Kinoform Lenses Research Articles

PyMOE: Mask design and modeling for micro optical elements and flat optics

We introduce a new open-source software package written in Python to design and model micro optical elements, such as diffractive lenses, holograms, as well as other components within the broad area of flat optics, and generate their corresponding (production-ready) lithography mask files. To this aim, the package provides functions to design a multitude of kinoform lenses, phase masks and holograms, but is versatile and the user can implement any arbitrary numerical or analytical optical component designs. For validating the designs, this package provides scalar diffraction propagation to simulate optical field propagation in different regimes covering near- and far-field regions (Fresnel, Fraunhofer and Rayleigh-Sommerfeld). Particularly, by implementing Rayleigh-Sommerfeld propagation, we demonstrate accurate field propagation within near- and far-field ranges, providing versatility and accuracy. Importantly, the package allows to directly export production-ready multilevel/binary lithography mask files of the designed optical components. Additionally, metasurface masks can conveniently be generated for any user-defined meta-element library given as input. Finally, the software package capabilities are illustrated with examples of mask design and modeling of diffractive lenses, holograms, and metasurfaces susceptible of being fabricated via lithography techniques. Beyond lithography, the package can also straightforwardly be used in other applications requiring mask generation, such as beam shaping, optical trapping and digital holography.

Multi-trap optical tweezers based on kinoform Silver Mean lenses

In this paper, we present the design and implementation of multi-trap optical tweezers based on new quadrifocal kinoform lenses. The phase distribution of these diffractive lenses is characterized by the Silver Mean sequence. The focusing properties of the resulting aperiodic DOEs coined Kinoform Silver Mean Lenses (KSMLs) are numerically examined. It is shown that, under monochromatic illumination, a KSML drives most of the incoming light into four single foci whose focal lengths are related to the Silver ratio. In this way, a KSML improves the diffraction efficiency of binary Fresnel Silver Mean Zone Plates. Through experimental results, the simultaneous trapping of particles in the four focal planes and their three-dimensional manipulation is demonstrated.

Terahertz focusing blazed diffractive optical elements for frequency demultiplexing

This study presents the novel optical passive components for spatial frequency division demultiplexing of terahertz (THz) radiation. Four different diffractive optical elements (DOEs) were designed as the combination of phase kinoform lenses and phase blazed diffraction gratings. The designed structures were verified in numerical simulations and they showed the promising results. Subsequently, they were manufactured using fused deposition modeling (FDM) 3D printing technology from highly transparent cyclic olefin copolymer (COC). The manufactured structures were examined in the experimental setup. The results matched numerical simulations. Thus, eight frequencies in the range from 150 GHz to 220 GHz every 10 GHz were spatially separated. The novel design solution guaranteed 63% higher relative efficiency compared to the reference DOE. The presented study can be suitable as the application for 6G technology telecommunication systems as the spatial frequency division demultiplexing component for the THz radiation band.

PMMA based compound kinoform lenses for sub-150 nm hard x-rays focusing

It is the first time to fabricate the polymethyl methacrylate (PMMA) based compound kinoform lenses (CKLs) for nano-focusing of hard x-rays. The PMMA CKLs with a physical aperture of 160 µm and a focal length of 20 mm are designed and fabricated by x-ray LIGA technology at the Beijing Synchrotron Radiation Facility. To improve the stiffness of the PMMA lines, PMMA sheets with high molecular weight are fabricated, and the results revealed that the PMMA lines with higher molecular weight were much stronger. After optimization, CKLs with the narrowest lines of 4 µm width can achieve 110 µm height and 2.99 nm surface roughness without deformation. The CKLs were tested at the Diamond Light Source, which provided a focal width of 122 nm for 12 keV x rays. Though the PMMA has a poor radiation tolerance, it has a better process tolerance, and it can lay a good foundation for the fabrication of SU8 based CKLs by LIGA technology, which has a better radiation tolerance. Compared to the Si CKLs fabricated by dry etching, the PMMA CKLs are higher in depth, smoother at the sidewall, and have better nanofocusing.

Partially coherent light propagation through a kinoform lens.

