Binary Zone Plate Research Articles

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.

Enhanced imaging with binary circular Dammann Fresnel zone plate

We introduce a novel approach in optical engineering by combining Dammann gratings with binary Fresnel zone plates to create a unique hybrid optical element with enhanced energetic efficiency of its focal spots. Traditionally, binary Fresnel zone plates focus light at multiple points with varying intensities, while Dammann gratings are renowned for their efficient and uniform light splitting capabilities. Our innovation lies in merging these two elements and generating a binary circular Dammann (varying along the radial direction) Fresnel zone plate that concentrates most of the incident light into a small and desired number of focused points with equal intensities, rather than distributing light’s energy non-equally across multiple points. This novel design significantly enhances the efficiency and precision of light manipulation. It opens new possibilities in applications requiring high-intensity focal points, such as in advanced medical imaging and in accurate scientific measurements. By redefining the conventional roles of these optical elements, our research contributes an advancement to the field, paving the way for innovative solutions in various optical applications.

Generation of ultra-intense vortex laser from a binary phase square spiral zone plate.

With the development of ultra-intense laser technology, the manipulation of relativistic laser pulses has become progressively challenging due to the limitations of damage thresholds for traditional optical devices. In recent years, the generation and manipulation of ultra-intense vortex laser pulses by plasma has attracted a great deal of attention. Here, we propose a new scheme to produce a relativistic vortex laser. This is achieved by using a relativistic Gaussian drive laser to irradiate a plasma binary phase square spiral zone plate (BPSSZP). Based on three-dimensional particle-in-cell (3D-PIC) simulations, we find that the drive laser has a phase difference of π after passing through the BPSSZP, ultimately generating the vortex laser with unique square symmetry. Quantitatively, by employing a drive laser pulse with intensity of 1.3 × 1018~W/cm2, a vortex laser with intensity up to 1.8 × 1019~W/cm2, and energy conversion efficiency of 18.61% can be obtained. The vortex lasers generated using the BPSSZP follow the modulo-4 transmutation rule when varying the topological charge of BPSSZP. Furthermore, the plasma-based BPSSZP has exhibited robustness and the ability to withstand multiple ultra-intense laser pulses. As the vortex laser generated via the BPSSZP has high intensity and large energy conversion efficiency, our scheme may hold potential applications in the community of laser-plasma, such as particles acceleration, intense high-order vortex harmonic generation, and vortex X/γ-ray sources.

High-efficiency metalenses for zone-plate-array lithography

To date, zone-plate-array lithography has employed an array of binary pi-phase zone plates, each 135 μm in diameter, operating at 405 nm wavelength, in conjunction with a spatial-light modulator and a moving stage, to expose large-area patterns in photoresist without a mask. Although the low focal efficiency (<34%) and high background (>66%) of such zone plates can be mitigated via proximity-effect correction, increased focal efficiency would enable higher quality patterning. To that end, we have designed flat, diffractive-optical “metalenses.” Each is first divided into Fresnel zones, across which the effective index-of-refraction is modulated by forming appropriate pillars or holes such that diffracted beams interfere constructively at the focal spot, located 100 μm in front of the lens plane. The diffraction efficiency of each zone is simulated using rigorous-coupled-wave analysis. A genetic algorithm is then used to determine if higher efficiency can be achieved by repositioning of the pillars or modifying their widths. MEEP software is used to predict focal efficiency of the completed metalens design. Scanning-electron-beam lithography was used to fabricate effective-index-modulated metalenses in CSAR-62 e-beam resist. In some cases, the focal properties and efficiencies of such structures were measured, yielding focal efficiencies up to 54%. In other cases, the e-beam-written pattern was transferred into a spin-on hard mask and then into an organic dielectric of 1.9 index of refraction using reactive ion etching. Focal efficiencies up to 69% are predicted for such structures, a significant improvement over the binary pi-phase zone plates used previously.

Generalized binary spiral zone plates with a single focus obtained by feedforward neural network.

Traditional spiral zone plates (SZPs) have been widely used to generate optical vortices, but this structure suffers from multiple focuses. To eliminate high-order foci, the current method is to design a binary structure that has a sinusoidal transmittance function along the radial direction. With the rapid development of artificial neural networks, they can provide alternative methods to design novel SZPs with a single focus. In this paper, we first propose the concept of generalized binary spiral zone plates (GBSZPs), and train a feedforward neural network (FNN) to obtain the mapping relationship between the relative intensity of each focus and the structural parameters of GBSZPs. Then the structural parameters of GBSZPs with a single focus were predicted by the trained FNN. It is found by simulations and experiments that the intensities of high-order foci can be as low as 0.2% of the required first order. By analyzing the radial transmittance function, it is found that this structure has a different distribution function from the previous radial sinusoidal function, which reveals that the imperfect radial sinusoidal form also can guide the design of binary zone plates to eliminate high-order foci diffraction. These findings are expected to direct new avenue towards improving the performance of optical image processing and quantum computation.

