Light propagation analysis in graded index fiber—review and applications

The quadratic graded index (GRIN) is a fiber that gives physical interpretation of the recently introduced mathematical operation coined the fractional Fourier transform (FRT). This paper reviews the FRT, GRIN, and their relations. Possible applications are demonstrated. In particular the Talbot effect inside the GRIN is analyzed.     

Sub‐microsecond‐resolved multi‐speckle X‐ray photon correlation spectroscopy with a pixel array detector

Small‐angle X‐ray photon correlation spectroscopy (XPCS) measurements spanning delay times from 826 ns to 52.8 s were performed using a photon‐counting pixel array detector with a dynamic range of 0–3 (2 bits). Fine resolution and a wide dynamic range of time scales was achieved by combining two modes of operation of the detector: (i) continuous mode, where data acquisition and data readout are performed in parallel with a frame acquisition time of 19.36 µs, and (ii) burst mode, where 12 frames are acquired with frame integration times of either 2.56 µs frame^?1 or 826 ns frame^?1 followed by 3.49 ms or 1.16 ms, respectively, for readout. The applicability of the detector for performing multi‐speckle XPCS was demonstrated by measuring the Brownian dynamics of 10 nm‐radius gold and 57 nm‐radius silica colloids in water at room temperature. In addition, the capability of the detector to faithfully record one‐ and two‐photon counts was examined by comparing the statistical distribution of photon counts with expected probabilities from the negative binomial distribution. It was found that in burst mode the ratio of 2 s to 1 s is markedly smaller than predicted and that this is attributable to pixel‐response dead‐time.     

Collimating Montel mirror as part of a multi‐crystal analyzer system for resonant inelastic X‐ray scattering

Advances in resonant inelastic X‐ray scattering (RIXS) have come in lockstep with improvements in energy resolution. Currently, the best energy resolution at the Ir L₃‐edge stands at ～25 meV, which is achieved using a diced Si(844) spherical crystal analyzer. However, spherical analyzers are limited by their intrinsic reflection width. A novel analyzer system using multiple flat crystals provides a promising way to overcome this limitation. For the present design, an energy resolution at or below 10 meV was selected. Recognizing that the angular acceptance of flat crystals is severely limited, a collimating element is essential to achieve the necessary solid‐angle acceptance. For this purpose, a laterally graded, parabolic, multilayer Montel mirror was designed for use at the Ir L₃‐absorption edge. It provides an acceptance larger than 10 mrad, collimating the reflected X‐ray beam to smaller than 100 µrad, in both vertical and horizontal directions. The performance of this mirror was studied at beamline 27‐ID at the Advanced Photon Source. X‐rays from a diamond (111) monochromator illuminated a scattering source of diameter 5 µm, generating an incident beam on the mirror with a well determined divergence of 40 mrad. A flat Si(111) crystal after the mirror served as the divergence analyzer. From X‐ray measurements, ray‐tracing simulations and optical metrology results, it was established that the Montel mirror satisfied the specifications of angular acceptance and collimation quality necessary for a high‐resolution RIXS multi‐crystal analyzer system.     

光学系统折射率温度效应的模拟计算

提出一种计算折射率温度效应的新方案。该方案通过拟合有限元热分析得到离散节点温度,在透镜中建立连续的温度场。在计算CODE V光线追迹时,自编子程序根据追迹点的温度和输入数据,实时计算并返回相对折射率及其梯度信息,使折射率温度效应导致的光程变化的计算更为准确。在计算时可以把波长、大气压、折射率温度系数等作为自定义参量,输入到子程序中,使相对折射率的计算更为灵活。最后对一个红外光学系统进行了计算误差分析,得到了像质的变化情况,验证了该方案的可行性。     

In situ multi‐axial loading frame to probe elastomers using X‐ray scattering

An in situ tensile–shear loading device has been designed to study elastomer crystallization using synchrotron X‐ray scattering at the Synchrotron Soleil on the DiffAbs beamline. Elastomer tape specimens of thickness 2 mm can be elongated by up to 500% in the longitudinal direction and sheared by up to 200% in the transverse direction. The device is fully automated and plugged into the TANGO control system of the beamline allowing synchronization between acquisition and loading sequences. Experimental results revealing the evolution of crystallization peaks under load are presented for several tension/shear loading sequences.     

