Binary Zone Plate Research Articles

The tight focusing of laser radiation using 4-sector polarization converter

A laser beam with mixed linear-radial polarization formed by reflection of a linearly polarized light from a 4-sector micropolarizer was focused using a binary zone plate in a focal spot with diameters 0.35±0.02 and 0.38±0.02 of a wavelength.

Hybrid curved nano-structured micro-optical elements.

Tailoring the spatial degree of freedom of light is an essential step towards the realization of advanced optical manipulation tools. A topical challenge consists of device miniaturization for improved performance and enhanced functionality at the micron scale. We demonstrate a novel approach that combines the additive three-dimensional (3D) structuring capability of laser polymerization and the subtractive subwavelength resolution patterning of focused ion beam lithography. As a case in point hybrid (dielectric/metallic) micro-optical elements that deliver a well-defined topological shaping of light are produced. Here we report on hybrid 3D binary spiral zone plates with unit and double topological charge. Their optical performances are compared to corresponding 2D counterparts both numerically and experimentally. Cooperative refractive capabilities without compromising topological beam shaping are shown. Realization of advanced designs where the dielectric architecture itself is endowed with singular properties is also discussed.

Fabrication and characterization of high-efficiency double-sided blazed x-ray optics.

The focusing efficiency of conventional diffractive x-ray lenses is fundamentally limited due to their symmetric binary structures and the corresponding symmetry of their focusing and defocusing diffraction orders. Fresnel zone plates with asymmetric structure profiles can break this limitation; yet existing implementations compromise either on resolution, ease of use, or stability. We present a new way for the fabrication of such blazed lenses by patterning two complementary binary Fresnel zone plates on the front and back sides of the same membrane chip to provide a compact, inherently stable, single-chip device. The presented blazed double-sided zone plates with 200 nm smallest half-pitch provide up to 54.7% focusing efficiency at 6.2 keV, which is clearly beyond the value obtainable by their binary counterparts.

Fabrication of self-standing binary Gabor zone plate and its single order diffraction

The Gabor zone plate is an ideal zone plate with single focus spot, which has the potential applications in spectroscopy, X-ray imaging, etc. However, the Gabor zone plate is very difficult to prepare because of its sinusoidal transmission characteristic, thereby restricting its applications. Traditionally, the zone plate is prepared on the transparent substrate such as quartz glass, polyimide, etc. This restricts the applications of Gabor zone plates in the extreme ultraviolet and soft X-ray frequency band due to the strong absorption of quartz and polyimide in such bands.In this work, we report a method of preparing the self-standing binary Gabor zone plate by using the focused ion beam direct writing. By combining the techniques of focused ion beam and chemical wet etching, the binary Gabor zone plate with self-standing and curved structure is fabricated. The main characteristic parameters of the Gabor zone plate are as follows: the diameter of 1400 m, the radius of the first zone 90 m, the outset zone number of 60, and a gold absorber thickness of 500 nm. The focusing properties of the self-standing binary Gabor zone plate are measured at different transfer distances with a 355 nm laser. The experimental results show that the high-order focus is removed with only the first-order focus spot reserved, and the focal distance is 2.28 cm, which is in agreement with the theoretical value of 2.41 cm. The self-standing Gabor zone plate is free from the influence of the substrate. Therefore, this kind of binary Gabor zone plate has potential applications in ultraviolet and soft X-ray regions.

Focusing single-order diffraction transmission grating with a focusing plane perpendicular to the grating surface.

By combining the single-order dispersion properties of quasi-sinusoidal single-order diffraction transmission gratings (QSTG) and the single-foci focusing properties of annulus-sector-shaped-element binary Gabor zone plate (ASZP), we propose a novel focusing single-order diffraction transmission grating (FSDTG). Different from the diffraction patterns of a normal transmission grating (TG), it has a focusing plane perpendicular to the grating surface. Numerical simulations are carried out to verify its diffraction patterns in the framework of Fresnel-Kirchhoff diffraction. Higher-order diffraction components of higher harmonics can be effectively suppressed by the FSDTG we designed. And we find that the focal depth and resolving power are only determined by the structure parameters of our FSDTG by theoretical estimations.