Silicon Fresnel Zone Plate Metalens with Subwavelength Gratings.

Metalenses are planar optical components that have demonstrated immense potential for integrated optics. In particular, they are capable of high-efficiency subwavelength focusing without the bulkiness of traditional lenses. Dielectric metalenses operating in the C-band typically employ relatively tall, amorphous silicon structures arranged in a periodic array. Phase control spanning from 0 to 2π is accessed by varying the geometry of these scattering structures. The full 2π phase range is necessary to impose a hyperbolic focusing phase profile, but this is difficult to achieve without custom fabrication practices. In this work, we propose a binary phase Fresnel zone plate metalens designed for the standard 500 nm silicon-on-insulator platform. Our design uses subwavelength gratings with trapezoidal segmentation to form concentric rings. The effective index of the grating is set with the duty cycle using a single full-etch step to form the binary phase profile of the zone plate. The metalens design can be easily tuned to achieve longer focal lengths at different wavelengths. It offers a simple platform for high-throughput wavelength-scale focusing elements in free-space optics, including for microscopy and medical imaging.

A compound Kinoform/Fresnel zone plate lens with 15 nm resolution and high efficiency in soft x-ray

X-ray microscope as an important nanoprobing tool plays a prevailing role in nano-inspections of materials. Despite the fast advances of high resolution focusing/imaging reported, the efficiency of existing high-resolution zone plates is mostly around 5% in soft x-ray and rapidly goes down to 1%–2% when the resolution approaches 10 nm. It is well known that the rectangular zone shape, beamstop, limited height/width ratios, material absorption of light and structural defects are likely responsible for the limited efficiency. Although zone plates with Kinoform profile are supposed to be efficient, progress for achieving both high resolution (<30 nm) and high efficiency (>5%) have hardly been addressed in soft x-ray. In this work, we propose a compound Kinoform/Fresnel zone plate (CKZP) by combing a dielectric Kinoform zone plate with a 15 nm resolution zone plate. Greyscale electron beam lithography was applied to form the 3D Kinoform zone plate and atomic layer deposition was carried out to form the binary zone plate. Optical characterizations demonstrated 15 nm resolution focusing/imaging with over 7.8% efficiency in soft x-ray. The origin of the efficiency improvement behind the proposed compound lens is theoretically analyzed and discussed.

Binary square spiral zone plates trimmed with quasi-random dots for single-order focusing

How to realize a square spiral zone plates with a single focus is still plagued by the trade-off between structural complexity and fabrication difficulty. Here, we propose a new single optical element, named Quasi-random dots Square Spiral Zone Plates (QDSSZPs), to suppress high-order foci. The key idea of this design is to reshape the structure of a square spiral zone plates using a quasi-random distribution of rectangular dots to make it sinusoidal in transmittance. Numerical simulations and experimental results show that the QDSSZPs has a good single-order focus characteristic and can effectively suppress undesired high-order foci, which is almost consistent with the theoretical prediction. The characteristic of suppressing high-order foci in the QDSSZPs has broad applications in imaging and microscopy.

Extended depth of field of a diffraction limited imaging system using a spatial light modulator based intensity compensated polarization coded aperture

Reducing the aperture size is a conventional technique to obtain extended depth of field (DOF) of an imaging sytem, but it is obscured by depleting illumination. Polarization coded apertures (PCAs) can be employed to circumvent this critical artifact. We experimentally demonstrate intensity compensated polarization encrypted apertures, which are designed using the polarization modulation characteristics of LC-SLM. PCAs are not limited by the aperture size and hence far-field point spread function (PSF) can be more conveniently recorded using these PCAs. We experimentally show that DOF of a diffraction limited lens and axial intensity of binary Fresnel zone plate (BFZP) is enhanced using PCAs with nominal intensity loss.

Optical vortices: A methodology for generating single-focus phase singularity with binary square spiral zone plates

<p indent="0mm">Since 1992, the British researcher Allen demonstrated theoretically and experimentally that vortex beams have orbital angular momentum, many novel optical physical phenomena have been discovered through the study of optical vortices, and they have a wide application prospect in optical manipulation, optical communication, photonic chip and other fields. By combining the advantages of square spiral zone plate and Gabor zone plate, a novel binary single focused square spiral zone plate is designed to realize the optical vortex with square symmetry and alleviate the influence of the higher order foci in the propagation direction. The theoretical results are consistent with the experimental results. This finding has potential in the applications of multi-particle manipulation and 3D imaging.