A novel multi‐detection technique for three‐dimensional reciprocal‐space mapping in grazing‐incidence X‐ray diffraction

A new scattering technique in grazing‐incidence X‐ray diffraction geometry is described which enables three‐dimensional mapping of reciprocal space by a single rocking scan of the sample. This is achieved by using a two‐dimensional detector. The new set‐up is discussed in terms of angular resolution and dynamic range of scattered intensity. As an example the diffuse scattering from a strained multilayer of self‐assembled (In,Ga)As quantum dots grown on GaAs substrate is presented.     

A high‐accuracy complex‐phase method of simulating X‐ray propagation through a multi‐lens system

The propagation of X‐ray waves through an optical system consisting of many X‐ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite‐difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X‐ray waves through a multi‐lens system. The reasons for using a very detailed difference grid are investigated. It was shown that the wave phase becomes a function, very quickly increasing with increasing distance from the optical axis, after the wave has passed through the multi‐lens system. If the phase is a quickly increasing function of the coordinates perpendicular to the optical axis, then the electric field of the wave is a quickly oscillating function of these coordinates, and thus a very detailed difference grid becomes necessary to describe such a wavefield. To avoid this difficulty, an equation for the phase function is proposed as an alternative to the equation of the electric field. This allows reliable and accurate simulations to be carried out when using the multi‐lens system. An equation for the phase function is derived and used for accurate simulations. The numerical error of the suggested method is estimated. It is shown that the equation for the phase function allows efficient simulations to be fulfilled for the multi‐lens system.     

Optical performance of materials for X‐ray refractive optics in the energy range 8–100 keV

A quantitative analysis of the crucial characteristics of currently used and promising materials for X‐ray refractive optics is performed in the extended energy range 8–100 keV. According to the examined parameters, beryllium is the material of choice for X‐ray compound refractive lenses (CRLs) in the energy range 8–25 keV. At higher energies the use of CRLs made of diamond and the cubic phase of boron nitride (c‐BN) is beneficial. It was demonstrated that the presence of the elements of the fourth (or higher) period has a fatal effect on the functional X‐ray properties even if low‐Z elements dominate in the compound, like in YB₆₆. Macroscopic properties are discussed: much higher melting points and thermal conductivities of C and c‐BN enable them to be used at the new generation of synchrotron radiation sources and X‐ray free‐electron lasers. The role of crystal and internal structure is discussed: materials with high density are preferable for refractive applications while less dense phases are suitable for X‐ray windows. Single‐crystal or amorphous glass‐like materials based on Li, Be, B or C that are free of diffuse scattering from grain boundaries, voids and inclusions are the best candidates for applications of highly coherent X‐ray beams.     

Portable multi‐anvil device for in situ angle‐dispersive synchrotron diffraction measurements at high pressure and temperature

A recently developed portable multi‐anvil device for in situ angle‐dispersive synchrotron diffraction studies at pressures up to 25 GPa and temperatures up to 2000 K is described. The system consists of a 450 ton V7 Paris–Edinburgh press combined with a Stony Brook `T‐cup' multi‐anvil stage. Technical developments of the various modifications that were made to the initial device in order to adapt the latter to angular‐dispersive X‐ray diffraction experiments are fully described, followed by a presentation of some results obtained for various systems, which demonstrate the power of this technique and its potential for crystallographic studies. Such a compact large‐volume set‐up has a total mass of only 100 kg and can be readily used on most synchrotron radiation facilities. In particular, several advantages of this new set‐up compared with conventional multi‐anvil cells are discussed. Possibilities of extension of the (P,T) accessible domain and adaptation of this device to other in situ measurements are given.     

GROIN: a fast optical adjustment of a Kirkpatrick–Baez set‐up

A very simple and compact optical device aimed at the fast adjustment, alignment and bending of the mirrors of a Kirpatrick–Baez system used in the X‐ray domain is described.     