Sharp focusing of linearly polarized asymmetric Bessel beam

We conduct the numerical and experimental study of sharp focusing of a linearly polarized asymmetric Bessel beam with topological charge n = 3 and a crescent-shaped transverse intensity pattern. Using the Debye integral, we show that in the focal plane of a high NA aplanatic lens (NA = 0.9 – 0.95) the intensity distribution is also crescent-shaped. Using the FDTD method it is shown that a binary zone plate with NA = 0.995 also forms a crescent-shaped focal spot that is rotated around the optical axis. An asymmetric Bessel beam was generated using a spatial light modulator (SLM) and focused using an immersion objective with NA = 1.25. A crescent-shaped intensity pattern formed in the focal plane was rotated by 90 degrees relative to the SLM-aided crescent.

Diffraction theory of high numerical aperture subwavelength circular binary phase Fresnel zone plate.

An analytical model of vector formalism is proposed to investigate the diffraction of high numerical aperture subwavelength circular binary phase Fresnel zone plate (FZP). In the proposed model, the scattering on the FZP's surface, reflection and refraction within groove zones are considered and diffraction fields are calculated using the vector Rayleigh-Sommerfeld integral. The numerical results obtained by the proposed phase thick FZP (TFZP) model show a good agreement with those obtained by the finite-difference time-domain (FDTD) method within the effective extent of etch depth. The optimal etch depths predicted by both methods are approximately equal. The analytical TFZP model is very useful for designing a phase and hybrid amplitude-phase FZP with high-NA and short focal length.

Experimental verification 3D subwavelength resolution beyond the diffraction limit with zone plate in millimeter wave

ABSTRACTThe results of experimental investigations of resolution power of millimeter‐wave phase reversal binary Fresnel zone plate with short focal distance are described. It has been experimentally shown that in the near‐field of single diffractive lens with subwavelength focal distance without the immersion medium a resolution of 0.3–0.4 were obtained. The “Abbe barrier” can be completely broken by such diffractive lenses with unique three‐dimensional super resolution. Also it was experimentally shown the focal spot in the high numerical aperture diffractive lenses is no longer an Airy pattern and focal intensity distribution is not circularly symmetric. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:2436–2439, 2014

High-efficiency zone-plate optics for multi-keV X-ray focusing

High-efficiency nanofocusing of hard X-rays using stacked multilevel Fresnel zone plates with a smallest zone width of 200 nm is demonstrated. The approach is to approximate the ideal parabolic lens profile with two-, three-, four- and six-level zone plates. By stacking binary and three-level zone plates with an additional binary zone plate, the number of levels in the optical transmission function was doubled, resulting in four- and six-level profiles, respectively. Efficiencies up to 53.7% focusing were experimentally obtained with 6.5 keV photons using a compact alignment apparatus based on piezoelectric actuators. The measurements have also been compared with numerical simulations to study the misalignment of the two zone plates.

Self-similarity in radial Walsh filters and axial intensity distributions in the far-field diffraction pattern

Pupil plane filtering by radial Walsh filters is a convenient technique for tailoring the axial intensity distribution near the focal plane of a rotationally symmetric imaging system. Radial Walsh filters, derived from radial Walsh functions, form a set of orthogonal phase filters that take on values either 0 or π phase, corresponding to +1 or -1 values of the radial Walsh functions over prespecified annular regions of the circular filter. Order of these filters is given by the number of zero-crossings, or equivalently phase transitions within the domain over which the set is defined. In general, radial Walsh filters are binary phase zone plates, each of them demonstrating distinct focusing characteristics. The set of radial Walsh filters can be classified into distinct groups, where the members of each group possess self-similar structures. Self-similarity can also be observed in the corresponding axial intensity distributions. These observations provide valuable clues in tackling the inverse problem of synthesis of phase filter in accordance with prespecified axial intensity distributions. This paper reports our observations on self-similarity in radial Walsh filters of various orders and corresponding axial intensity distributions.

