Phase singularities near reverse energy flows intightly focused optical vortices.

A reverse energy flow is theoretically demonstrated to occur in the interference pattern generated by four plane waves with linear polarization. In some regions of the interference pattern, the right-handed triplets of plane-wave vectors k $({k}_{z}>0)$, E, and H (comprising a wave vector and $\mathbf{E}$- and H-field vectors) sum up to form an electromagnetic field described by a right-handed triplet of vectors k $({k}_{z}<0)$, E, and H. It is in these regions that the negative propagation of light occurs. On the optical axis the orbital energy flow, proportional to the light intensity, is shown to be positive, while the spin flow is negative and exceeds the orbital flow in magnitude. That is why the on-axis summary energy flow is negative. The magnitude of the reverse flow on the optical axis is two times lower than that of the intensity. A similar mechanism may apply to the case of sharply focusing a laser beam with second-order polarization or phase singularity. Using two identical micro-objectives with a numerical aperture of 0.95, it has been demonstrated experimentally that the intensity on the optical axis near the focus of an optical vortex with a topological charge of 2 is zero for right circular polarization and nonzero for left circular polarization. This confirms that in the latter case there is the reverse flow of light energy on the optical axis, since in the center of the measured energy flow distribution there is a very weak local maximum (the Arago spot) aroused due to diffraction of the forward flow by a circle with a diameter of 300 nm (the diameter of the tube with the reverse flow). Comparing the numerical and experimental intensity distributions, it is possible to determine the diameter of a ``tube'' with the reverse flow. For a numerical aperture of 0.95 and a wavelength of 532 nm, the diameter of the tube of the reverse flow along the optical axis is 300 nm. It is also shown experimentally that when an optical beam with second-order cylindrical polarization is focused with a numerical aperture of 0.95, there is a circularly symmetric energy flow in the focus with a very weak flow in the center (the Arago spot), whose distribution is determined by diffraction of the forward flux by an $\ensuremath{\sim}300$-nm-diameter circular area, where the energy flow is reverse. This also confirms that in the latter case, there is a reverse energy flow on the optical axis.

In this work, it is theoretically and numerically demonstrated that an astigmatic transformation of a νth-order edge dislocation (shaped as a zero-intensity straight line) of a coherent light field—where ν =n + α is a real positive number, n is integer, and 0 <α <1 is fractional—produces n optical elliptic vortices (screw dislocations) with topological charge (TC) −1, which are arranged on a straight line perpendicular to the edge dislocation and found at Tricomi function zeros. We also reveal that at a distance from the said optical vortices (OV), an extra OV with charge −1 is born on the same straight line, which departs to the periphery with α tending to zero, or gets closer to the n OVs with α tending to 1. Additionally, we find that a countable number of OVs (intensity nulls) with charge −1 are produced at the field periphery and arranged on diverging hyperbolic curves equidistant from the straight line of the n main intensity nulls. These additional OVs, which we term as ‘escort’, either approach the beam center, accompanying the extra ‘companion’ OV if 0 <α <0.5, or depart to the periphery, whereas the ‘companion’ keeps close to the main OVs if 0.5 <α <1. At α =0 or α = 1, the ‘escort’ OVs are shown to be at infinity. At fractional ν, the TC of the whole optical beam is theoretically shown to be infinite. Numerical simulation results are in agreement with the theoretical findings.

It is shown in this work that, with strong focusing of a beam with optical vortex and circular polarization, three energy flows take place in the focal plane: direct longitudinal, reverse longitudinal and azimuthal transverse flows. Calculations are made analytically using the Richards–Wolf formalism and by numerical simulation. Moreover, the energy rotation at different lengths from the optical axis occurs in different directions. Therefore, the focal plane intersects along the optical axis only part of the initial beam energy per unit time. The same energy part (other things being equal) intersects the focal plane along the positive direction of the optical axis when an optical vortex with cylindrical polarization is focused. The difference is that, if an optical vortex is present, then the transverse energy flux at the focus rotates around the optical axis. If an optical vortex is not present (a beam with only cylindrical polarization), then the average transverse flow in the focal plane is zero, though, in some regions in the focal plane, the flow is directed towards the optical axis and, in other regions, away from it. This behavior of the transverse energy flow at the focus (flow direction towards the optical axis and away from the optical axis) of a cylindrical vector beam can be deemed another kind of Hall effect.