Combining wave optics propagation and geometric ray tracing, the mutual optical intensity (MOI) model is extended to quantitatively simulate the propagation of partially coherent light through a kinoform lens at high speed. The MOI model can provide both a high accuracy and a high efficiency simulation. The intensity and coherence degree distributions at the focal plane are calculated using the MOI model. It is beneficial to improve the focusing capability of the kinoform lens by reducing the coherence or increasing the number of lens steps. In addition, increasing the number of steps is also beneficial to increase the photon flux and reduce the depth of focus.

Design optimization of one-dimensional aberration-free x-ray gradually focusing lenses

In our previous work, we proposed a new design method for an aberration-free x-ray refractive focusing lens based on an ideal Cartesian oval shape to solve the aberration problem in x-ray compound refractive focusing. In this paper, we propose an optimization method for this new lens. By reducing the aperture of each lens, we achieve the objective of increasing the effective aperture and improving the focusing performance of the lens. The simulation of the beam propagation method shows that the focusing performance of the optimized lenses is better in compound refractive lens shape but worse in the kinoform shape. This is different from the results obtained with the conventional kinoform lens. After further comparison, we found that this is because the step height of the kinoform lens is small when the lens aperture is very small, resulting in a strong diffraction effect that weakens the focusing performance of the lens. Further modifications to the structure of the kinoform lens are needed to improve this phenomenon.

X-ray propagation through a kinoform lens.

Combining geometric ray tracing and wave optics propagation, a new simulation model named LWF is established to calculate the full coherent X-ray propagation through a kinoform lens. The LWF model is used to analyze the X-ray propagation through long and short kinoform lenses and calculate the intensity distribution at the focal plane. When the aperture is large, the focal spot for the long kinoform lens is smaller than that for the short kinoform lens. Due to the use of the geometric ray-tracing method to calculate the beam propagation inside the kinoform lens, the LWF model takes a low number of transversal wavefront segments, i.e. a short time, to achieve high accuracy. The simulation times for the one-dimensional and two-dimensional LWF models are 0.025 s and 5.3 s, respectively, with a calculation error of less than 0.5%. The high efficiency and high accuracy make the LWF model a strong tool in designing kinoform lenses.

Adiabatically focusing X-rays to the nanometer scale by one dimensional long kinoform lenses: comparison between an ideal Cartesian oval refocusing lens and a parabolic lens.

The nano-focusing performance of adiabatically designed Cartesian oval refocusing lenses is compared with other well known compound refractive lenses with parabolic profiles (both simple concave and kinoform types). Using beam propagation method (BPM) simulation, it is shown that our design based on oval lenses does significantly improve the focusing properties compared to other parabolic lens based designs, e.g. adiabatically focusing lenses (AFLs), which doesn't take into account of the refocusing effect. This points to the importance of optimizing complex lens design in improving nano-focusing lens performance.

High-accuracy computation of hard X-ray focusing and imaging for refractive optics.

A mathematical apparatus for solving problems of X-ray wave propagation through complex optical systems, when the lens thickness can change with jumps, is developed and presented. The developed method is based on the use of the superposition of oriented Gaussian beams, which satisfy the Helmholtz equation with high accuracy. The wave propagation in air and through kinoform and ordinary lenses is considered. Focusing and imaging properties are compared for both types of X-ray optics. The diffraction effects arising due to thickness jumps in the kinoform lenses and the influence of these jumps on the X-ray focusing and imaging are investigated. The prospect of using the developed theory for X-ray optics applications is discussed.

3D nanoprinted kinoform spiral zone plates on fiber facets for high-efficiency focused vortex beam generation.

