Kinoform optics applied to X‐ray photon correlation spectroscopy

Moderate‐demagnification higher‐order silicon kinoform focusing lenses have been fabricated to facilitate small‐angle X‐ray photon correlation spectroscopy (XPCS) experiments. The geometric properties of such lenses, their focusing performance and their applicability for XPCS measurements are described. It is concluded that one‐dimensional vertical X‐ray focusing via silicon kinoform lenses significantly increases the usable coherent flux from third‐generation storage‐ring light sources for small‐angle XPCS experiments.     

On aberrations in saw‐tooth refractive X‐ray lenses and on their removal

The X‐ray lens, which is composed of opposing canted saw‐tooth structures, originally assembled from cut‐out pieces from long‐playing records, is understood by recognizing that an incident plane X‐ray wave will traverse a varying number of triangular prisms in them. The refraction will deflect any beam towards the prism tips and the variation of the deflection angle, which grows linearly with the number of traversed prisms, can result in X‐ray focusing. The structure offers focusing flexibility by simply changing the taper angle. This report will discuss the aberrations arising in the saw‐tooth structure in its simplest form with identical prisms. It is found that the saw‐tooth structures in low‐Z materials with focal length below 1 m provide less flux density in the focal spot than stacks of one‐dimensionally focusing refractive lenses with identical transmission function. This is due to excessive aberrations in the regular structure, which are absent in stacks of concave lenses, and which limit the focusing to spot sizes of just submicrometre dimensions, as measured experimentally for some lenses. It will be shown that this limitation can be overcome by appropriately modifying the prism shape. Then the image size could be reduced by about an order of magnitude to the diffraction limit with competitive numbers even below 0.1 µm. Microfabrication techniques are identified as the appropriate means for producing the structures.     

High‐energy X‐ray optics with silicon saw‐tooth refractive lenses

Silicon saw‐tooth refractive lenses have been in successful use for vertical focusing and collimation of high‐energy X‐rays (50–100 keV) at the 1‐ID undulator beamline of the Advanced Photon Source. In addition to presenting an effectively parabolic thickness profile, as required for aberration‐free refractive optics, these devices allow high transmission and continuous tunability in photon energy and focal length. Furthermore, the use of a single‐crystal material (i.e. Si) minimizes small‐angle scattering background. The focusing performance of such saw‐tooth lenses, used in conjunction with the 1‐ID beamline's bent double‐Laue monochromator, is presented for both short (～1:0.02) and long (～1:0.6) focal‐length geometries, giving line‐foci in the 2 µm–25 µm width range with 81 keV X‐rays. In addition, a compound focusing scheme was tested whereby the radiation intercepted by a distant short‐focal‐length lens is increased by having it receive a collimated beam from a nearer (upstream) lens. The collimation capabilities of Si saw‐tooth lenses are also exploited to deliver enhanced throughput of a subsequently placed small‐angular‐acceptance high‐energy‐resolution post‐monochromator in the 50–80 keV range. The successful use of such lenses in all these configurations establishes an important detail, that the pre‐monochromator, despite being comprised of vertically reflecting bent Laue geometry crystals, can be brilliance‐preserving to a very high degree.     

Impacts of Refraction Index Mismatch on Performance of Target Detection and Imaging by Using Flat LHM Lens

Refraction index mismatch between flat left-handed metamaterial (LHM) lens and its surrounding medium generally destroys the focusing of flat LHM lens and degrades the performance of near-field target detection by using flat LHM lens. For LHM lens of refraction index mismatch within ±30%, numerical simulations demonstrate that lenses with large refraction index may suffer less resolution degradation than lenses with small refraction index, and the enhancement of refocused microwave backscattered from target can be subsided by up to approximately 5.5dB. The refraction index mismatch will also shift the target position in the reconstructed image so that theoretical prediction of target position needs to be modified.     

