Linear Zone Plates Research Articles

Method for a deflection-type refractometer measuring the fringe shift by using linear Fresnelzone plates.

This study describes the design and performance of a deflection-type refractometer based on measuring the fringe shift from the Fresnel diffraction pattern to solve some major limitations of conventional differential refractometers, such as measurement range, resolution, zero balancing, and monitoring analysis. The refractometer apparatus comprises a coherent light source, linear Fresnel zone plate, measuring cell, and image capture device mounted on a movable platform. The distance measurement unit is configured to detect fringe deflection due to the difference in refractive index between the sample and the reference. To achieve this, distance measurements with an accuracy of a few nanometers by using the local frequency method and fringe shift measurement method are quite feasible. The uncertainty in this technique is determined by the smallest change in the longitudinal displacement of the image for which the CCD camera can detect a change in pixel position. The refractive index is obtained with a highly extended measurement range of at least ±0.4R I U and precision of the order of 2×10-4 R I U. A numerical comparison between computer simulation of the diffraction patterns that occur when the linear Fresnel zone plate is illuminated by a plane light traveling parallel to the z axis.

Novel fabrication and designs for hybrid optical elements with wider angle field of view by using integrated direct laser lithographic system

Hybrid optical elements, which are diffraction pattern arrays fabricated on curved refractive optical elements, have the ability to widen the field of view angle, and improve optical performance, by combining refraction and diffraction. As such, they have high potential in next-generation optical devices. However, manufacturing a high resolution diffraction pattern array that fully covers the curve of the refracted optical surface, so that the normal vectors of every pattern are perpendicular to the tangent plane of the refractive lens surface, is challenging. Furthermore, the lack of diffractive pattern designs corresponding to the curvature makes it difficult to replace curved microlens arrays with hybrid optics. In this study, a direct laser lithographic system combined with an auto-focus system and high accuracy rotational system was built to fabricate the diffractive patterns array on a cylindrical lens. This approach provides a method to manufacture hybrid optical elements with wider field of view. In addition, we proposed novel designs of a linear zone plate (LZP) and elliptical zone plate (EZP) on a cylindrical lens that can be used for focusing light beam into lines and points, respectively. These hybrid optics exhibit superior performance in both diffraction efficiency and resolution, 25% better than traditional diffractive optical elements. An array of two types of zone plates were fabricated fully along the curve of the cylindrical lens using the proposed system, giving a 20° angle field of view, which acts like a curved cylindrical lens array and 1D curved microlens array. The performance of these hybrid optical elements were evaluated by optical verification system and simulation.

Diffractive analysis of spiral checkerboard zone plate

This work studies the unique behavior of spiral checkerboard zone plates under plane wave illumination. The element is constructed by superimposing two orthogonal helical linear zone plates. Based on their topological charge, various structured beams are generated whose structures display fascinating dynamics. Structure transforming, vortex pair production, annihilation, and the interaction of dipole and singular vortices, are some of the observed phenomena during the beam propagation produced by the element. On top of all that, we see the interaction of screw dislocations in the way that they get closer together when the diffracted beam propagates toward the focus, and they move away from each other as the beam moves away from the focus.

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.

Capability of topological charge-based orthogonal zone plate in generating sharp focal spot and ring-like beam

We aim to present an orthogonal symmetric-based diffractive lens which has unique focusing properties. Structure of the element is based on the framework of orthogonal zone plate which is constructed by overlaying two perpendicular linear zone plates with opposite topological charges. We illustrate that the proposed element has sharper focal spot as well as longer focal depth than square and circular zone plate. Apart from having smaller spot size, it also generates a ring-like pattern at a given distance from the focus which depends on topological charge. Maintaining its shape in a distance equal to focal depth may be considered as an interesting feature of the generated annular beam. It is also demonstrated that numerical simulations are verified by experiments.

Appearance of fractional vortex dipoles by using spiral linear zone plate

We present a novel technique based on linear zone plate (LZP) by which linear singularities regarded as fractional vortex dipoles are efficiently generated. Our approach requires applying spiral phase to a LZP, so fractional vortex dipoles are then acquired. By also implementing transverse phase shift to the spiral LZP, we are able to equally divide the number of the produced dark beams carrying mixed phase dislocations into two transverse separate parts. As a result, by varying a so called the controlling parameter the lateral positions of the focused fractional vortex dipoles are changed. Since we are able to generate dark beams in different and specific linear positions, therefore we suggest these features will be of great interest in one-dimensional optical trapping. All results are completely verified by experimental works.

Focusing specification of cross-like Fresnel zone plate

Focusing characteristics of cross like Fresnel zone plate is well analyzed. This element is composed of two perpendicular linear Fresnel zone plates. Focusing properties of the element is compared to a classic and square Fresnel zone plate. Analysis clarify that focusing of the elements is well corrected in comparison to square Fresnel zone plate. Resolution is noticeably increased, DC noise and diffraction efficiency are substantially reduced and also secondary maxima have been evidently suppressed. Theoretical results have been completely verified by experiment.