Ultrashort Laser Pulse Focusing by Amplitude and Phase Zone Plates

In this paper, using the frequency-dependent finite-difference time-domain method, a femtosecond cylindrical vector beam of second-order focusing binary zone plates (BZP) is investigated. It is shown that the relief material has a significant effect on the electromagnetic field formed in the focal plane. It is also shown that, in the case of tight focusing of a second-order cylindrically polarized laser pulse, a reverse energy flux is formed in the focus near the optical axis. For the quartz BZP, the energy backflow is maximum. For aluminum and chromium BZPs, the reverse energy flux is approximately two times less, and there is no energy backflow in the focus formed by the gold BZP. This study will be useful for surface nanostructuring applications where a focused short pulse is applied.

Creating axial bifocal spots by solving the binary phase zone plate in inverse in 4Pi focusing system

We propose an approach to obtain bifocal spots with variable axial distance in 4Pi focusing system. The approach is to inversely solve the radii of a binary phase zone plate (BPZP) according to the conceived 4Pi focal field distribution. The ring radius of the BPZP solved in reverse has an analytic expression by the Richards-Wolf vector diffraction theory, which is directly related to the axial offset distance of the bifocal spots. With the BPZP designed by the analytic expression to modulate the incident radially polarized beam, bifocal spots with variable axial distance can be achieved in the 4Pi focusing region, and two focal spots have the same size. Moreover, some special focal fields, such as optical chain and optical cage, can also be created by selecting suitable axial offset distance to design the BPZP for modulating radially polarized beam. In addition, axial multi-spherical spots can also be generated by superposition of a BPZP and an annular obstruction.

Generation of single-focus phase singularity by the annulus-quadrangle-element coded binary square spiral zone plates

Generation of single-focus phase singularity by the annulus-quadrangle-element coded binary square spiral zone plates

High sensitivity refractive index sensing using zone plate metasurfaces with a conical phase profile

In this paper, we showed how a bulky Axicon lens can be transformed to a compact binary zone plate with conical phase profile. We built three zone plates made of three different materials and designed each zone plate to be used in high sensitivity refractive index sensing. This work is complementary to another work we have done before in which we showed mathematically how maximum sensitivity can be achieved in case of using an Axicon lens in sensing. The zone plates are designed to generate a Bessel–Gauss beam at the wavelength of 3.3 microns at which the absorption of methane gas is maximum leading to a maximum change in the refractive index. The generated intensity in the output is very sensitive to any slight change in the refractive index of the surrounding medium. Therefore, if an optical detector is positioned at the point of maximum change in the intensity with refractive index, we can easily measure the change in refractive index and hence the percentage of the gas with very high sensitivity.

Single-focus phase singularity generated by spiral zone plate with quasi-random distributed quantum dots

We report on a new vortex lens for producing a single-focus phase singularity which is termed as a quasi-random-dot-array binary spiral zone plates (QBSZPs). Differing from the abrupt transitions of the conventional spiral zone plates (SZPs), the key idea of the QBSZPs is to realize a sinusoidal transmittance by properly arranging lots of quantum dot arrays which take on the values of 0 and 1 in two dimensions. In this typical design, the number density of the selected primitives obey sinusoidal distribution along the radial direction and quasi-random in the azimuthal direction. Theoretical analysis indicates that the higher-order foci which inevitably exist in the SZPs have been indeed effectively suppressed with the QBSZPs. Moreover, the focusing performance of the QBSZPs is influenced by the ratio of circumcircle diameter of the primitives to the outermost zone width. These findings, which have been demonstrated by the performed experiment, may offer a new direction towards improving the performance of biomedical imaging, quantum computation and optical manipulation.

Trapezoid-kinoform zone plate lens - a solution for efficient focusing in hard X-ray optics.

X-ray microscopes are powerful tools in the nano-inspection of materials owing to their ultra-high resolution at the molecular level. However, the focusing efficiency of binary zone plate lenses as key components in such probes is merely 5% in practice, hindering their application in advanced scientific research. Although kinoform zone plate lenses are in principle supposed to possess high efficiency beyond binary ones, little progress has been reported so far due to the shortage of both a theoretical calculation approach and greyscale lithography for generating fine three-dimensional (3D) kinoform zones of the lenses. This paper reports our theoretical work for a modified beam propagation method to compute the focusing performance and state-of-the-art 3D greyscale electron beam lithography for kinoform zone plate lenses. Three different zone shapes - binary, kinoform and top-flat kinoform (nicknamed the trapezoid-kinoform) - were compared both theoretically and experimentally. Theoretical calculations suggest, for the first time, that the trapezoid-kinoform zone plate gives rise to the highest focusing efficiency among the three lenses, which was proved by optical characterization of the fabricated lens with hard X-rays. As high as 40% of the focusing efficiency by Au trapezoid-kinoform lenses with resolution of 250 nm at 8 keV has been achieved, which is two times higher than that of binary zone plate lenses. The origin of the enhanced efficiency in the trapezoid-kinoform zone plate lens was explained by the joint contributions from both the refraction through the kinoform slope and the diffraction through the top flat part of the trapezoid-kinoform zone plate. Such a breakthrough in focusing efficiency sheds light on the further development of X-ray lenses with both high resolution and high efficiency.