A multi‐MHz single‐shot data acquisition scheme with high dynamic range: pump–probe X‐ray experiments at synchrotrons

The technical implementation of a multi‐MHz data acquisition scheme for laser–X‐ray pump–probe experiments with pulse limited temporal resolution (100 ps) is presented. Such techniques are very attractive to benefit from the high‐repetition rates of X‐ray pulses delivered from advanced synchrotron radiation sources. Exploiting a synchronized 3.9 MHz laser excitation source, experiments in 60‐bunch mode (7.8 MHz) at beamline P01 of the PETRA III storage ring are performed. Hereby molecular systems in liquid solutions are excited by the pulsed laser source and the total X‐ray fluorescence yield (TFY) from the sample is recorded using silicon avalanche photodiode detectors (APDs). The subsequent digitizer card samples the APD signal traces in 0.5 ns steps with 12‐bit resolution. These traces are then processed to deliver an integrated value for each recorded single X‐ray pulse intensity and sorted into bins according to whether the laser excited the sample or not. For each subgroup the recorded single‐shot values are averaged over ～10⁷ pulses to deliver a mean TFY value with its standard error for each data point, e.g. at a given X‐ray probe energy. The sensitivity reaches down to the shot‐noise limit, and signal‐to‐noise ratios approaching 1000 are achievable in only a few seconds collection time per data point. The dynamic range covers 100 photons pulse^?1 and is only technically limited by the utilized APD.     

Development of fast,simultaneous and multi‐technique scanning hard X‐ray microscopy at Synchrotron Soleil

A distributed fast‐acquisition system for synchronized multi‐technique experiments is presented, in which the collection of metadata and the asynchronous merging of large data volumes from multiple detectors are managed as part of the data collection process. This fast continuous scanning scheme, named FLYSCAN, enables measurement of microscopy data on a timescale of milliseconds per pixel. Proof‐of‐principle multi‐technique experiments, namely scanning X‐ray fluorescence spectrometry combined with absorption, differential phase contrast and dark‐field imaging, have been performed on biological and geological samples.     

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.     

Characterisation of carbonaceous materials using Raman spectroscopy: a comparison of carbon nanotube filters,single‐ and multi‐walled nanotubes,graphitised porous carbon and graphite

Multi‐walled carbon nanotube (MWCNT) filters have been recently synthesised which have specific molecular filtering capabilities and good mechanical strength. Optical and scanning electron microscopy (SEM) reveals the formation of highly aligned arrays of bundles of carbon nanotubes having lengths up to 500 µm. The Raman spectra of this material along with four other carbonaceous materials, commercially available single‐walled carbon nanotubes (SWCNTs) and MWCNTs, graphitised porous carbon (Carbotrap) and graphite have been recorded using two‐excitation wavelengths, 532 and 785 nm, and analysed for band positions and shape with special emphasis paid to the D‐, G‐ and G′‐bands. A major difference between the different MWCNT varieties analysed is that G‐bands in the MWCNT filters exhibit almost no dispersion, whereas the other MWCNTs show a noticeable dispersive behaviour with a change in the excitation wavelength. Spectral features similar to those of the MWCNT filter varieties were observed for the Carbotrap material. From the line shape analysis, the intensity ratio, I_D/I_G, of the more ordered MWCNT filter material using the integral G‐band turns out to be two times lower than that of the less ordered MWCNT filter product at both excitation wavelengths. This parameter can, therefore, be used as a measure of the degree of MWCNT alignment in filter varieties, which is well supported also by our SEM study. Copyright © 2008 John Wiley & Sons, Ltd.     

Quantum‐optical analogies using photonic structures

Engineered photonic waveguides have provided in the past decade an extremely rich laboratory tool to visualize with optical waves the classic analogues of a wide variety of coherent quantum phenomena encountered in atomic, molecular or condensed‐matter physics. As compared to quantum systems, optics offers the rather unique advantage of a direct mapping of the wave function evolution in coordinate space by simple fluorescence imaging or scanning tunneling optical microscopy techniques. In this contribution recent theoretical and experimental advances in the field of quantum‐optical analogies are reviewed. Special attention is devoted to some relevant optical analogies based on the use of curved photonic structures, including: coherent destruction of tunneling in driven bistable potentials; coherent population transfer and adiabatic passage in laser‐driven multilevel atomic systems; quantum decay control and Zeno dynamics; electronic Bloch oscillations and Zener tunneling, Anderson localization and dynamic localization in crystalline potentials.     