Focusing performance of a multilayer Laue lens with layer placement error described by dynamical diffraction theory.

The multilayer Laue lens (MLL) is essentially a linear zone plate with large aspect ratio, which can theoretically focus hard X-rays to well below 1 nm with high efficiency when ideal structures are used. However, the focusing performance of a MLL depends heavily on the quality of the layers, especially the layer placement error which always exists in real MLLs. Here, a dynamical modeling approach, based on the coupled wave theory, is proposed to study the focusing performance of a MLL with layer placement error. The result of simulation shows that this method can be applied to various forms of layer placement error.

Generation of double line focus and 1D non-diffractive beams using phase shifted linear Fresnel zone plate

Abstract Phase shifted linear Fresnel zone plates are presented for the first time. These diffractive elements are linear Fresnel zone plates in which their phase are laterally shifted. The impact of the phase shifting on their diffractive and focusing properties are studied. It is demonstrated that by shifting the phase, two parallel linear beams can be generated at the focal plane. Furthermore, as they are propagating, a non-diffractive line-shaped beam is generated at a given distance from the focus. Transverse intensity profile of the beam at different distances as well as its cross section of propagation along the optical axis clearly shows that the intensity profile of the beam is really kept unchanged as it is propagated. All results are completely verified by experiments.

Precision alignment of integrated optics in hybrid microsystems.

We achieve submicrometer precision in the integration of micro-optics with surface electrode ion traps. The high-precision alignment is accomplished using off-axis linear Fresnel zone plates (FZPs). Four pairs of FZPs are fabricated on the optics chip that contains the high numerical aperture microlens, a diffractive optical element (DOE). The four pairs of FZPs enable alignment in six translational and rotational degrees of freedom. Four corresponding alignment rulers are etched in the top metal layer of the ion trap, enabling quantification of misalignment. The integration of optics for efficient light delivery and the collection of fluorescence from trapped ions are key to achieving scalability in quantum information processing. An accurate and precise approach to the integration of DOEs advances the scalability of surface electrode ion traps and many other hybrid microsystems.

Kinoform diffractive lenses for efficient nano-focusing of hard X-rays.

A nano-focusing module based on two linear Fresnel zone plates is presented. The zone plates are designed to generate a kinoform phase profile in tilted geometry, thus overcoming the efficiency limitations of binary diffractive structures. Adjustment of the tilt angle enables tuning of the setup for optimal efficiency over a wide range of photon energies, ranging from 5 to 20 keV. Diffraction efficiency of more than 50% was measured for the full module at 8 keV photon energy. A diffraction limited spot size of 100 nm was verified by ptychographic reconstruction for a lens module with a large entrance aperture of 440 μm × 400 μm.

Ultra-high aspect ratio high-resolution nanofabrication for hard X-ray diffractive optics.

Although diffractive optics have played a major role in nanoscale soft X-ray imaging, high-resolution and high-efficiency diffractive optics have largely been unavailable for hard X-rays where many scientific, technological and biomedical applications exist. This is owing to the long-standing challenge of fabricating ultra-high aspect ratio high-resolution dense nanostructures. Here we report significant progress in ultra-high aspect ratio nanofabrication of high-resolution, dense silicon nanostructures using vertical directionality controlled metal-assisted chemical etching. The resulting structures have very smooth sidewalls and can be used to pattern arbitrary features, not limited to linear or circular. We focus on the application of X-ray zone plate fabrication for high-efficiency, high-resolution diffractive optics, and demonstrate the process with linear, circular, and spiral zone plates. X-ray measurements demonstrate high efficiency in the critical outer layers. This method has broad applications including patterning for thermoelectric materials, battery anodes and sensors among others.

Metal-assisted etching of silicon molds for electroforming

Ordered arrays of high-aspect-ratio micro/nanostructures in semiconductors stirred a huge scientific interest due to their unique one-dimensional physical morphology and the associated electrical, mechanical, chemical, optoelectronic, and thermal properties. Metal-assisted chemical etching enables fabrication of such high aspect ratio Si nanostructures with controlled diameter, shape, length, and packing density, but suffers from structure deformation and shape inconsistency due to uncontrolled migration of noble metal structures during etching. Hereby the authors prove that a Ti adhesion layer helps in stabilizing gold structures, preventing their migration on the wafer surface while not impeding the etching. Based on this finding, the authors demonstrate that the method can be used to fabricate linear Fresnel zone plates.

Sliced linear zone plates for hard X-ray radiation

Linear zone plates for hard (E > 10 keV) X rays are considered. The technology of the plates includes cutting magnetron-sputtered W5Si3/Si multilayer coatings. The results of numerical computation suggest that this pair of materials provides a high efficiency in the first and second diffraction orders. It is found experimentally that good multilayer structures consisting of several hundreds of layers can be synthesized on silicon and glass substrates. It is shown that they can be cut by ion etching the multilayer coating through a mask.

