Short-scan interferometric interrogation and multiplexing of fibre Bragg grating sensors

We describe an interferometric technique for the demodulation of serial fibre Bragg grating sensor arrays, yielding absolute measurement of the individual grating mean wavelengths. The composite beam reflected from the array illuminates a scanning Michelson interferometer but, in contrast to spectral measurement by Fourier Transform Spectroscopy, our technique requires an OPD scan far shorter than the coherence length of the grating reflections. The technique is based on the high-resolution measurement of the phases of the complex analytic signals and of the relationship of these phases to interferometric delay. The analytic signals are derived via the Hilbert transform, allowing frequency domain filtering of individual signals within the signal processing. The technique has yielded a resolution of 0.007 nm for an OPD scan of 1.2 mm.     

Space-variant polarization manipulation for far-field polarimetry by use of subwavelength dielectric gratings

A method for polarimetric measurement that uses a discrete space-variant subwavelength dielectric grating is presented. One retrieves the polarization state by measuring the far-field intensity of a beam emerging from the grating followed by a polarizer. The analysis for a partially polarized, quasi-monochromatic beam is performed by use of the beam coherence polarization matrix along with an extended van Cittert-Zernike theorem. We experimentally demonstrate polarization measurements of both fully and partially polarized light.     

A combination of laser-induced grating and transient-absorption experiments for investigation of laser pulse properties and fast molecular relaxation processes

A repetitive low-power laser-pulse apparatus has been developped which allows both absorption relaxation and light-induced grating experiments without changing geometry or components. The influence of pulse width and coherence time on the diffracted intensity correlation function is discussed for a weak amplitude grating in terms of a simplified theory. From the corresponding absorption relaxation signals including the coherent coupling contribution some easy ways for detecting vibronic-relaxation, intersystem-crossing and orientational-relaxation times are deduced. The advantage of the in-situ measurement of the amplitude grating autocorrelation function leads to a precise zero-delay calibration of the transient absorption equipment. Furthermore one gets the response function for the absorption experiments from the grating experiments, if stable mode-locking operation of the argon laser is reached. This condition can be controlled either by the time course of the absorption or grating signals. A surprisingly short coherence length is detected for the cavity-dumped laser beam. A reliable check of the coherent-coupling theory confirms the theoretical assumptions incorporated into the fast-relaxation signal analysis. Experiments on dye molecules show high triplet yield of heavy-atom substituted dyes and fast rotational diffusion of oblong molecular rotors.     

Quantitative coherence analysis of dual phase grating x-ray interferometry with source grating

Dual phase grating x-ray interferometry is compatible with common imaging detectors,and abandons the use of an absorption analyzer grating to reduce the radiation dose.When using x-ray tubes,an absorbing source grating must be introduced into the dual phase grating interferometer.In order to attain a high fringe visibility,in this work we conduct a quantitative coherence analysis of dual phase grating interferometry to find how the source grating affects the fringe visibility.Theoretical analysis shows that with the generalized Lau condition satisfied,the fringe visibility is influenced by the duty cycle of the source grating and the transmission through the grating bar.And the influence of the source grating profile on the fringe visibility is independent of the phase grating type.Numerical results illustrate that the maximum achievable fringe visibility decreases significantly with increasing transmission in the grating bar.Under a given transmission,one can always find an optimal duty cycle to maximize the fringe visibility.These results can be used as general guidelines for designing and optimizing dual phase grating x-ray interferometers for potential applications.     

Measurement of the spatial coherence function of undulator radiation using a phase mask

A measurement of the horizontal coherence function of 7.9 keV radiation from an undulator beam line at the Advanced Photon Source is reported. X-ray diffraction from a phase-shifting mask was used, and the coherence function was measured as a function of the width of beam-conditioning slits in the beam line. The coherence distribution is found to be best described by a Lorentzian function.     