We present a method for achieving the cylindrical vector beams (CVBs) and optical vortex generation in a solid-core ring fiber (SCRF) by using an acoustically induced fiber grating (AIFG). Theoretical analysis shows that the SCRF can introduce a refractive index difference of ~10-5 between the first group of adjacent high-order degenerate vector modes. In the experiment, the transmission spectra of AIFG constructed with the SCRF depicts three separate resonance peaks with 3-dB bandwidth and resonance wavelength interval of 0.16 and 2.5 nm, respectively, revealing that the high-order degenerate vector modes have been effectively separated. On the basis of the separation of the degenerate vector mode, the CVBs and the ±1-order optical vortex are further experimentally generated at three separate wavelengths using the AIFG.

Investigation of the influence of parameters of silver, aluminum, gold, and chromium spiral zone plates on the longitudinal component of Umov-Pointing vector in produced optical vortices by using the frequency-dependent finite-difference time-domain method is presented. It is shown that the aluminum spiral zone plate with a relief height of 50 nm gives an optical vortex with the smallest longitudinal component of Umov-Pointing vector on the optical axis. The gold spiral zone plate is the least effective for the formation of vortex beams with a reverse energy flow.

Through theoretical calculation, the analytical expression for the cross-spectral density function of vortex beam with and without edge dislocation during transmission in turbulent atmosphere and free space is obtained. The calculation result is used for researching the influences of edge dislocation on optical vortex transmission. The research shows that due to the edge dislocation, when the optical vortex's topological charge is greater than +1, the optical vortex will no longer carry out steady transmission in the free space transmission. Instead, it will divide into two optical vortices, and the distance between them will gradually increase as the transmission distance increases. Optical vortex will split in turbulent atmosphere propagation. Due to the edge dislocation, when the topological charge of optical vortex is greater than +2, it is found that the distance between one optical vortex and other optical vortices is much larger than that between other optical vortices. Besides, when there's an edge dislocation, the greater the light wavelength and the structure constant are, the smaller the distance between the optical vortex and the edge dislocation on the source plane is, and the evolution of the optical vortex will be accelerated.

Nonlinear propagation effects on high-power optical-vortex pulses in anisotropic crystals is reported. Nonlinear effects on optical-vortex pulse generation through the spin-orbit interaction and its propagation in an anisotropic crystal is investigated.The beam of the left-circularly-polarized optical vortex pulse is focused on one of the surfaces of a LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> or rutile crystal (NC) by a convex lens L1. After propagating along the optic axis of the crystal, the beam is collimated by another convex lens L2.

Photonic nanojets (PNJs) are subwavelength jet-like propagating waves generated by illuminating a dielectric microstructure with an electromagnetic wave, conventionally a linearly polarized plane wave. Here, we study the donut-like PNJ produced when a circularly polarized vortex beam is used instead. This novel PNJ also has a reverse energy flow at the donut-like focal plane depending on both the optical vortex topological charge and microsphere size. Our tunable PNJ, which we investigate numerically and analytically, can find applications in optical micromanipulation and trapping.

In a number of theoretical (J. Opt. 6, 259 (2004)) and experimental (Opt Express 19, 5760 (2011)) works, an original fractional-TC optical vortex (with TC standing for topological charge) was shown to evolve into an integer optical vortex whose TC is equal to the nearest (i) smaller integer, if the fractional part is smaller than 1/2, and (ii) larger we show that the initial fractional optical vortex evolves into an integer optical vortex with TC equal to the nearest (i) smaller integer, if the fractional part is smaller than 0.12, and (ii) larger integer, if the fractional part is larger than 0.12. This can be explained by the fact that the additional center integer, if the fractional part is larger than 1/2. In this work, using numerical simulation, of singularity is generated on the beam periphery characterized by near zero-intensity (a millionth of the maximum), thus prohibiting the experimental detection, but allowing a numerical assessment.

The number of zero lines of the real and imaginary parts of the optical vortex (OV), both are the same as the topological charge (TC), and all of these lines intersect at one point where the phase singularity is. Furthermore, zero crossings distribute regularly on the transverse plane of the OV lattice. Zero lines of the real and imaginary parts of the non-diffracting fields without OV that generated by multi-waves interference are periodic but coincident. We stack two groups of these kind of zero lines which can be regarded as a set of zero lines of the real part and a set of zero lines of the imaginary part respectively, to satisfy the cross state of zero lines of an OV lattice. Then two groups of multi-waves corresponding to the two fields can be obtained. The expected OV lattice that generated by the two groups of engineered waves interference together is validated through both numerical simulations and experiments.