Point focusing with flat and wedged crossed multilayer Laue lenses

Point focusing measurements using pairs of directly bonded crossed multilayer Laue lenses (MLLs) are reported. Several flat and wedged MLLs have been fabricated out of a single deposition and assembled to realise point focusing devices. The wedged lenses have been manufactured by adding a stress layer onto flat lenses. Subsequent bending of the structure changes the relative orientation of the layer interfaces towards the stress‐wedged geometry. The characterization at ESRF beamline ID13 at a photon energy of 10.5 keV demonstrated a nearly diffraction‐limited focusing to a clean spot of 43 nm × 44 nm without significant side lobes with two wedged crossed MLLs using an illuminated aperture of approximately 17 µm × 17 µm to eliminate aberrations originating from layer placement errors in the full 52.7 µm × 52.7 µm aperture. These MLLs have an average individual diffraction efficiency of 44.5%. Scanning transmission X‐ray microscopy measurements with convenient working distances were performed to demonstrate that the lenses are suitable for user experiments. Also discussed are the diffraction and focusing properties of crossed flat lenses made from the same deposition, which have been used as a reference. Here a focal spot size of 28 nm × 33 nm was achieved and significant side lobes were noticed at an illuminated aperture of approximately 23 µm × 23 µm.     

Negative index photonic crystal lenses based on carbon nanotube arrays

We report a novel utilization of periodic arrays of carbon nanotubes in the realization of diffractive photonic crystal lenses. Carbon nanotube arrays with nanoscale dimensions (lattice constant 400 nm and tube radius 50 nm) displayed a negative refractive index in the optical regime where the wavelength is of the order of array spacing. A detailed computational analysis of band gaps and optical transmission through the nanotubes based planar, convex and concave shaped lenses was performed. Due to the negative-index these lenses behaved in an opposite fashion compared to their conventional counter parts. A plano-concave lens was established and numerically tested, displaying ultra-small focal length of 1.5 μm (～2.3 λ) and a near diffraction-limited spot size of 400 nm (～0.61 λ).     

Doped single‐walled carbon nanotubes and low‐mobility graphene: impact of disorder and dopants on electronic magnetotransport

The impact of disorder introduced by intentional and unintentional (environmental) dopants on the charge transport has been investigated in boron‐ and nitrogen‐doped single‐walled carbon nanotubes, and in low‐mobility monolayer graphene. For doped single‐walled nanotubes a theoretically not predicted plateau‐like region and onsets of oscillatory behaviour in the conductance for boron‐ and nitrogen‐doped nanotubes were observed, respectively. The oscillatory behaviour suggests interplay between the dopants and the helical movement of charges along the tube due to the magnetic field. For low‐mobility graphene the simultaneous appearance of the filling‐factor 2 and 3 plateau was observed in the Quantum‐Hall regime. This is attributed to an electron‐spin–isospin interaction mediated through the high disorder. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations

Flat lenses are designed by means of graded negative refractive index-based photonic crystals （PCs） constructed using air-holes tuned with different shapes. By gradually modifying the filling factor along the transverse direction, we obtain the graded negative index-based lenses for the purpose of focusing an incident plane wave. The finite-difference and timedomain （FDTD） algorithm is adopted for numerical calculation. Our calculation results indicate that these lenses can finely focus incident plane waves. Moreover, for the same size of air-holes, the focusing properties of the lens with rectangular air-holes are better than those with the other shaped air-holes. The graded negative index PCs lenses could possibly enable new applications in optoelectronic systems.     

X‐ray focusing by the system of refractive lens(es) placed inside asymmetric channel‐cut crystals

An X‐ray one‐dimensionally focusing system, a refracting–diffracting lens (RDL), composed of Bragg double‐asymmetric‐reflecting two‐crystal plane parallel plates and a double‐concave cylindrical parabolic lens placed in the gap between the plates is described. It is shown that the focal length of the RDL is equal to the focal distance of the separate lens multiplied by the square of the asymmetry factor. One can obtain RDLs with different focal lengths for certain applications. Using the point‐source function of dynamic diffraction, as well as the Green function in a vacuum with parabolic approximation, an expression for the double‐diffracted beam amplitude for an arbitrary incident wave is presented. Focusing of the plane incident wave and imaging of a point source are studied. The cases of non‐absorptive and absorptive lenses are discussed. The intensity distribution in the focusing plane and on the focusing line, and its dependence on wavelength, deviation from the Bragg angle and magnification is studied. Geometrical optical considerations are also given. RDLs can be applied to focus radiation from both laboratory and synchrotron X‐ray sources, for X‐ray imaging of objects, and for obtaining high‐intensity beams. RDLs can also be applied in X‐ray astronomy.     