硬X射线相位光栅的设计与研制

针对在普通实验室和医院实现40—100keVX射线相衬成像的需求,考虑到成像系统参数、X射线源空间相干特性及光栅衍射效率,设计出硅基相位光栅结构参数.利用我们已发展的光助电化学刻蚀技术研制出直径为5英寸的相位光栅,其空间周期为5.6μm,线宽为2.8μm,深度为40—70μm.在理论分析的基础上,通过提高硅片两端有效工作电压和修正Lehmann电流密度公式,解决了实际刻蚀过程中出现的钻蚀问题.由实验结果可知,本方案对制作大面积高精度相位光栅十分有效。     

Generation of light carrying orbital angular momentum via induced coherence grating in cold atoms

We report on the generation of light carrying orbital angular momentum through Bragg diffraction into an electromagnetically induced coherence grating in a degenerate two-level system of cold cesium atoms. The induced Zeeman coherence grating is shown to contain the spatial phase structure of the incident beams. The exchange of phase information between a light beam with orbital angular momentum and a long-lived atomic coherence opens up the way to process quantum information encoded in a multidimensional state space.     

Synchrotron beam coherence: a spatially resolved measurement

We report a precise and spatially resolved measurement of the complex degree of coherence of a one-dimensional 1.5-keV beam produced by a third-generation synchrotron source. The method of phase-space tomography is used, which requires only measurements of the x-ray intensity. We find that the field is statistically stationary to within experimental error, the correlations are very well approximated by a Gaussian distribution, and the measured coherence length is in excellent agreement with expectations.     

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.     

Transient gratings in a nonlinear medium

The excitation of a phase transient grating induced by two equal pulses from the same laser, which intersect in a nonlinear (cubic) medium, is considered theoretically. The grating parameters are calculated. The grating amplitude is shown to be spatially non-uniform and to be described by the pulse autocorrelation function, a display of the pulse coherence and of the two-pulse interference pattern. The diffraction problem of the induced grating is then solved using the electrodynamic perturbation theory. The diffraction efficiency of the grating is calculated. It is shown that the measurement of the spectral intensity of the probe light diffracted from the induced grating enables the complete computation of the grating amplitude. Such a measurement may be carried out for the whole of the time of grating decay after the excitation of the grating. Some possible applications of the induced grating are considered. The medium parameters and the autocorrelation trace of the single pulse may be determined. The shape and duration of a bandwidth-limited pulse or the spectrum of an arbitrary one are shown to be measurable.     

Single shot spatial and temporal coherence properties of the SLAC Linac Coherent Light Source in the hard x-ray regime

We measured the transverse and longitudinal coherence properties of the Linac Coherent Light Source (LCLS) at SLAC in the hard x-ray regime at 9 keV photon energy on a single shot basis. Speckle patterns recorded in the forward direction from colloidal nanoparticles yielded the transverse coherence properties of the focused LCLS beam. Speckle patterns from a gold nanopowder recorded with atomic resolution allowed us to measure the shot-to-shot variations of the spectral properties of the x-ray beam. The focused beam is in the transverse direction fully coherent with a mode number close to 1. The average number of longitudinal modes behind the Si(111) monochromator is about 14.5 and the average coherence time τ(c)=(2.0±1.0) fc. The data suggest a mean x-ray pulse duration of (29±14) fs behind the monochromator for (100±14) fc electron pulses.     

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.     

Thick-grating non-divergent focussing device: 2-D analysis

The two-dimensional analysis of a recently reported thick grating Bragg diffraction focussing device is carried out using Solymar's coupled-wave approach. It is shown that the device is capable of operating as a non-divergent lens with beam contraction ratios of better than 100:1, and conversion efficiencies of nearly 100%. It is also shown that it can operate as a novel kind of Fourier spectrum analyser, the focussed diffracted intensity being proportional (as a function of Bragg condition violation) to the modulus squared of the Fourier transform of the incident finite beam. The focussing properties are studied as functions of incident beam profile, width and position, grating strength and Bragg condition violation. Poynting vector optics is used successfully to predict (in conjunction with the dispersion surfaces of x-ray dynamical theory) the off-Bragg behaviour in the focal plane. It is likely that the device could be used as avariable ratio beam contractor in integrated optics, where the grating strength could be controlled (interdigital electrode system) electrooptically.     