Polarizing and focusing properties of reflective fresnel zone plate

Polarizing and focusing properties of binary Fresnel zone plate (FZP) designed for x-ray was investigated experimentally in visible range for wavelengths 405 nm, 445 nm, and 633 nm. It was shown that peripheral FZP zones rotate the direction of polarization of linearly-polarized incident light on angle equal to doubled angle between incident polarization and relief direction. Illuminated by red and blue linearly polarized light FZP forms 3 focal spots, located on distances that decrease with wavelength decreasing. Minimal focal spot on distance of 105 um above the surface was elliptical and has maximal intensity 9 times larger than the intensity of incident light, and half maximum diameter of diffractive limit of our optical system (2 of wavelength). Peripheral part of FZP forms diffractive limited focal point on distance of 2.8 um that has diameter 9 of wavelength.

Effect of the shadowing in high-numerical-aperture binary phase Fresnel zone plates

Shadowing occurs for the groove zone plate when radiation origin from one zone of the zone plate must pass through another before reaching the focus point. Using the vector diffraction theory, we study the influence of the shadowing on the focusing properties of binary phase Fresnel zone plates (FZPs). The results show that a low-numerical-aperture (NA) FZP can be treated as an ideal in-plane FZP and the shadowing effect can be neglected. For a high-NA FZP, however, the shadowing effect from the etch depth has to be considered. Owing to the shadowing, the intensity of focusing spot decreases markedly and the size of focusing spot increases slightly in a high-NA FZP. The optimal etching depth of an actual FZP is smaller than that of an ideal FZP.

Analysis of near-field subwavelength focusing of hybrid amplitude–phase Fresnel zone plates under radially polarized illumination

The near-field focusing properties of actual hybrid amplitude–phase binary subwavelength Fresnel zone plates (HBSFZPs) are studied theoretically. The analysis based on the exact vector angular spectrum method is done for a radially polarized beam incident on the HBSFZPs. The results show that the near-field subwavelength focusing with a long depth of focus can be obtained using an HBSFZP, which is very useful for near-field subwavelength photolithography and high-resolution microscopy. The position of the actual focus in the near-field focusing HBSFZPs depends on the evanescent wave rather than the propagating wave. The etch depth has an important influence on focusing properties of HBSFZPs.

The Beynon Gabor zone plate: a new tool for de Broglie matter waves and hard X-rays? An off axis and focus intensity investigation

Optical elements based on Fresnel zones are used in a range of applications, from X-ray telescopy to microscopy and recently also in the manipulation of de Broglie matter waves. In 1992 Beynon and co-workers presented a binary Gabor type zone plate (henceforth referred to as the Beynon Gabor zone plate). Because this zone plate has no higher order foci, it is in principle a very attractive candidate for focusing of de Broglie matter waves and in some cases X-rays. So far the Beynon Gabor zone plate investigations presented in the literature have concentrated on the intensity distribution along the optical axis and in the focal plane. Here we present a detailed numerical investigation of the Beynon Gabor zone plate, including an investigation of the off-optical axis, off focal plane intensity distribution for point source illumination. We show that at integer fractions of the focal length, the beam becomes nearly toroidal (doughnut-shaped). This offers potentially interesting new possibilities for de Broglie matter wave and X-ray optics, for example in STED-like applications. We further show that the increased intensity at the focal point predicted in the literature for a particular Beynon Gabor zone plate transmission function configuration is an artifact due to the lack of sampling nodes. We support our calculations with experimental measurements in the visible light range, using a Beynon Gabor zone plate fabricated with electron beam lithography.

Subwavelength focusing of laser light by microoptics

Near-field scanning optical microscope (NSOM) measurements revealed that a linearly polarized Gaussian beam of wavelength λ = 532 nm focused with a binary zone plate (ZP) of focal length λ, radius 7 μm, and groove depth 510 nm, fabricated in hydrogen silsesquioxane, produces a focal spot of size FWHM = (0.44 ± 0.02)λ, with the side lobes being lower than 10% of the intensity peak in the focus. Replacing the incident 532 nm wavelength with a 633 nm wavelength resulted in a 1.8 times shorter focal length and a tighter (in terms of wavelengths) focal spot of FWHM = (0.40 ± 0.02)λ. This value is smaller than the scalar diffraction-limited size in vacuum, FWHM = 0.51λ. This is the smallest focal spot so far experimentally obtained for a binary phase ZP and the root-mean-square deviation of the experimental curve from a FDTD simulation is 5%. We show that the metallic pyramid-shaped cantilever with a 100-nm-hole in the tip that is used in the NSOM is only able to detect the transverse electric field component. The FDTD simulation showed such a cantilever to be over 3 times more sensitive to the transverse electric field component than to the longitudinal one. Using the Richards–Wolf (RW) formulae, the near-focus intensity distribution can be calculated with 6% error for focal lengths larger than 4λ. It is usually assumed that the Debye theory and the RW formulae are only valid for focal lengths much larger than the incident wavelength. By FDTD simulation, we showed that when illuminating the ZP by a radially (rather than linearly) polarized beam, a decrease in the focal spot transverse size did not result in a substantially reduced total volume of focus (4%).

