Spiral Zone Plate Research Articles

Measuring the topological charge of an x-ray vortex using a triangular aperture

In this paper, for the first time, we demonstrate that the topological charge of a hard x-ray vortex can be measured by a single diffraction pattern from a triangular aperture. The x-ray vortex was produced by a spiral Fresnel zone plate (SFZP) with topological charges of ±1. The triangular aperture was placed in the proximity of the focal plane of the SFZP. Explicit diffraction patterns, which agreed well with the calculated results, were observed and they were rotated by 180° by inverting the sign of the topological charge.

Tailoring focused optical vortices by using spiral forked plates.

We propose and experimentally demonstrate a single optical element, termed as spiral forked plates (SFPs), to simultaneously generate two tightly focused optical vortices (OVs). The key idea is to combine a spiral zone plate (SZP) and a forked grating (FG) through a logic XOR operation. Both theoretical and experimental results demonstrate that SFPs not only can completely suppress the undesirable zeroth (central) order diffraction, but also can further manipulate the topological charges (TCs) of the two resultant focused OVs by varying the TCs of the SZP and FG, following the so-called TC transformation rule. Thus, SFPs show promising potential for advancing the shrinking and integrating applications of orbital angular momentum superpositions.

Composite Spiral Zone Plate

A new kind of optical element, i.e., composite spiral zone plate (CSZP), is proposed to generate a twin-vortex beam along the optic axis in this paper. The axial diffraction property of the CSZP is analyzed theoretically and experimentally. The results demonstrate that the CSZP can possess two focused vortices with the same intensity peak, different topological charges, and customized axial positions. The proposed optical device exhibits significant potential for various applications including three-dimensional optical manipulation.

Simulation of the Optical Vortices Generation by the Silver Spiral Zone Plates

The formation of an optical vortex by a silver spiral zone plate was presented by using the finite-difference time-domain method implemented in FullWVE (RSoft). Both the left and right circularly polarized Gaussian beams at the wavelength of 532 nm have been used as an incident light. Spiral zone plate with the topological charge of 2 μm the diameter of 8 μm and the focal length of 532 nm made in 100 nm silver film produces an optical vortex with the maximum intensity of 55 a.u. at the focal plane.

Binary diffractive optics for 3D-demultiplexing of OAM beams

We propose to use a combination of spiral Fresnel zone plates (SFZPs) and binary diffractive gratings in order to realize 3D-demultiplexing of vortex beams – laser beams having an orbital angular momentum (OAM). It is known that binary and blazed fork-shaped diffractive gratings are widely used for demultiplexing of OAM beams and their analysis. In contrast to the fork-shaped gratings, in the case of SFZPs the diffraction orders differ in their focus positions along the propagation axis. A combination of these two approaches allows us to perform the socalled 3D-demultiplexing of OAM beams.

Realizing a Gauss hypergeometric beam described as 2F1 (a, b, c; x2) by Bessel spiral zone plate

The apodizing spiral zone plate with Bessel functions shows interesting focusing behavior in the generation of a variety of uni- and multiannular (specially biannular) azimuthal and annular vortex beams carrying screw and annular phase dislocation. Theoretically, studies utilizing scalar diffraction integrals show generation of hypergeometric F21(a,b,c;x2) beams. Then, considering two important parameters, the order of the Bessel functions and topological charge, their impacts and roles in the features of the generated focused beams are examined. Simulation and experimental results are in very good agreement with each other.

Energy backflow in the focus of an optical vortex

By employing Richards-Wolf formulae for an aplanatic system, we show that when tightly focusing a left-hand circularly polarized optical vortex with the topological charge 2 and an arbitrary apodization function, an on-axis energy backflow occurs in the focus plane, which is verified by a negative optical-axis projection of the Poynting vector. This result is numerically reconfirmed using the rigorous FDTD-based analysis of diffraction of a left-hand circularly polarized plane wave by a spiral zone plate with the topological charge 2 and a numerical aperture of ~1. Significantly, the back and direct flows of energy are comparable in magnitude. While the on-axis energy backflow is shown to take place on the entire axis, its maximum is attained in the focal plane, quickly decaying with distance from the focus. The on-axis depth of backflow on which it drops by a factor of two is nearly the same as the depth of focus, while the transverse spot in which the energy backflow occurs is approximately equal to the Airy disk.

