Off-axis Shift Research Articles

A metalens for detecting fractional-order optical vortices

In this work, a metalens for detecting an incident field with a fractional topological charge ranging from – 2 to 0 is proposed. The metalens is based on a spiral zone plate with a topological charge of 1.5. A change in the topological charge of the incident beam is numerically shown to lead to an off-axis shift of the focal spot from the center, with the intensity maximum value also changing. This results in a 6.9-fold change in the on-axis intensity while the topological charge of the incident beam changes from –0.6 to –1.5. The on-axis intensity at the focus is also shown to be affected by the rotation of the fractional vortex beam. This makes it possible to use the proposed metalens for measuring the angle of rotation of the incident beam in the range from 0 to 110°.

Superposition of two Laguerre-Gaussian beams shifted from the optical axis

Topological charges (TC) of a superposition of two Laguerre-Gauss (LG) beams (0,m) and (0,n) symmetrically shifted from the optical axis are found in this work. It is shown that if m=n, then the TC of the superposition is equal to n. That is, two identical off-axis LG beams have the net TC as that of a single LG beam. If m<n, then the net TC of the superposition can take one of four values: TC1=(m+n)/2, TC2=TC1+1, TC3=TC1+1/2, and TC4=TC1–1/2. Criteria for choosing one of the four TC values are also established. In the absence of the off-axis shift of the two LG beams, the net TC of the superposition is equal to n, i.e. the larger of the two TC. And for an arbitrarily small off-axis shift, the net TC either remains the same as it was before the shift, or decreases by an even number. This is explained by the fact that an even number of optical vortices with TC=–1 "comes" from infinity, which compensate for the same number of optical vortices with TC=+1 in the superposition. It is also interesting that when superimposing two off-axis LG beams with certain tilts to the optical axis such that the superposition is structurally stable, an infinite number of screw dislocations with TC=+1 are formed on some line. The net TC of such a su-perposition is infinite.

Topological charge of two parallel Laguerre-Gaussian beams

We analytically, numerically, and experimentally determine a topological charge (TC) of the sum of two axisymmetric off-axis Laguerre-Gaussian (LG) beams with the indices (0, m) and (0, n). In particular, we find that at m = n, the combined beam has TC = n, which suggests that the sum of two identical off-axis LG beams has the TC of an individual constituent LG beam. At m < n, the TC of the sum is found to take one of the following four values: TC1 = (m + n)/2, TC2 = TC1 + 1, TC3 = TC1 + 1/2, and TC4 = TC1 – 1/2. We also establish rules for selecting one of the four feasible values of TC. For the sum of two on-axis LG beams, TC of the superposition equals the larger constituent TC, i.e. TC = n. Meanwhile following any infinitesimally small off-axis shift, TC of the sum either remains equal to the pre-shift TC or decreases by an even number. This can be explained by an even number of optical vortices (OV) with TC = –1 instantly ‘arriving’ from infinity that compensate for the same number of OV with TC = +1 born in the superposition. We also show that when two LG beams with different parity are swapped in the superposition, the topological charge of the superposition changes by 1. Interestingly, when superposing two off-axis LG beams tilted to the optical axis so that their superposition produces a structurally stable beam, an infinite number of screw dislocations with TC = +1 are arranged along a certain line, with the total TC of the superposition equal to infinity.

Electromagnetic phase coherence gratings for atmospheric applications.

We propose using electromagnetic phase coherence gratings (EMPCGs) for fine spatial segregation in polarimetric components of stationary beams on their propagation in atmospheric turbulence. Unlike for other beams, e.g., non-uniformly correlated EM beams, the off-axis shifts occurring in polarimetric components of EMPCGs are shown to be invariant with respect to the local turbulence strength. This effect may lead to implementation of novel techniques for direct energy, imaging, and wireless optical communication systems operating in the presence of turbulent air.