Efficiency and coherence preservation studies of Be refractive lenses for XFELO application

Performance tests of parabolic beryllium refractive lenses, considered as X‐ray focusing elements in the future X‐ray free‐electron laser oscillator (XFELO), are reported. Single and double refractive lenses were subject to X‐ray tests, which included: surface profile, transmissivity measurements, imaging capabilities and wavefront distortion with grating interferometry. Optical metrology revealed that surface profiles were close to the design specification in terms of the figure and roughness. The transmissivity of the lenses is >94% at 8 keV and >98% at 14.4 and 18 keV. These values are close to the theoretical values of ideal lenses. Images of the bending‐magnet source obtained with the lenses were close to the expected ones and did not show any significant distortion. Grating interferometry revealed that the possible wavefront distortions produced by surface and bulk lens imperfections were on the level of ～λ/60 for 8 keV photons. Thus the Be lenses can be succesfully used as focusing and beam collimating elements in the XFELO.     

Mechanical properties of carbon nanotubes

A variety of outstanding experimental results on the elucidation of the elastic properties of carbon nanotubes are fast appearing. These are based mainly on the techniques of high-resolution transmission electron microscopy (HRTEM) and atomic force microscopy (AFM) to determine the Young’s moduli of single-wall nanotube bundles and multi-walled nanotubes, prepared by a number of methods. These results are confirming the theoretical predictions that carbon nanotubes have high strength plus extraordinary flexibility and resilience. As well as summarising the most notable achievements of theory and experiment in the last few years, this paper explains the properties of nanotubes in the wider context of materials science and highlights the contribution of our research group in this rapidly expanding field. A deeper understanding of the relationship between the structural order of the nanotubes and their mechanical properties will be necessary for the development of carbon-nanotube-based composites. Our research to date illustrates a qualitative relationship between the Young’s modulus of a nanotube and the amount of disorder in the atomic structure of the walls. Other exciting results indicate that composites will benefit from the exceptional mechanical properties of carbon nanotubes, but that the major outstanding problem of load transfer efficiency must be overcome before suitable engineering materials can be produced. Received: 17 May 1999 / Accepted: 18 May 1999 / Published online: 29 July 1999     

Applying the finite-thickness model to designs of cylindrical microlenses with small -numbers

The finite-thickness model (FTM) is applied to the design of cylindrical microlenses based on the wave-front interference principle, rather than the existing zero-thickness model (ZTM). This design method is very simple in physics and highly efficient in computations. For cylindrical lenses with different f-numbers (from f/1.5 to f/0.6), the detailed designs by using both the FTM and the ZTM are carried out. To show the superiority of the FTM to the ZTM, we investigate the focal performance of all the designed lenses based on rigorous electromagnetic theory and the boundary element method. Numerical results reveal that the constructed cylindrical lenses by the FTM are witnessed to exhibit much better focusing performance than those by the ZTM, especially for the small f-numbers.     

Electrical properties of transparent carbon nanotube networks prepared through different techniques

Ultra‐thin, optically transparent and electrically conducting films of pure carbon nanotubes (CNTs) are widely studied thanks to their promise for broad applications. In the present work, we study and compare different deposition techniques for the production of these networks: dip‐coating, spray‐coating, vacuum filtration and electrophoretic deposition on a quartz glass using single‐walled carbon nanotubes (SWCNTs) produced by the HiPCo method. In order to optimize the networks, besides the various deposition techniques we also investigate how the optical and electrical properties vary if the networks are fabricated from different CNTs, all synthesized by the CVD method: SWCNTs, DWCNTs and MWCNTs. As the main criteria for evaluating the quality of these CNT networks we measure the electrical surface resistance at a certain optical transmittance and correlate it to the morphology (homogeneity and roughness) of the networks. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aspherical lens shapes for focusing synchrotron beams

Aspherical surfaces required for focusing collimated and divergent synchrotron beams using a single refractive element (lens) are reviewed. The Cartesian oval, a lens shape that produces perfect point‐to‐point focusing for monochromatic radiation, is studied in the context of X‐ray beamlines. Optical surfaces that approximate ideal shapes are compared. Results are supported by ray‐tracing simulations. Elliptical lenses, rather than parabolic, are preferred for nanofocusing X‐rays because of the higher peak and lower tails in the intensity distribution. Cartesian ovals will improve the gain when using high‐demagnification lenses of high numerical aperture.     