Multiple optical vortices generated by azimuthal fractal spiral zone plates based on liquid crystal spatial light modulator

Azimuthal fractal spiral zone plates (AFSZPs) with particular fractal characteristics are proposed which have the ability to increase the number of foci comparing with conventional spiral zone plates. The generated beams possess sequence of optical vortices along the propagation direction with preset resolution. Numerical simulations are carried out under plane wave illumination and the good performance of this fractal diffractive optical elements are verified experimentally based on a programmable phase-only liquid-crystal spatial light modulator (SLM). In addition, the effects on the axial irradiance and resolution of foci caused by variations of parameters are also presented.

Helical reverse flux of light of a focused optical vortex

Using the Richards–Wolf formalism, we show that if an optical vortex with a topological charge of 3 and with left (opposite) circular polarization is sharply focused by an aplanatic system, then in the focal plane there is a reversed flux of light energy near the optical axis (on the axis itself it is zero), which is only 2–3 times less than the forward energy flux in the focus. It is also shown that near the optical axis the reverse flux propagates along a counterclockwise helix (spiral) around the optical axis. The reverse flux near the optical axis is also demonstrated by the FDTD-simulation of diffraction of a circularly polarized plane wave by a third-order spiral zone plate with a numerical aperture of about 1. A Rayleigh microparticle trapped in the area of such a focus should move in the opposite direction with respect to the direction of beam propagation.

Azimuthal-segmented linear zone plate: 1D beam structurer and topological charge detector

Unique linear structured light beams carrying fractional vortex dipoles in the shape of either a transverse elliptical beam or a transverse bottle-like beam are presented and studied. These beams are generated using a novel diffractive element produced by a given combination of two phase-shifted spiral linear zone plates with equal but opposite helicities. The impact of the topological charge upon the beams is surveyed and demonstrated to be that the size of the beams is quietly controlled by the charge. As an interesting application, we demonstrate that the element may be simply used to measure the topological charge of a vortex optical beam. On the other hand, when the element is illuminated by a vortex beam, the focused pattern is modulated so the number and direction of the modulated fringes easily reveal the sign and modulus of the topological charge. The experimental results verify that the simulation works well.

Mirror-rotation-symmetrical single-focus spiral zone plates.

In this Letter, we report mirror-rotation-symmetrical single-focus spiral zone plates (MS-SZPs) fabricated by femtosecond laser direct writing. The novel optical element can generate a single-focus vortex beam, owing to the element's complicated continuous surface. The MS-SZP surface possesses reverse mirror-rotation symmetry, which ensures that the transfer element has the same surface morphology as the original element. Both the transfer element and original element have good optical properties. The single-focus behavior was investigated by a microscopic imaging system and found to be in good agreement with theoretical simulation results. The innovative optical component is expected to be widely used in optical communication, quantum computation, optical manipulation, and other fields.

Diffraction by a radial phase modulated spiral zone plate of abruptly autofocusing beams generated with multiple Bessel-like beams

In this paper, we present the generation of optical vortices using an abruptly autofocusing beam that is combined from multiple Bessel-like beams, diffracted by a radial phase shift modulated spiral zone plate (RSSZP). The analytical formula for the diffracted wave field amplitude of the produced beam is derived based on the Fresnel diffraction integral formula. The results show that the intensity distributions of the produced output beam in radial direction are determined by the initial beam parameters and the RSSZP parameters, such as shifting parameter and topological charge. The present work gives also the diffraction by a RSSZP of a fundamental Gaussian beam which is deduced as a particular case in this investigation.

Considerable diversity in generation light-arm beams using multi-twisted phase structure zone plate

We aim here to present a novel Fresnel zone plate- based element which is referred to as multi-twisted zone plate. This element is a zone plate whose phase structure is multi-spirally shifted. It is made of the binary combination of two radial phase shifted spiral zone plate. Given the produced structure, two various-charged vortices are generated prior to the focal plane and following it. Focusing and defocusing behaviors of the element are surveyed theoretically and verified by experiments. Depending on the total charge, a variety of light-arm beams is generated. Further studies elucidate that the charge of the prefocus-formed vortex gradually transforms to the charge of the post focus-formed vortex. Simulation predictions are verified by experiment in order to explore its feasibility.

Characterization of the focusing performance of axial line-focused spiral zone plates.