Propagation dynamics of radially polarized symmetric Airy beams in the fractional Schrödinger equation

We analyze the propagation dynamics of radially polarized symmetric Airy beams (R-SABs) in a (2+1)-dimensional optical system with fractional diffraction, modeled by the fractional Schrödinger equation (FSE) characterized by the Lévy index, α. The autofocusing effect featured by such beams becomes stronger, while the focal length becomes shorter, with the increase of α. The effect of the intrinsic vorticity on the autofocusing dynamics of the beams is considered too. Then, the ability of R-SABs to capture nano-particles by means of radiation forces is explored, and multiple capture positions emerging in the course of the propagation are identified. Finally, we find that the propagation of the vortical R-SABs with an off-axis shift leads to rupture of the ring-shaped pattern of the power-density distribution.

Asymmetric multi-vortex solitons in nonlocal nonlinear media

This paper introduces a series of asymmetric multi-vortex solitons, which made up of Gaussian beam and embedded multi off-axis shift vortex, in nonlocal nonlinear media. The analytical expression of the soliton trajectory is derived, and the other propagation properties, such as the intensity distribution, the rotating period, and the orbital angular momentum (OAM) are all investigated. It is found that the initial displacement of the soliton mass center, which can be controlled by selecting the appropriate shift values of the off-axis vortexes, can determine the trajectory of the optics beam. The OAM also depending on the shift values of the vortexes. Obviously, the controllable propagation of the asymmetric multi-vortex beam has important academic value and application prospect in optical switches, or be used as optical tweezers and wrenches.

Controllable propagation path of imaginary value off-axis vortex soliton in nonlocal nonlinear media

Both imaginary value off-axis solitons and imaginary value off-axis vortex solitons are analytically obtained in nonlocal nonlinear media. The imaginary value off-axis solitons can do the snakelike propagations resulting from that the soliton phase $$\Theta $$ are period functions, and the propagation paths (including propagation directions and reverse points) of such solitons can be controlled by selecting the appropriate imaginary values b and c. Due to the position-changed vortex phase, the imaginary value off-axis vortex solitons revolve clockwise or counterclockwise along the controllable elliptical trajectories of different orientations depending on their imaginary off-axis shifts. The controllable vortexes may be used as optical tweezers and wrenches, and the controllable mass centers may have potential application in all-optical controlling.

Simple Analytical Approximate Formulation for the Shielding Effectiveness of a Metallic Panel With Apertures

The present paper is proposing a methodological approach for predicting the Shielding Effectiveness (SE) of metallic walls with various apertures, supported by software simulations. First, the SE modeling for a single aperture is addressed, whereas, at the difference with an homogeneous barrier, the transmission through a slot of given length behaves as a dipole that re-radiates some of the incident RF power. Because of this, the re-radiated field behind the barrier -hence the SE- becomes dependent of the barrier-to-target distance. Next, the SE for a single row of apertures is addressed, with an attempt for quantifying its dependency upon N identical holes and their individual separation. A further step is treating the SE for an array of NxM holes, including the effect of an off-axis shift target location. Some of the simulation results are compared with those obtained by using a few, widely-used simple formulae, trying to characterize their limitations, and proposing correction factors as the discrepancy typically increase with the barrier-to-target distance.

Orbital angular momentum of Gaussian optical vortices with displaced point of phase singularity

A simple formula is obtained to describe the normalized orbital angular momentum (OAM) of a Gaussian beam after passing through a shifter spiral phase plate (SPP). The formula shows that while being equal to the topological charge at the zero off-axis shift, the OAM becomes fractional with increasing shift and it is tending to zero exponentially. Analytic expressions of the complex amplitude of the Gaussian beam having passed through the off-axis SPP show that as the beam propagates, the isolated intensity null moves from the initial point defined by the vector of the SPP’s center shift along a straight line perpendicular to the said vector. Using a liquid crystal light modulator, crescent-shaped beams are experimentally generated.

Generation of optical Bessel beams with arbitrarily curved trajectories using a magnetic-liquid deformable mirror.