On the use of clessidra prism arrays in long‐focal‐length X‐ray focusing

Clessidra (hour‐glass) X‐ray lenses have an overall shape of an old hour glass, in which two opposing larger triangular prisms are formed of smaller identical prisms or prism‐like objects. In these lenses, absorbing and otherwise optically inactive material was removed with a material‐removal strategy similar to that used by Fresnel in the lighthouse lens construction. It is verified that when the single prism rows are incoherently illuminated they can be operated as independent micro‐lenses with coinciding image positions for efficient X‐ray beam concentration. Experimental data for the line width and the refraction efficiency in one‐dimensional focusing are consistent with the expectations. Imperfections in the structures produced by state‐of‐the‐art deep X‐ray lithography directed only 35% of the incident intensity away from the image and widened it by just 10% to 125 µm. An array of micro‐lenses with easily feasible prism sizes is proposed as an efficient retrofit for the refocusing optics in an existing beamline, where it would provide seven‐fold flux enhancement.     

Fabrication of gradient refractive index ball lenses using the method of combination of ion exchanging and sagging

Based on the Fick’s diffusion equations, the distribution function of refractive index of a gradient refractive index ball lens (GRIN ball lens/GBL) is derived. Lithium containing silicate glass is fabricated and GRIN ball lenses (GBLs) which diameters are from 0.3 mm to 3.0 mm are made by the method of combination of Ion exchanging and sagging in sodium nitrate. Refractive index profiles of these GBLs are measured by interferometer, and the performances such as effective focal length (EFL), back focal length (BFL) and numerical aperture (NA) between GBLs and homogeneous ball lenses (HBLs) are compared. Results show that the distribution of the index of refraction is parabolic curve and its Δn is about 0.0002, the performances of the former are super to the latter.     

Synthesis of a fresnel acoustic lens for acoustic brightness thermometry

The applicability of different types of Fresnel acoustic lenses as antenna array systems in acoustic brightness thermometry of biological tissues is theoretically and numerically analyzed. On the basis of the technical feasibility criterion formulated for these systems, the wavelength suitable for the use in acoustic thermographs with arrays in the form of Fresnel lenses is determined. The focusing properties of different Fresnel lenses are analyzed. A method for constructing Fresnel lenses that is based on varying the focusing distances is proposed. The method provides an opportunity to design trifocal antenna systems with improved focusing properties.     

Highly selective growth of vertically aligned double‐walled carbon nanotubes by a controlled heating method and their electric double‐layer capacitor properties

Vertically aligned double‐walled carbon nanotubes (DWCNTs) with the highest selectivity of 90% were synthesized by a controlled heating method and their electric double‐layer capacitor characteristics were evaluated. DWCNT arrays had a specific capacitance of 83 F/g, which is one of the highest values among CNT arrays in a nonaqueous solution and is almost equivalent to that for single‐walled CNT (SWCNT) arrays reported previously. At the same specific capacitance, DWCNTs with superior structural properties are more promising for practical capacitors than SWCNTs. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffraction theory applied to X‐ray imaging with clessidra prism array lenses

Clessidra (hourglass) lenses, i.e. two large prisms each composed of smaller identical prisms or prism‐like objects, can focus X‐rays. As these lenses have a periodic structure perpendicular to the incident radiation, they will diffract the beam like a diffraction grating. Refraction in the prisms is responsible for blazing, i.e. for the concentration of the diffracted intensity into only a few diffraction peaks. It is found that the diffraction of coherent radiation in clessidra lenses needs to be treated in the Fresnel, or near‐field, regime. Here, diffraction theory is applied appropriately to the clessidra structure in order to show that blazing in a perfect structure with partly curved prisms can indeed concentrate the diffracted intensity into only one peak. When the lens is entirely composed of identical perfect prisms, small secondary peaks are found. Nevertheless, the loss in intensity in the central peak will not lead to any significant widening of this peak. Clessidras with perfect prisms illuminated by full coherent X‐ray radiation can then provide spatial resolutions, which are consistent with the increased aperture, and which are far below the height of the single small prisms.     

Focusing femtosecond X‐ray free‐electron laser pulses by refractive lenses

The possibility of using a parabolic refractive lens with initial X‐ray free‐electron laser (XFEL) pulses, i.e. without a monochromator, is analysed. It is assumed that the measurement time is longer than 0.3 fs, which is the time duration of a coherent pulse (spike). In this case one has to calculate the propagation of a monochromatic wave and then perform an integration of the intensity over the radiation spectrum. Here a general algorithm for calculating the propagation of time‐dependent radiation in free space and through various objects is presented. Analytical formulae are derived describing the properties of the monochromatic beam focused by a system of one and two lenses. Computer simulations show that the European XFEL pulses can be focused with maximal efficiency, i.e. as for a monochromatic wave. This occurs even for nanofocusing lenses.