In this paper, we propose and demonstrate an all-fiber high-efficiency focused vortex beam generator. The generator is fabricated by integrating a kinoform spiral zone plate (KSZP) on the top of the composite fiber structure using fs-laser two-photon polymerization 3D nanoprinting. The KSZP with spiral continuous-surface relief feature is designed by superimposing a spiral phase into a kinoform lens, which can efficiently concentrate and transform an all incident beam to a single-focus vortex beam, without the undesired zero-order diffracted light and extra high-order focus. Under arbitrary polarized light incident conditions, experiment results show that the focusing efficiency and vortex purity of the all-fiber generators are over 60% and 86%, respectively, which is much higher than that of a traditional binary SZP integrated on an optical fiber facet. In addition, characteristics of the generated vortex beam, such as focal spot, focal length and vortex topological charge are numerically designed and experimentally investigated. The experimental results agree well with the numerical simulation model using the FDTD algorithm. Due to the compact size, flexible design, polarization insensitivity, high focusing efficiency and high vortex purity, the proposed all-fiber photonic devices have promising potential in optical communication, particle manipulation and quantum computation applications.

A study of greyscale electron beam lithography for a 3D round shape Kinoform lens for hard X-ray optics

For high quality imaging of materials in nanoscale by hard X-ray optics, high resolution lenses with high focusing/imaging efficiency are needed. Refraction based conventional Kinoform lenses with 1D linear configuration in Si has been attempted for decades, but there has still been no sign of success due to the enormous difficulty in fabrication. This paper proposes a novel configuration of golden Kinoform lenses with round shape on a plate, in which each zone maintains the typical 3D parabolic profile as seen in the traditional 1D counterpart. The major focus in this work is on the generation of the 3D profile in e-beam resist through greyscale electron beam lithography (EBL) as the template for the golden Kinoform lens. Systematic study of the greyscale lithography conditions, including the comparisons of resists, developers and charge distributions, has been conducted by using Monte Carlo simulation as well as e-beam lithography. Initial results have been achieved for replicating the desired 3D profile of the golden Kinoform lens in the resist. Using the generated profile in resist as templates, the golden Kinoform lens with 200 μm diameter and 3.5 μm height has been successfully fabricated, for the first time, which will hopefully replace the existing Fresnel zone plates for hard X-ray imaging with high resolution and high efficiency.

Ultimate limitations in the performance of kinoform lenses for hard x-ray focusing

Diffractive x-ray lenses suffer from limited focusing efficiency, which can be improved by replacing the binary nanostructures of the lenses with kinoforms. Here we present the first example of kinoform lenses for x rays and compare their efficiency with those of binary Fresnel zone plates (FZPs), realized through gray-scale-focused Xe ion beam lithography. Unexpectedly, experimental results indicate lower focusing efficiencies of kinoform lenses compared to binary FZPs between 5–7 keV. Simulations that include absorption reveal that kinoform lenses can only provide a limited boost in the diffraction efficiency in multi-keV x-ray energies and for impractical lens thicknesses. Combined with significant challenges in kinoform lens fabrication, the modest gains of this approach may suggest that it is not the path to increasing focusing efficiency.

Mathematical Tool for Calculating the Microstructure of a Harmonic Kinoform Lens

The paper presents a mathematical tool based on the requirement of tautochronism in each of the diffraction orders of a harmonic kinoform lens, which was used as the basis to develop a method for calculating the lens microstructure. The method provides a limitation of the relative longitudinal chromatism of the lens to a given level. In addition, it allows obtaining the initial parameters necessary for the ray calculation and optimization of an optical system with a harmonic kinoform lens using well-known commercial optical design computer programs.

Kinoform and saw-tooth X-ray refractive lenses development at SSRF

Here we describe the effort made at Shanghai Synchrotron Radiation Facility (SSRF) to develop X-ray refractive lenses for real beamline applications. Fabrication process of silicon and germanium based kinoform lenses are optimized to increase the height-width aspect ratio and decrease the roughness. Saw-tooth lenses made with a new fabrication process based on dry etching are also described. Focusing effect for both kinoform and saw-tooth lenses are tested at Shanghai Synchrotron.