A full comparative analysis of the chain of phase singularities generated when a quasi-plane wave and a Gaussian beam pass a double-phase-ramp (DPR) converter is presented based on the theoretical and experimental data. The overall output beam structure includes a system of interrelated optical vortices (OVs) whose linear trajectories form a threedimensional singular skeleton which can be applied for the trapping and guiding of microparticles. An internal structure of each individual phase singularity is characterized by the OV topological charge and by the morphology parameters of the equal intensity ellipses in the OV-core area. The rectilinear equidistant OV trajectories form a chain in the transverse cross section, and their identical morphology parameters can be useful for the applications to metrology and micromanipulation. As a separate result, we consider the DPR-induced transformations of the incident Laguerre-Gaussian beams of the lowest orders and show that the incident multicharged OVs are transformed into small sub-chains of the OVs located in the near-axial region.

Vortex beams, known as a typical form of structured light, possess numerous applications in various fields. Their widespread application prospects have then sparked an in-depth analysis of the generation and manipulation of vortex modes in an active cavity, as well as the development of high-performance vortex lasers. In this paper, we report on a new class of highly efficient and high-power Nd:YAG vortex lasers in a robust and compact configuration, which allows direct generation of vortex beams with an easily controllable topological charge both in the continuous-wave and pulsed operation regimes. The on-demand generation of intracavity vortex modes is realized based on a Q-plate by controlling the geometric phase inside the laser resonator. The maximum output power in the continuous-wave regime is 4.11 W with a slope efficiency of 37.9%. Besides, the vortex pulses are also achieved by including a Cr:YAG crystal in the cavity as a saturable absorber. The shortest pulse width is 142.8 ns at a pulse repetition rate of 232.6 kHz, with a maximum average output power of 1.05 W. Vortex modes with other topological charges can be obtained by simply changing the corresponding Q-plate without sacrificing the lasing efficiency. The experimental results can shed some light on the design and building of highly efficient and high-power vortex lasers together with a well-defined controllable topological charge, aiming at some specific applications.

Given by the Shannon theorem, the data rate in a single mode fiber is approaching the capacity limit of 100 Tbit/s, which even applies to all existing wavelength division multiplexing and advanced modulation formatting techniques. Optical vortex beams, including orbital angular momentum (OAM) beams with phase singularities and cylindrical vector beams (CVBs) with polarization singularities, are orthogonally structured light beams providing new degrees of freedom for multiplexing optical communication, for which the multiplexer is the key component. Although there are various OAM detection approaches such as the optical geometric transformation and vortex grating, CVB sorting with high efficiency and large dynamic range has not been demonstrated before. In this work, we propose and demonstrate an efficient approach for multiple coaxial CVB sorting based on the spin-dependent optical geometric transformation using the Pancharatnam–Berry optical element device fabricated with the photoaligned liquid crystal....

The article explores technical capabilities of the method for limiting the parameters of the reverse energy flow of an induction motor as a means of controlling its electromagnetic parameters based on the application of a short-circuited stator winding. This is due to the need to suppress the reverse EMF of an asynchronous motor of a multi-machine electrotechnical complex of a mine site which is in a freewheel state after a protective supply turning off. It is established that in such electrotechnical complex of mines asynchronous machines of medium and high power are able to create long-term reverse energy flows the presence of which creates a precedent for maintaining the dangerous state of the electrical complex if the cause of the protective switch-off is a short circuit in the power connection or ground leakage. The known and currently developed technical means for detec­ting the emergency condition of the power grid by autonomous means operate on the basis of monitoring parameters on the side of the motor connections which determines the practical relevance of the presented research in the rational direction of the technical implementation of the device for suppressing reverse energy flows. The main idea of the article is disclosed in the justification of the structure of the model of an asynchronous motor represented as an electrogenerating link with an additional stator winding designed to generate impact on the electromagnetic parameters of the engine. The processes that occur when a short-circuit in this winding is induced, taking into account the existing sizes of power transformers used in the modern electrotechnical complex of mines and the cable network, were investigated. The parameters of the additional stator winding were determined which reduce the currents and voltages to safe values in the circuit of the action of the reverse energy flows of the induction motor and the duration of the reverse EMF existence at a safe level.

Formation of optical vortices with topological charge [formula omitted] and [formula omitted] by use of the S-waveplate