Subwavelength superfocusing with a dipole-wave-reciprocal binary zone plate

We propose an idea of using a convergent dipole wave at the aperture, radiated from a dipole at distance of z0, to produce a perfect focusing at z0. We verified this idea through simulation and experimental observation. It is demonstrated that the zone plate designed based on the idea can provide a subwavelength superfocusing by effectively bending the surface waves in a Fresnel region of 100 nm to a couple of wavelengths and is suitable for a situation where a superresolution at a micro working distance is essential.

Microstructure formation in a thick polymer by electrostatic-induced lithography

This article demonstrates the manufacturing of microstructures in a thick polymer using electrostatic-induced lithography. Unlike previous work reported elsewhere, it focuses on the fabrication of structures from meso- to micro-scale. The electrostatic-induced lithography technique is proven to work with not only dc voltage but also ac voltage. Microstructures including microchannels, sinusoidal surface profile microstructures, waveguide core, microlens array and binary Fresnel zone plate have been successfully fabricated. The aspect ratio obtained for some samples is up to 4.5:1. The whole fabrication process is fast, cost-effective in terms of the simple experimental setup and no photosensitive material is needed. This process is expected to find applications in microfluidics, photonics or micro-opto-electro-mechanical systems.

Realizing a Gabor zone plate with quasi-random distributed hexagon dots

We propose a quasi-random-dot-array binary Gabor zone plate (QBGZP) with focusing properties of single order foci only. These features are verified with simulations and experiments in the visible light region. Moreover, we find that the performance of QBGZP, which is composed of hexagon patterns, is determined by the ratio of hexagon circumcircle diameter to the outermost zone width. The QBGZP offers a potential alternative for focusing and imaging in the soft x-ray and extreme ultraviolet region.

PERIODIC TRANSMISSION OF CIRCULAR BINARY FRESNEL ZONE PLATES WITH ETCHING DEPTH AND SUBSTRATE

Based on the scattering theory and the Green function method, a dynamical theory is given for calculating the difiraction of deeply-etched gratings with a stratifled structure substrate. The key of our method is that the patterned grating structure is considered as a perturbation to the unpatterned stratifled structure rather than to vacuum. Using the flrst-order Born approximation and in the Fresnel difiraction region, we obtain a simple analytical expression, which can be used to calculating the scattering intensity of deeply-etched circular binary Fresnel zone plates with a stratifled substrate (MDECBFZPs). The numerical results show that the focusing intensity at the foci of the MDCBFZP changes periodically with the etching depth and the thickness of the substrate fllm. Our results are in good agreement with FDTD simulations.

Tight focusing of partially polarized vortex beams by binary phase Fresnel zone plates

Based on vectorial Debye theory, the focusing properties of partially polarized vortex beam by high numerical aperture Fresnel zone plate are investigated. The effects of the numerical apertures of and the phase difference of binary phase Fresnel zone plates, the topological charge of vortex beam and the degree of polarization of incident beam on the intensity distribution and degree of coherence in the focal plane are investigated in detail. It is shown that elliptical light spots and the flat top beam can be obtained by selecting certain parameters. Studies of degree of coherence reveal that the degree of coherence between x and y components of the electric field, which is zero in the source plane, is improved in the focal plane for vortex beam, but it is hardly changed for the nonvortex beam. It is also proved that any two of the three electric field components Ex, Ey and Ez are completely coherent everywhere in the focal region if the incident light beam is linearly polarized.