Coherence and wavefront characterization of Si‐111 monochromators using double‐grating interferometry

A study of the coherence and wavefront properties of a pseudo‐channel‐cut monochromator in comparison with a double‐crystal monochromator is presented. Using a double‐grating interferometer designed for the hard X‐ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel‐cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.     

Coherence properties of individual femtosecond pulses of an x-ray free-electron laser

Measurements of the spatial and temporal coherence of single, femtosecond x-ray pulses generated by the first hard x-ray free-electron laser, the Linac Coherent Light Source, are presented. Single-shot measurements were performed at 780?eV x-ray photon energy using apertures containing double pinholes in "diffract-and-destroy" mode. We determined a coherence length of 17 μm in the vertical direction, which is approximately the size of the focused Linac Coherent Light Source beam in the same direction. The analysis of the diffraction patterns produced by the pinholes with the largest separation yields an estimate of the temporal coherence time of 0.55?fs. We find that the total degree of transverse coherence is 56% and that the x-ray pulses are adequately described by two transverse coherent modes in each direction. This leads us to the conclusion that 78% of the total power is contained in the dominant mode.     

Characterization of the transverse coherence of hard synchrotron radiation by intensity interferometry

The transverse coherence of x rays was measured with an intensity interferometer using a 120-microeV-bandwidth monochromator operating at 14.41 keV. By analyzing the transverse coherence profiles, a vertical source profile of a 25-m long undulator of SPring-8, as well as the coherence degradation by a phase object in the beam path, were quantitatively characterized.     

Two-dimensional x-ray beam phase sensing

We present a new method to analyze quantitatively the wave front of a partially coherent x-ray beam. The technique is based on the use of two-dimensional speckle patterns combined with digital image correlation algorithms and offers a pixel size resolution, a high accuracy, and a reduced sensitivity to mechanical vibrations thanks to a very simple setup. The requirements on transverse and longitudinal coherence are also low. Finally, we show how the method can be used for phase contrast imaging applications by a single sample exposure process.     

An analysis of the second order spatial coherence of stationary laser oscillators with a Fabry-Perot resonator

We investigate in this paper the results yielded by a rigorous application of second order spatial coherence theory to a Gaussian TEM-multimode laser beam. Formulae for a qualitative discussion and a quantitative evaluation of the second order spatial coherence properties of a laser oscillator with an arbitrary number of longitudinal and/or transverse Gaussian TEM-modes of oscillation are derived and considered for some practically important cases.     

Shearing interferometer for quantifying the coherence of hard x-ray beams

We report a quantitative measurement of the full transverse coherence function of the 14.4 keV x-ray radiation produced by an undulator at the Swiss Light Source. An x-ray grating interferometer consisting of a beam splitter phase grating and an analyzer amplitude grating has been used to measure the degree of coherence as a function of the beam separation out to 30 microm. Importantly, the technique provides a model-free and spatially resolved measurement of the complex coherence function and is not restricted to high resolution detectors and small fields of view. The spatial characterization of the wave front has important applications in discovering localized defects in beam line optics.     

Coherence properties of the radiation from X-ray free electron laser

We present a comprehensive analysis of coherence properties of the radiation from X-ray free electron laser (XFEL). We consider practically important case when XFEL is optimized for maximum gain. Such an optimization allows to reduce significantly parameter space. Application of similarity techniques to the results of numerical simulations allows to present all output characteristics of the optimized XFEL as functions of the only parameter, ratio of the emittance to the radiation wavelength, . Our studies show that optimum performance of the XFEL in terms of transverse coherence is achieved at the value of the parameter of about unity. At smaller values of the degree of transverse coherence is reduced due to strong influence of poor longitudinal coherence on a transverse one. At large values of the emittance the degree of transverse coherence degrades due to poor mode selection. Comparative analysis of existing XFEL projects, European XFEL, LCLS, and SCSS is presented as well.     

Generation of doublet spectral lines at self-seeded X-ray FELs

Self-seeding schemes, consisting of two undulators with a monochromator in between, aim to reduce the bandwidth of SASE X-ray FELs. We recently proposed to use a new method of monochromatization exploiting a single crystal in Bragg transmission geometry for self-seeding in the hard X-ray range. The obvious and technically possible extension is to use such kind of monochromator setup with two (or more) crystals arranged in a series to spectrally filter the SASE radiation at two (or more) closely-spaced wavelengths within the FEL gain band. This allows for the production of doublet (or multiplet) spectral lines. Exploitations of such mode of operation involve any situation where there is a large change in cross-section over a narrow wavelength range. In this paper we consider the simultaneous operation of the LCLS hard X-ray FEL at two closely spaced wavelengths. We present simulation results for the LCLS baseline, and we show that this method can produce fully coherent radiation shared between two longitudinal modes. Mode spacing can be easily tuned within the FEL gain band, i.e. within 10 eV. An interesting aspect of the proposed scheme is a way of modulating the electron bunch at optical frequencies without a seed quantum laser. In fact, the XFEL output intensity contains an oscillating “mode-beat” component whose frequency is related to the frequency difference between the pair of longitudinal modes considered. Thus, at saturation one obtains FEL-induced modulations of energy loss and energy spread in the electron bunch at optical frequency. These modulations can be converted into density modulation at the same optical frequency with the help of a weak chicane installed behind the baseline undulator. Powerful coherent radiation can then be generated with the help of an optical transition radiation (OTR) station, which have important applications. In this paper we briefly consider how the doublet structure of the XFEL generation spectra can be monitored by an optical spectrometer. Furthermore, the OTR coherent radiation pulse is naturally synchronized with the X-ray pulses, and can be used for timing the XFEL to high power conventional lasers with femtosecond accuracy for pump-probe applications.     