We propose a new strategy to curve the trajectory of the central lobe of a zero-order Bessel beam and a first-order Bessel beam along their propagation axis. Our method involves modifying the phase of a beam that is incident on an adaptive mirror. As examples, we show that the most intense lobe of the beam can follow a parabolic trajectory, a cubic trajectory, or a trajectory made by a combination of these orders. By using a phase correction emulating the effect of cylindrical mirrors, the central lobe always preserves its symmetry. Theoretical simulations were reproduced in the laboratory using a magnetic-liquid deformable mirror. The parabolic trajectory of the 60-μm central spot of a zero-order Bessel beam exhibits a 0.6-mm off-axis shift after 30-cm-length propagation.

Fractional orbital angular momentum of a Gaussian beam with an embedded off-axis optical vortex

We theoretically and experimentally study asymmetric Gaussian optical vortices generated via diffracting a Gaussian beam by an off-axis spiral phase plate or amplitude "fork" hologram. It is shown that depending on the magnitude of the off-axis shift the laser beam can acquire a crescent-shaped cross-section, which rotates on propagation. We obtain an analytical expression for the orbital angular momentum (OAM) of such a beam, which appears to be fractional. We show that with increasing off-axis shift, the OAM decreases parabolically. The experimental results are in qualitative agreement with theory and numerical simulation.

Conservation theorems for the orbital angular momentum of a superposition of shifted optical vortices

We proved two conservation theorems for the orbital angular momentum (OAM) of a superposition of identical optical vortices with an arbitrary radially symmetric shape, integer topological charge n, and arbitrary off-axis shift. The normalized OAM of such a superposition for any real weights equals the OAM of each individual beam contributing to the superposition. If the beam centers are located on a straight line passing through the origin, then, even if the superposition weights are complex, the normalized OAM of the whole superposition equals that of each contributing beam. These theorems allow of generating vortex laser beams with different (not necessarily radially symmetric) intensity distribution, but with the same OAM. The results of numerical simulation are given for superpositions of Bessel beams, Hankel-Bessel, Bessel-Gaussian and Laguerre-Gaussian beams.

Structural basis for the assembly and gate closure mechanisms of the Mycobacterium tuberculosis 20S proteasome.

Mycobacterium tuberculosis (Mtb) possesses a proteasome system analogous to the eukaryotic ubiquitin-proteasome pathway. Mtb requires the proteasome to resist killing by the host immune system. The detailed assembly process and the gating mechanism of Mtb proteasome have remained unknown. Using cryo-electron microscopy and X-ray crystallography, we have obtained structures of three Mtb proteasome assembly intermediates, showing conformational changes during assembly, and explaining why the beta-subunit propeptide inhibits rather than promotes assembly. Although the eukaryotic proteasome core particles close their protein substrate entrance gates with different amino terminal peptides of the seven alpha-subunits, it has been unknown how a prokaryotic proteasome might close the gate at the symmetry axis with seven identical peptides. We found in the new Mtb proteasome crystal structure that the gate is tightly sealed by the seven identical peptides taking on three distinct conformations. Our work provides the structural bases for assembly and gating mechanisms of the Mtb proteasome.

Color image projection based on Fourier holograms

A method of color image projection is experimentally validated. It assumes a simultaneous illumination of a spatial light modulator (SLM) with three laser beams converging in a common point on a projection screen. The beams are masked with amplitude filters so that each one illuminates one third of the area of the SLM. A Fourier hologram of a chosen color component of an input image is calculated, and its phase pattern is addressed on a corresponding part of the SLM area. A full-color flat image is formed on the screen as a result of color mixing. Additional techniques of image optimization are applied: time-integral speckle averaging and an off-axis shift of a zero-order peak. Static and animated experimental results of such a color holographic projection with a good image quality are presented.