A unique approach to accurately measure thickness in thick multilayers

X-ray optics called multilayer Laue lenses (MLLs) provide a promising path to focusing hard X-rays with high focusing efficiency at a resolution between 5 nm and 20 nm. MLLs consist of thousands of depth-graded thin layers. The thickness of each layer obeys the linear zone plate law. X-ray beamline tests have been performed on magnetron sputter-deposited WSi(2)/Si MLLs at the Advanced Photon Source/Center for Nanoscale Materials 26-ID nanoprobe beamline. However, it is still very challenging to accurately grow each layer at the designed thickness during deposition; errors introduced during thickness measurements of thousands of layers lead to inaccurate MLL structures. Here, a new metrology approach that can accurately measure thickness by introducing regular marks on the cross section of thousands of layers using a focused ion beam is reported. This new measurement method is compared with a previous method. More accurate results are obtained using the new measurement approach.

Thinning and polishing of cross-section of depth-graded WSi2/Si multilayer for linear zone plate application

A linear zone plate named multilayer laue lens (MLL) is fabricated using a depth-graded multilayer structure. The lens shows considerable potential in focusing an X-ray beam into a nanometer scale with high efficiency. In this letter, a depth-graded multilayer consisting of 324 alternating WSi2 and Si layers with a total thickness of 7.9 \mu m is deposited based on the thickness sequence according to the demands of the zone plate law. Subsequently, the multilayer sample is sliced and thinned to an ideal depth along the cross-section direction using raw abrasives and diamond lapping. Finally, the cross-section is polished by a chemical mechanical polishing (CMP) technique to remove the damages and improve the surface smoothness. The final depth of the MLL is approximately 7 μm with an achieved aspect ratio greater than 400. Results of scanning electron microscopy (SEM) and atomic force microscopy (AFM) indicate that interfaces are sharp, and the multilayer structure remains undamaged after the thinning and polishing processes. The surface roughness achieved is 0.33 nm.

Bonded Multilayer Laue Lens for focusing hard X-rays

We have fabricated partial Multilayer Laue Lens (MLL) linear zone plate structures with thousands of alternating WSi 2 and Si layers and various outermost zone widths according to the Fresnel zone plate formula. Using partial MLL structures, we were able to focus hard X-rays to line foci with a width of 30 nm and below. Here, we describe challenges and approaches used to bond these multilayers to achieve line and point focusing. Bonding was done by coating two multilayers with AuSn and heating in a vacuum oven at 280–300 °C. X-ray reflectivity measurements confirmed that there was no change in the multilayers after heating to 350 °C. A bonded MLL was polished to a 5–25 μm wedge without cracking. SEM image analyses found well-positioned multilayers after bonding. These results demonstrate the feasibility of a bonded full MLL for focusing hard X-rays.

Sectioning of multilayers to make a multilayer Laue lens

We report a process to fabricate multilayer Laue lenses (MLL's) by sectioning and thinning multilayer films. This method can produce a linear zone plate structure with a very large ratio of zone depth to width (e.g., >1000), orders of magnitude larger than can be attained with photolithography. Consequently, MLL's are advantageous for efficient nanofocusing of hard x rays. MLL structures prepared by the technique reported here have been tested at an x-ray energy of 19.5 keV, and a diffraction-limited performance was observed. The present article reports the fabrication techniques that were used to make the MLL's.

Numerical modeling of optical properties of a system of two zone plates for focusing hard synchrotron radiation

Results of numerical experiments on focusing of a monochromatic spherical wave by a system of two linear zone plates are reported. Calculations were performed for a photon energy of 12.3985 keV and zone plates with a radius of the first zone of 5 μm, a number of zones of 628, and an aperture of 250 μm. To calculate the Kirchhoff integrals, the double Fourier transform method was used and the fast Fourier transform procedure on a grid with a number of points 65 536 = 216 was applied. On the basis of the calculation results, a conclusion was drawn that two zone plates operate as one with a doubled phase shift in zones with a material if the longitudinal distance between them is smaller than 1/3 of the focus depth and the transverse displacement is smaller than 1/3 of the outermost zone width (the focus size). If the distance (displacement) exceeds the focus depth (size), the two zone plates operate independently, similar to refracting lenses with a set of different focusing orders, including the zero order. The nature of the moire pattern at a transverse displacement of the zone plates is discussed.

Nanometer focusing properties of Fresnel zone plates described by dynamical diffraction theory

The x-ray focusing properties of linear Fresnel zone plates have been derived by solving the Helmholtz equation for the field propagating through the zones. We consider the imaging of a point object into the first diffraction order of a volume zone plate having its zones parallel to the optical axis. For plane wave illumination, the focal spot size is limited by the same material-dependent but wavelength-independent value that affects waveguide focusing. In marked contrast, for the one-to-one imaging condition, corresponding to specular reflection of the x rays from the zone boundaries, the image is found to have a minimal spot size approximately equal to the outermost zone width. Unlike x-ray waveguides, zone plates therefore do not appear to possess a fundamental limit to the smallest spot size to which they can focus.