Controlling near-field focusing of a mesoscale binary phase plate in an optical radiation field with circular polarization

Binary Fresnel zone plates (ZP) are one of the most frequently used focusing elements of inplane optical schemes in micro- and nanophotonics. With a decrease in the diameter and focal distance of the ZP to meso-wavelength sizes, the parameters of the focusing region begin to be significantly influenced by features of the ZP design (material, thickness, relief depth). The spatial structure of the focal spot formed in the near-field is investigated by the numerical finite elements (FEM) simulations of the transmission of a plane optical wave through a mesoscale binary phase ZP. We show that there is a range of optimal etching depths of the ZP ridges and optimal thicknesses of the plate substrate, at which the best focusing of the incident optical wave is realized in terms of the maximum field intensity and the minimum size of the focal spot. In addition, a concept of a super-focusing binary phase ZP with an immersion layer in the form of a truncated cone fabricated of ZP material is proposed, which makes it possible to focus the circularly polarized light wave into a subdiffraction region with a half-width of about "lambda"/2n (n is the ZP refractive index).

Achromatic focusing effect of metasurface-based binary phase Fresnel zone plate

Traditional binary phase Fresnel zone plate (BPFZP) fails to provide a single-layered solution for multi-wavelength achromatic focusing. In this article, by combining metasurfaces and BPFZP model, we propose an ultra-thin single-layered transmissive achromatic phase Fresnel zone plate (PFZP) with large numerical aperture (NA) working in the visible range that is hardly possible using traditional Fresnel zone plate. We present designs of both monochromatic and achromatic BPFZP displaying almost equal simplicity despite lens size or NA while possessing moderate focusing efficiency attributed to the BPFZP model. The achromatic BPFZP designed consists of periodic cylindrical TiO2 nanopillars with thickness of 375 nm, holds NA of 0.97 and experiences average focal distance deviation of 8%. The circularly-symmetric composing antennas also provide the achromatic BPFZP with polarization-independence performance. This design method with certain error robustness makes it feasible for large-scale fabrication and compact integration with CCD/CMOS or fiber devices for future multi-wavelength applications with high resolution.

Study of focusing parameters of wavelength-scale binary phase Fresnel zone plate

Binary Fresnel zone plates (FZP) are among the most commonly used focusing elements of 2D-planar optical circuits in micro- and nano-photonics. When the diameter and focal distance of a FZP are reduced to the wavelength dimensions, the parameters of the focal area experience strong influence by FZP constructive design (material, thickness, depth of zone relief). By means of the numerical simulations, the near-field diffraction of monochromatic optical wave on a wavelength-scale binary phase plate is investigated. We found a range of optimal depths of zone plate grooves etching as well as substrate thicknesses providing the best focusing of the incident circularly polarized optical wave in terms of maximum field intensity and minimum size of the focal spot. A certain improvement of these focus parameters can be achieved by filling the zone grooves with a dielectric having a specific refractive index contrast against the FZP substrate. Additionally, the concept of a super-focus binary phase plate with a solid immersion layer (SIL) in the form of a truncated cone made of the ZP substrate material is proposed. Similar to conventional SIL device, this flat SIL-FZP can focus a circularly polarized optical radiation into a subdiffraction spot with a full-width of the order λ/2n (n is FZP refraction index).

Bypassing the resolution limit of diffractive zone plate optics via rotational Fourier ptychography

Diffractive zone plate optics uses a thin micro-structure pattern to alter the propagation direction of the incoming light wave. It has found important applications in extreme-wavelength (extreme ultraviolet or soft X-ray) imaging where conventional refractive lenses do not exist. The resolution limit of zone plate optics is determined by the smallest width of the outermost zone. In order to improve the achievable resolution, significant efforts have been devoted to the fabrication of very small zone width with ultrahigh placement accuracy. Here, we report the use of a diffractometer setup for bypassing the resolution limit of zone plate optics. In our prototype, we mounted the sample on two rotation stages and used a low-resolution binary zone plate to relay the sample plane to the detector. We then performed both in-plane and out-of-plane sample rotations and captured the corresponding raw images. The captured images were processed using a Fourier ptychographic procedure for resolution improvement. The final achievable resolution of the reported setup is not determined by the smallest width structures of the employed binary zone plate; instead, it is determined by the maximum angle of the out-of-plane rotation. In our experiment, we demonstrated 8-fold resolution improvement using both a resolution target and a titanium dioxide sample. The reported approach may be able to bypass the fabrication challenge of diffractive elements and open up new avenues for microscopy with extreme wavelengths.