Transverse-longitudinal coherence function of a sound field for line-of-sight propagation in a turbulent atmosphere

Using the narrow-angle and Markov approximations, a formula for the transverse-longitudinal coherence function of a sound field propagating in a turbulent atmosphere with temperature and wind velocity fluctuations is derived. This function, which applies to observation points that are arbitrarily located in space, generalizes the transverse coherence function (coherence when the observation points are in a plane perpendicular to the sound propagation path), which has been studied extensively. The new result is expressed in terms of the transverse coherence function and the extinction coefficient of the mean sound field. The transverse-longitudinal coherence function of a plane sound wave is then calculated and studied in detail for the Gaussian and von Kármán spectra of temperature and wind velocity fluctuations. It is shown, for relatively small propagation distances, that the magnitude of the coherence function decreases in the longitudinal direction but remains almost constant in the transverse direction. On the other hand, for moderate and large propagation distances, the magnitude of the coherence decreases faster in the transverse direction than in the longitudinal. For some parameters of the problem, the coherence function has relatively large local maxima and minima as the transverse and longitudinal coordinates are varied. With small modifications, many results obtained in the paper can be applied to studies of electromagnetic wave propagation in a turbulent atmosphere.     

Phonon dispersion in graphite

We measured the dispersion of the graphite optical phonons in the in-plane Brillouin zone by inelastic x-ray scattering. The longitudinal and transverse optical branches cross along the Gamma-K as well as the Gamma-M direction. The dispersion of the optical phonons was, in general, stronger than expected from the literature. At the K point the transverse optical mode has a minimum and is only approximately 70 cm(-1) higher in frequency than the longitudinal mode. We show that first-principles calculations describe very well the vibrational properties of graphene once the long-range character of the dynamical matrix is taken into account.     

Longitudinal coherence measurements of a transient collisional x-ray laser

We present what is to our knowledge the first longitudinal coherence measurement of a transient inversion collisional x-ray laser. We investigated the picosecond output of a Ni-like Pd x-ray laser at 14.68 nm generated by the COMET laser facility at the Lawrence Livermore National Laboratory. Interference fringes were generated with a Michelson interferometer setup in which a thin multilayer membrane was used as a beam splitter. We determined the longitudinal coherence for the 4d1S0 --> 4p1P1 lasing transition to be approximately 400 microm (1/e half-width) by changing the length of one interferometer arm and measuring the resultant variation in fringe visibility. The inferred gain-narrowed linewidth of approximately 0.29 pm is a factor of 4 less than previously measured in quasi-steady-state x-ray laser schemes.     

Energy flux of a Gaussian beam in microwave band beyond the paraxial approximation

Through the analytic method beyond the paraxial approximation, the energy flux for the general fields of a Gaussian laser beam in microwave band (∼10⁸–10¹⁰ Hz) with different diffraction angles and longitudinal positions are derived. The results indicate a Gaussian beam (GB) has a certain number of transverse energy flux, and it would be enhanced with larger diffraction angle. In the range of beyond paraxial approximation, the transverse flux plays an important role in energy distribution, so that it cannot be ignored when the GB is highly focused. Meanwhile both transverse and longitudinal energy decay along the propagation direction, and the proportion of transverse energy far from beam axis is much more than the counterpart in paraxial area. The transverse energy as mainly characteristic of GB will be much useful for the interactions between electromagnetic field and other field.     

Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams

By expanding the Debye theory into the tight focusing of partially coherent field, the intensity and spatial correlation properties of partially coherent radially polarized vortex beams are studied. Expressions are derived for the intensity distribution and the spectral degree of coherence in the focal region. It is found that the intensity and the transverse and longitudinal coherence degrees in the focal region change with the variation of the topological charge and coherence length of the vortex beam. In addition, the degree of coherence is shown to exhibit phase singularities.     