Carbon contamination of soft X‐ray beamlines: dramatic anti‐reflection coating effects observed in the 1 keV photon energy region

Carbon contamination is a general problem of under‐vacuum optics submitted to high fluence. In soft X‐ray beamlines carbon deposit on optics is known to absorb and scatter radiation close to the C K‐edge (280 eV), forbidding effective measurements in this spectral region. Here the observation of strong reflectivity losses is reported related to carbon deposition at much higher energies around 1000 eV, where carbon absorptivity is small. It is shown that the observed effect can be modelled as a destructive interference from a homogeneous carbon thin film.     

Characterization and on‐line adjustment of the sagittal‐bent Laue crystal profile

The sagittal‐bent Laue monochromator can provide an ideal way to focus high‐energy X‐ray beams. However, the anticlastic curvature induced by sagittal bending has a great influence on the crystal performance. Thus, characterizing the bent‐crystal shape is very important for predicting the performance of the bent‐crystal monochromator. In this paper the crystal profile is measured by off‐line optical metrology and on‐line X‐ray experiments. The off‐line results showed that the bent‐crystal surface could be well fitted to a saddle surface apart from a redundant cubic term which was related to the different couples applied on the crystal. On‐line characterization of the meridional and the sagittal radius of the bent crystal includes double‐crystal topography and ray‐tracing measurement. In addition, the double‐crystal topography experiment could be used as a quick diagnostic method for the bending condition adjustment. The sagittal radius of the bent crystal was characterized through a ray‐tracing experiment by using a particularly designed tungsten mask. Moreover, rocking curves under different bending conditions were measured as well. The results were highly consistent with analytical results derived from the elastic theory. Furthermore, radii along different vertical positions under various bending conditions were measured and showed a quadratic relationship between the vertical positions and the meridional radii.     

Soft X‐ray refractive index by reconciling total electron yield with specular reflection: experimental determination of the optical constants of graphite

The complex refractive index of many materials is poorly known in the soft X‐ray range across absorption edges. This is due to saturation effects that occur there in total‐electron‐yield and fluorescence‐yield spectroscopy and that are strongest at resonance energies. Aiming to obtain reliable optical constants, a procedure that reconciles electron‐yield measurements and reflection spectroscopy by correcting these saturation effects is presented. The procedure takes into account the energy‐ and polarization‐dependence of the photon penetration depth as well as the creation efficiency for secondary electrons and their escape length. From corrected electron‐yield spectra the absorption constants and the imaginary parts of the refractive index of the material are determined. The real parts of the index are subsequently obtained through a Kramers–Kronig transformation. These preliminary optical constants are refined by simulating reflection spectra and adapting them, so that measured reflection spectra are reproduced best. The efficacy of the new procedure is demonstrated for graphite. The optical constants that have been determined for linearly polarized synchrotron light incident with p‐ and s‐geometry provide a detailed and reliable representation of the complex refractive index of the material near π‐ and σ‐resonances. They are also suitable for allotropes of graphite such as graphene.     

Comparative study of multilayers used in monochromators for synchrotron‐based coherent hard X‐ray imaging

A systematic study is presented in which multilayers of different composition (W/Si, Mo/Si, Pd/B₄C), periodicity (from 2.5 to 5.5 nm) and number of layers have been characterized. In particular, the intrinsic quality (roughness and reflectivity) as well as the performance (homogeneity and coherence of the outgoing beam) as a monochromator for synchrotron radiation hard X‐ray micro‐imaging are investigated. The results indicate that the material composition is the dominating factor for the performance. By helping scientists and engineers specify the design parameters of multilayer monochromators, these results can contribute to a better exploitation of the advantages of multilayer monochromators over crystal‐based devices; i.e. larger spectral bandwidth and high photon flux density, which are particularly useful for synchrotron‐based micro‐radiography and ‐tomography.