时空分辨软x射线谱诊断技术研究

利用平焦场光栅谱仪、门控宽微带x射线分幅相机及可见光CCD设计了一套时空及高谱分辨x 射线诊断系统，利用该x射线诊断系统通过一系列的实验研究建立了同时具有时间、空间及 高谱分辨x射线谱诊断技术，该技术已经成功应用于辐射加热样品的吸收谱，获得了较好的 实验结果. 关键词： x射线吸收谱 诊断技术 时空分辨     

Experimental measurement of the four-dimensional coherence function for an undulator x-ray source

A full measurement of the four-dimensional coherence function from an undulator beam line is reported. The analysis is based on the observation that the data are consistent with a coherence function that is mathematically separable. The effective source size can be altered by changing the width of the exit slit, and the complete coherence function is presented for two settings. We find, to within experimental error, that the four-dimensional complex degree of coherence can be described as a real Gaussian function that depends only on the difference of the spatial coordinates.     

Characterization of the 46.9-nm soft X-ray laser beam from a capillary discharge

Intense lasing had been obtained from argon plasma in the soft X-ray region from a capillary discharge plasma system. Different diagnostics have been used to characterize the lasing properties by recording the temporal, spatial, and spectral profiles of the emission. The divergence measurement indicates that the soft X-ray laser beam has good directionality with a divergence of 3.5 mrad. The spectrum of the laser beam measured using a transmission grating showed intense lasing line at 46.9 nm. Diffraction orders as high as 10th orders were observed. The temporal profile recorded with a vacuum diode showed a distinct laser peak with a pulse width ~1.2 ns (FWHM). In addition, the coherence of the X-ray laser beam was also confirmed from the high-contrast interference fringes (visibility ~85 %) recorded using double slits.     

Distributed strain sensor based on dynamic grating in polarization-maintaining erbium-doped fiber

A novel distributed fiber-optic strain sensor based on dynamic grating in polarization-maintaining erbium-doped fiber (PM-EDF) is demonstrated experimentally. The dynamic grating is written with light beams polarized along one primary polarization axis of the PM-EDF, and read with a light beam polarized along the other primary polarization axis. When a strain is applied to the fiber, the detected Bragg reflection frequency of the dynamic grating shifts in proportion to the birefringence change, which is proportional to the strain. By employing the technique of synthesis of optical coherence function, the dynamic grating is localized in a region that can be shifted to sweep along the fiber to determine the location of the strain. In the experiment, a spatial resolution of 20 cm is demonstrated.     

Effect of partial coherence on four-wave mixing in photorefractive materials via reflection grating approximation

We investigate the effect of beam coherence on four-wave mixing via reflection gratings in photorefractive media. For the case of phase conjugation, the results of our theoretical analysis indicate that partial coherence always leads to a drop of signal gain and phase conjugate reflectivity in non-depleted cases. In general, the mutual coherence of the signal beam and the pump beam can be enhanced due to the process of wave mixing. The mutual coherence of the phase conjugate beam and one of the pump beams depends on the beam intensity ratio as well as the optical path difference. This is distinctly different from the four-wave mixing case with a transmission grating. Received: 15 October 1999 / Revised version: 26 June 2000 / Published online: 7 February 2001     

New methods of fabricating gratings for deformation measurements: A review

Gratings have been widely accepted as practical and effective deformation carriers/sensors and are commonly used in many deformation measurement methods. Since the deformation measurement sensitivity is directly proportional to the grating frequency, and the measurement accuracy is strongly affected by the grating quality. Thus, it is crucial to prepare an appropriate grating on the specimen surface that is to be measured. Over the past few decades, an increasing number of grating fabrication methods have been developed, including holographic photolithography, electron beam lithography, focused ion beam etching, nanoimprinting, soft lithography, and others. Although substantial literature regarding grating fabrication can be found, a comprehensive review is still necessary to promote the application of these methods. This review introduces the technical details and characteristics of recently developed grating fabrication methods and provides suggestions of which grating fabrication methods to use in correspondence with different deformation measurement methods. Emphasis is placed on the introduction of grating fabrication processes and the quality and applicability of the resulting gratings.