Dosimetric changes induced by positional uncertainty of cutout in electron radiotherapy

AbstractDosimetric changes caused by the positional uncertainty of centring a small electron cutout to the machine central beam axis (CAX) of the linear accelerator (linac) were investigated. First, six circular cutouts with 4 cm diameter were made with their centres shifted off from the machine CAX for 0, 2, 4, 6, 8 and 10 mm using the 6 × 6 cm2 applicator. Then, the percentage depth doses (PDDs) at the machine CAX and cutout centre were measured using the 4, 9 and 16 MeV clinical electron beams produced by a Varian 21 EX linac. The cross- and in-line axis beam profiles were measured at depth of maximum dose (dm) and source-to-surface distance equal to 100 cm using a scanning water tank system and diode detector. When the cutout centre was shifted away from machine CAX for the electron beam with low energy of 4 MeV, the dm, depths of the 80 (R80) and 90% (R90) depth dose at the machine CAX had no significant change (<0.1 mm). For higher energies of 9 and 16 MeV beams, the dm were reduced with 0.45 and 1.63 mm per mm off-axis shift between the cutout centre and the machine CAX, respectively. The R80 and R90 were reduced with 0.7 mm per mm off-axis shift for both energies. When there was a 4 mm off-axis shift, the relative output factors for the 4, 9 and 16 MeV beams were reduced with 0.8, 1.6 and 0.5%, respectively. The isodose coverage of the in-line axis beam profile was reduced when the cutout centre was shifted away from machine CAX. It is important for radiation oncologists, dosimetrists, therapists and physicists to note such dosimetric changes in the electron radiotherapy to the patient, because such positional uncertainty is unavoidable in fabricating an electron cutout in the mould room.

Electron radiotherapy: a study on dosimetric uncertainty using small cutouts

This note investigated the dosimetric uncertainties due to the positional error when centring a small cutout to the machine central beam axis (CAX) in electron radiotherapy. A group of six circular cutouts with 4 cm diameter were made with their centres shifting 0, 2, 4, 6, 8 and 10 mm from the machine CAX for the 6 × 6 cm2 applicator. The per cent depth doses, beam profiles and output factors were measured using the 4, 9 and 16 MeV clinical electron beams produced by a Varian 21 EX linear accelerator. The 2D isodose distributions in the z–x (or cross-line) and z–y (or in-line) plane were calculated by Monte Carlo simulation using the EGSnrc system. When the cutout centre was shifted away from the machine CAX for the 4 MeV beam, the dm, R80 and R90 at the machine CAX had no significant change (<0.1 mm). For higher energies of 9 and 16 MeV beams, the dm was reduced by 0.45 and 1.63 mm per mm, between the cutout centre and the machine CAX with off-axis shift <6 mm respectively. R80 and R90 were reduced by more than 0.3 mm per mm off-axis shift for both energies. The isodose coverage of the in-line axis beam profile was reduced when the cutout centre was shifted away from machine CAX. It is important for oncology staff to note such dosimetric changes in the clinical electron radiotherapy, particularly when a high energy electron beam is used for small cutout. Such positional uncertainty is unavoidable in fabricating an electron cutout in the mould room.

Effects of aperture displacement in broad-beam ion extraction systems

Low-energy broad-beam ion sources cover a wide range of applications. Geometrical perturbations of the axial-symmetric extraction channels by off-axis shifts of the accelerator grid holes give rise to an ion beamlet tilt which under certain conditions is dependent on the beamlet current. In this study, the characteristics of the beamlet deflection are presented which were obtained by a three-dimensional trajectory simulation.

The effect of magnetic field configuration on plasma beam profiles in curved magnetic filters

Curved magnetic filters are commonly used with cathodic vacuum arcs to remove macroparticles from the plasma stream, making it suitable for the preparation of smooth, dense, and defect free films. Although a variety of filters have been investigated experimentally, the influence of the magnetic field configuration on the shape and position of the plasma beam at the filter exit has not been recognized. In this work the magnetic field configurations for a wide range of filter designs have been calculated and compared with measured beam profiles. The results show that the field configurations can be used to predict the dimensions of the plasma beam and in-plane off-axis shifts at the filter exit, as well as identifying regions of high loss. Magnetic field configuration calculations are shown to be a valuable design and optimization tool for curved magnetic field filters of various designs.