Comparative analysis of the Fresnel lens and the kinoform lens

Based on a unified approach in the ray approximation, the focusing properties of Fresnel lenses and kinoform lenses are considered and compared. Particular attention is paid to the energy efficiency, chromatic focal shift and resolving power of these elements. It is shown that the Fresnel lens with same-depth segments is an analogue of the harmonic kinoform lens operating in high diffraction orders. A mechanism of the formation of the diffraction pattern in the focal plane of a Fresnel lens with equidistant annular segments is analyzed. It is shown to differ from the corresponding diffraction pattern formed by a conventional refractive lens by a smaller amount of energy coming to the main maximum and a significant proportion of energy transferred to the side maxima. The target audience of this article is students and graduate students, as well as specialists in the fields of science and technology where optical methods and instruments play an ever increasing role.

Modeling of the Formation of Steep Portions of a Piecewise Continuous Profile in a One-Step Technology for Fabricating Diffractive Optical Elements using Oblique Laser Beams

This paper presents the results of modeling the most important component of a one-step technology of fabricating kinoform lenses in thick photoresist layers with increased diffraction efficiency due to the formation of backward slopes of Fresnel zones with a steepness of up to 90° using oblique laser beams. It is shown that this method of fabricating volume structures makes it possible to significantly increase the steepness of backward slopes of the zones in low-contrast photoresists (k = 3) and to form practically vertical slopes in moderate-contrast photoresists (k = 10).

Fabrication of high energy X-ray compound kinoform lenses using X-ray lithography

Nickel high energy X-ray compound kinoform lenses were fabricated by X-ray lithography technology at Beijing Synchrotron Radiation Facility. The nickel compound refractive lenses aim at focusing X-ray with 50 keV and the designed smallest width of the tooth-like segment is 2.5 μm. To keep the best morphology of the element, Au masks were made twice, whose thickness gradually increased. The fabrication process of compound lenses consists of three parts in general, including the intermediate mask (1.2 μm thick Au pattern) fabrication, the working mask (12 μm thick Au pattern) fabrication and the 300 μm high lenses fabrication. The intermediate mask was made by UV lithography (UV sample) and electron beam direct write lithography (EBDW sample) for comparison, and the EBDW sample had a better morphology than the UV sample at each step. Both samples were tested using the knife-edge scan method at BL13W1 beamline in Shanghai Synchrotron Radiation Facility, which provided the focal widths of 9.2 and 10.4 μm, and the photon flux gains of 6.9 and 5.4 for the EBDW and UV samples at an X-ray energy with 50 keV, respectively.

聚甲基丙烯酸甲酯材质硬X射线组合Kinoform透镜的制作

聚甲基丙烯酸甲酯材质硬X射线组合Kinoform透镜的制作

Large-aperture prism-array lens for high-energy X-ray focusing.

A new prism-array lens for high-energy X-ray focusing has been constructed using an array of different prisms obtained from different parabolic structures by removal of passive parts of material leading to a multiple of 2π phase variation. Under the thin-lens approximation the phase changes caused by this lens for a plane wave are exactly the same as those caused by a parabolic lens without any additional corrections when they have the same focal length, which will provide good focusing; at the same time, the total transmission and effective aperture of this lens are both larger than those of a compound kinoform lens with the same focal length, geometrical aperture and feature size. This geometry can have a large aperture that is not limited by the feature size of the lens. Prototype nickel lenses with an aperture of 1.77 mm and focal length of 3 m were fabricated by LIGA technology, and were tested using CCD camera and knife-edge scan method at the X-ray Imaging and Biomedical Application Beamline BL13W1 at Shanghai Synchrotron Radiation Facility, and provided a focal width of 7.7 µm and a photon flux gain of 14 at an X-ray energy of 50 keV.

Phase space of partially coherent light with discontinuous surfaces

We propagate partially coherent light through discontinuous surfaces and analyze the optical effects in phase space. The discontinuous surfaces are classified into two types, those with discontinuity in space and those with discontinuity in slope. Results are discussed based on the Wigner function. This approach explains the performance of segmented elements during the transition from the refractive into the diffractive regime. At first the diffraction effects generated by a single discontinuity (e.g. a phase step and a linear axicon) are investigated. Later on we discuss surfaces with periodic discontinuities, e.g. gratings, to study the formation of multiple diffracted orders. A kinoform lens is given as a further example to visualize the change from pure refraction to diffraction. Moreover, we present the beam homogenizing effect in phase space generated by lens arrays.