux, as well as the focal spot shape (a circle or a doughnut).

In this paper, we have investigated the focusing of a second-order cylindrical vector beam by using a high numerical aperture (NA) lens limited by a ring aperture using the Richards-Wolf formulae. It was shown that the range of negative on-axis projections of the Poynting vector could be increased by increasing the depth of focus through the use of a ring aperture. It was shown that when focusing light with a lens with NA = 0.95, the use of a ring aperture limiting the entrance pupil angle to 0.9 of maximum, allows the depth of the region of negative on-axis Poynting vector projections to be four times increased, with the region width remaining almost unchanged and varying from 0.357 to 0.352 of the incident wavelength. Notably, the magnitude of the reverse energy flow was found to be larger than the direct one by a factor of 2.5.

Using Jones matrices and vectors, we show that an optical metasurface composed of a set of subwavelength binary diffraction gratings and characterized by an anisotropic transmittance described by a polarization rotation matrix by the angle mφ, where φ is the polar angle, forms an m-th order azimuthally or radially polarized beam when illuminated by linearly polarized light, generating an optical vortex with the topological charge m upon illumination by circularly polarized light. Such a polarization-phase converter (PPC) performs a spin-orbit transformation, similar to that performed by liquid-crystal q-plates. Using a FDTD method, it is numerically shown that when illuminating the PPC by a uniformly (linearly or circularly) polarized field with topological charge m = 2 and then focusing the output beam with a binary zone plate, a reverse on-axis light flow is formed, being comparable in magnitude with the direct optical flow. Moreover, the reverse flows obtained when focusing the circularly polarized optical vortex with the topological charge m = 2 and the second-order polarization vortex are shown to be the same in magnitude.

In this study, we theoretically and experimentally investigate the propagation of a second-order cylindrical vector beam through an aluminum lens which forms a tight focus at the distance of the wavelength. Simulation by the finite-difference time-domain method and the Richards–Wolf formulae produces light field distributions which coincide with experimental measurements provided with scanning near-field optical microscopy. We demonstrate that a pyramidal metallized cantilever with a hole is more sensitive to the transversal component of intensity than to the full intensity or to the Umov–Poynting vector in areas of reverse energy flow.

In this paper, spin-orbital conversion in the tight focus of an axial superposition of a high-order (order m) cylindrical vector beam and a beam with linear polarization is theoretically and numerically considered. Although such a beam does not have a spin angular momentum in the initial plane and the third projection of its Stokes vector is equal to zero, subwavelength local regions with a transverse vortex energy flow and with the non-zero third Stokes projection (the longitudinal component of the spin angular momentum) are formed in the focal plane for an odd number m. This means that such a beam with an odd m has regions of elliptical or circular polarization with alternating directions of rotation (clockwise and counterclockwise) in the focus. For an even m, the field is linearly polarized at every point of the focal plane, and the transverse energy flux is absent. These beams can be used to create a micromachine in which two microparticles in the form of gears are captured in the focus of the beam into neighboring local areas in which the energy flow rotates in different directions, and therefore, these gears will also rotate in different directions.

We study coaxial superpositions of Gaussian optical vortices described by a geometric progression. The topological charge (TC) is obtained for all variants of such superpositions. The TC can be either integer or half-integer in the initial plane. However, it always remains integer when the light field propagates in free space. In the general case, the geometric progression of optical vortices (GPOV) has three integer parameters and one real parameter, values which define its TC. The GPOV does not conserve its intensity structure during propagation in free space. However, the beam can have the intensity lobes whose number is equal to one of the family parameters. If the real GPOV parameter is equal to one, then all angular harmonics in the superposition are of the same energy. In this case, the TC of the superposition is equal to the order of the average angular harmonic in the progression. Thus, if the first angular harmonic in the progression has the TC of k and the last harmonic has the TC of n, then the TC of the entire superposition in the initial plane is equal to (n + k)/2, but the TC is equal to n during propagation. The experimental results on generating of the GPOVs by a spatial light modulator are in a good agreement with the simulation results.

Using Richards-Wolf formulae it is shown that a tightly focused azimuthally-radially polarized m-th order laser beam with an arbitrary apodization function produces a reverse energy flow in the focal plane (m=2). If m=3, the reverse energy flow on the axis is equal to zero, increasing in the axis vicinity as the square of the distance to the axis. The azimuthally-radially polarized beam of the m-th order is an example of a polarization vortex. Previously, the reverse energy flow in the focus was obtained only for circularly polarized vortex beams with the topological charge m. Using the FDTD method and the Richards-Wolf formulae, we show numerically that in the focus of a zone plate such laser beams produce regions where the Poynting vector is opposite to the direction of the beam propagation.

Using the Richards-Wolf formulae for a diffractive lens, we show that in the focal plane of a sharply focused left-hand circularly polarized optical vortex with the topological charge 2 there is an on-axis backflow of energy (as testified by the negative axial projection of the Poynting vector). The result is corroborated by the FDTD-aided rigorous calculation of the diffraction of a left-hand circularly polarized plane wave by a vortex zone plate with the topological charge 2 and the NA≈1. Moreover, the back- and direct flows of energy are comparable in magnitude. We have also shown that while the backflow of energy takes place on the entire optical axis, it has a maximum value in the focal plane, rapidly decreasing with distance from the focus. The length of a segment along the optical axis at which the modulus of the backflow drops by half (the depth of backflow) almost coincides with the depth of focus, and the transverse circle in which the energy flow is reversed roughly coincides with the Airy disk.

Using a spiral microaxicon with the topological charge 2 and NA = 0.6 operating at a 532-nm wavelength and fabricated by electron-beam lithography, we experimentally demonstrate the rotation of a two-petal laser beam in the near field (several micrometers away from the axicon surface). The estimated rotation rate is 55 °/mm and linearly dependent on the on-axis distance, with the theoretical rotation rate being 53 °/mm. The experimentally measured rotation rate is found to be linear and coincident with the simulation results only on the on-axis segment from 1.5 to 3 mm. The experimentally measured rotation rate is 66 °/mm on the initial on-axis segment from 0 to 1.5 mm and 34 °/mm on the final segment of the beam path from 3 to 4.5 mm. The experimentally achieved rotation rate is higher than rotation rates of similar two-petal laser beams reported to date.

We numerically investigated the focusing of optical vortices with the wavelength λ = 532 nm and right-hand circular polarization by using a diffractive lens with the numerical aperture NA = 0.95. The simulation was carried out using the Richards-Wolf formulae and the FDTD-method. The focusing of optical vortices with topological charges equal to ±1 and ±2 was investigated. It was shown that the focusing of optical vortices with circular polarization by a wide-aperture diffractive lens can produce an intensity distribution with the negative value of the longitudinal component of the Poynting vector.

The industry of metatuff axes and adzes on the western coast of Onega Lake (Eneolithic period, ca. 3500 – 1500 cal. BC) allows assuming some sort of craft specialization. Excavations of a workshop site Fofanovo XIII, conducted in 2010-2011, provided an extremely large assemblage of artefacts (over 350000 finds from just 30 m2, mostly production debitage). An attempt to estimate the output of production within the excavated area is based on experimental data from a series of replication experiments. Mass-analysis with the aid of image recognition software was used to obtain raw data from flakes from excavations and experiments. Statistical evaluation assures that the experimental results can be used as a basement for calculations. According to the proposed estimation, some 500 – 1000 tools could have been produced here, and this can be qualified as an evidence of “mass-production”.