Axial line-focused spiral zone plates were developed for operation at optical wavelengths. The design, fabrication, and diffraction properties of the proposed element are presented. Numerical results showed that hollow beams could be generated, and that the element can be employed for a multi-wavelength operation. The hollow beam within the focal depth was demonstrated experimentally, using a charge-coupled device camera and sliding guide. The results were consistent with those obtained by the simulations. The proposed optical device exhibits significant potential for various applications including optical manipulation and lithography.

Fractal spiral zone plates

We present diffractive optical elements with an extended depth of focus, namely, fractal spiral zone plates (FSZPs), which combine a fractal structure and spiral zone plates (SZPs) to generate a sequence of coaxial vortices in the focal volume along the propagation direction. The axial irradiance of the FSZPs is examined both experimentally and in a simulation and is compared with that of SZPs and that of fractal zone plates. The focusing properties of the FSZPs with different parameters are investigated, and a potential application to edge-enhancement images is also shown.

Focusing airborne acoustic vortex beams by means of active diffraction gratings

New technologies to generate acoustic vortex beams (VB) have received increasing attention due to their interesting capabilities to transfer angular momentum to matter and to attract particles to the propagation axis. One of the recently reported methods to generate acoustic VB is the fabrication of active diffraction gratings, i.e., acoustic sources whose geometry and vibration mode emulate the field obtained after passing a plane wave through a given passive grating [1]. In this work, we extend this approach by using an active spiral zone plate to produce a beam with a helical and focused structure. This is obtained by gluing an electroactive ferroelectret film on top of a lower electrode structured on a printed circuit board, which in turn results easy and reliable. The broadband feature of the film makes it possible to generate VB throughout the range of interest for most applications in air. Experimental results are compared with numerical simulations. The proposed ultrasonic source opens up new possibilities for particle manipulation and rotation control of small objects. [1] R. D. Muelas H, J. F. Pazos-Ospina, and J. L. Ealo, “Active diffracting gratings for vortex beam generation in air,” J. Acoust. Soc. Am. 141(5), 3569–3569, 2017.

Realization of arbitrarily long focus-depth optical vortices with spiral area-varying zone plates

We provide a methodology to realize an optical vortex with arbitrarily long focus-depth. With a technique of varying each zone area of a phase spiral zone plate one can obtain optics capable of generating ultra-long focus-depth optical vortex from a plane wave. The focal property of such optics was analysed using the Fresnel diffraction theory, and an experimental demonstration was performed to verify its effectiveness. Such optics may bring new opportunity and benefits for optical vortex application such as optical manipulation and lithography.

Generation of X-ray vortex with ultra-long depth of focus using axial line-focused spiral zone plates

We propose axial line-focused spiral zone plates (ALFSZPs) for generating tightly focused X-ray vortex beams with ultra-long depth of focus (DOF) along the propagation direction. In this typical design, compared with the conventional spiral zone plates (SZPs) under the same numerical aperture (NA), the DOF of ALFSZPs has been extended to an ultra-length by optimizing the corresponding parameters. Besides, it also exhibits lower side lobes and smaller dark cores in the whole focus volume. The diameters of dark cores increase as the topological charge value increases.

Modeling of the optical vortex generation using a silver spiral zone plate

Using a FDTD-method implemented in the FullWAVE (RSoft) software, a process of generating optical vortices during the propagation of a left- or right-hand circularly polarized Gaussian pulse through a phase and amplitude spiral zone plate with topological charge 2, a diameter of 8 μm, and a focal length of 532 nm is numerically modeled. An investigation of the amplitude and phase distributions in the focal plane shows the presence of optical vortices with topological charge 2. Analysis of the longitudinal component of the Umov-Poynting vector shows the presence of an inverse energy flow in the focal plane. In the case of using an amplitude spiral zone plate, the magnitude of the reverse flow decreases sharply until it disappears completely for the left circularly polarized incident beams.

A spirally rotating backward flow of light

Using Richards-Wolf formulas, we show that when a left-hand circularly polarized optical vortex with the topological charge 3 is sharply focused in an aplanatic system, a backward near-axis energy flow is observed in the focal plane. While being zero on the axis, the backward flow is only 2-3 times smaller in magnitude than the incident energy flow coming to the focus. It is also shown that near the optical axis the reverse flow propagates spiraling counter-clockwise about the optical axis. The presence of the near-axis backward flow of energy is also shown by the FDTD-aided numerical simulation of diffraction of a circularly polarized plane wave by a third-order spiral zone plate with the NA ≈ 1. A Rayleigh microparticle captured in the focus vicinity is expected to move in the opposite direction to the beam propagation.