Three-dimensional generalization of the Van Cittert-Zernike theorem to wave and particle scattering

Coherence properties of primary partially coherent radiations (light, X-rays and particles) elastically scattered from a 3D object consisting of a collection of electrons and nuclei are analyzed in the Fresnel diffraction region and in the far field. The behaviour of the cross-spectral density of the scattered radiation transverse and along to the local direction of propagation is shown to be described by respectively the 3D Fourier and Fresnel transform of the generalized radiance function of a scattering secondary source associated with the object. A relativistic correct expression is derived for the mutual coherence function of radiation which takes account of the dispersive propagation of particle beams in vacuum. An effect of the spatial coherence of radiation on the temporal one is found; in the Fresnel diffraction region, in distinction to the field, both the longitudinal spatial coherence and the spectral width of radiation affect the longitudinal coherence. A solution of the 3D inverse scattering problem for partially coherent radiation is presented. It is shown that squared modulus of the scattering potential and its 2D projections can be reconstructed from measurements of the modulus and phase of the degree of transverse spatial coherence of the scattered radiation. The results provide a theoretical basis for new methods of image formation and structure analysis in X-ray, electron, ion, and neutron optics.     

Nonparaxial propagation of soliton-like laser beams-pulses in media with saturable nonlinearity

The theoretical analysis of manifestations of nonparaxiality of propagation (in the plane transverse to the direction of propagation of radiation) of soliton-like beams-pulses in self-focusing media with electronic saturable nonlinearity is carried out. It is shown that, in formation of such structures by pulses of a comparatively small duration, a modulation of the radiation intensity arises, which can result in a fragmentation of the beam in the longitudinal direction. The number and depth of such "jags" are governed by the power of the nonparaxial beam.     

Angular dispersive diffraction using a diamond-anvil pressure cell and synchrotron X-ray source

Abstract

Wavelength dispersive diffraction studies have been performed using a diamond-anvil pressure cell and bending magnet synchrotron produced radiation. A double-crystal monochromator was used to select 15 and 17 keV photons and a 80 μm diameter collimator was used to restrict the beam entering the pressure cavity. Parallelism between the incident beam and the collimator axis was assisted by computer control of the collimator. The image of the transmitted beam was observed using a Hamamatsu x-ray Vidicon and TV monitor, for this alignment. The diffracted beam was recorded on x-ray film using a double film cassette and exposure times ranged from 6 to 8 hours. Neither the exposure time nor the line width of the diffraction lines was significantly altered by replacement of the incident beam collimator with a slit system.     

Influence of source coherence on x-ray absorption spectroscopy

Core-level x-ray absorption spectroscopy measurements have been performed at the L3,2 edges of Fe and Co thin films. The degree of source coherence was varied using soft x rays from five different beam lines. We observe an increase of the L edge resonance intensities relative to the continuum states which we propose is due to the presence of transverse coherence in the exciting radiation.     

软X射线直线单色仪光场分布实验研究

合肥国家同步辐射光源软X射线直线单色仪配备三种不同参数的波带片和针孔光阑,通过调节波带片和针孔光阑间的距离可输出1.97—5.44nm波段的软X射线.利用高分辨正性光刻胶,记录了CZP₃₂和30μm针孔光阑组合下的准确聚焦和大离焦量时的软X射线衍射图,即直线单色仪输出的光场分布.获得了有关爱里斑及空间相干半径等实验数据,所得结果与理论计算相一致. 关键词：     

Spatial coherence measurements from two L-shape arrays in Shallow Water

In the Shallow Water’ 06 experiment, two L-shape arrays (ARRAY52 and ARRAY32) were deployed. The vertical line array (VLA) components of both ARRAY52 and ARRAY32 were exactly perpendicular to the direction of sound propagation. The horizontal line array (HLA) component of ARRAY52 was exactly perpendicular to the direction of sound propagation. The HLA component of ARRAY32 was exactly parallel to the direction of sound propagation. This configuration offered an opportunity to simultaneously analyze the three dimensional (3-D) spatial coherences: vertical, transverse horizontal and longitudinal horizontal. When the source and the receivers were below the thermocline, both the vertical and longitudinal horizontal coherence lengths in units of wavelength increased with increasing range and frequency. When the source was within the thermocline, the transverse horizontal coherence length in units of wavelength decreased with frequency and exhibited weak range dependence. The text was submitted by the authors in English.     

Optically trapping Rayleigh particles by using focused partially coherent multi-rotating elliptical Gaussian beams

By investigating the cross-spectral density of partially coherent multi-rotating elliptical Gaussian beams(REGBs) that propagate through a focusing optical system, we obtain the radiation force on a Rayleigh particle.The radiation force distribution is studied under different beam indexes, coherence widths, and elliptical ratios of the partially coherent multi REGBs. The transverse and the longitudinal trapping ranges can increase at the focal plane by increasing the beam index or decreasing the coherence width. The range of the trapped particle radii increases as the elliptical ratio increases. Furthermore, we analyze the trapping stability.