The coherence of low-frequency sound in shallow water in the presence of internal waves

The coherence time and transverse coherence length of a low-frequency (100–300 Hz) sound field that is formed by an omnidirectional point source at a distance of 10–30 km in a shallow-water acoustic waveguide, which is characteristic of an open ocean shelf, were estimated analytically and in a numerical experiment. An anisotropic field of background internal waves is considered as a source of spatiotemporal fluctuations. It is shown that the coherence time decreases as the frequency increases, and strongly depends on the perturbation-movement direction. The transverse coherence length is primarily determined by phase incursions that are related to the cylindrical shape of the acoustic-wave front. In the case of transverse propagation, background internal waves may lead to significant variations in this length. The introduction of compensating phase corrections during processing provides a considerable increase in the average transverse coherence length.     

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.     

Ghost interference with partially coherent radiation

Ghost interference with partially coherent radiation sources is studied using optical coherence theory. The visibility of the ghost interference fringes is strongly influenced by the transverse size and transverse coherence width of the source. An increase of the transverse source size leads to a decrease of the fringes' visibility. An increase of the transverse coherence results in an increase of the visibility. The difference between ghost interference formed with entangled photon pairs and with partially coherent light is discussed.     

Coherence resonance on a forbidden magnetic-dipole transition excited in optically oriented Cs atoms by two magnetic fields: an Inclined SHF field and a transverse RF field

It is shown that the coherence created by a resonance transverse superhigh-frequency (SHF) field induces, under the action of a longitudinal SHF and transverse radio-frequency (RF) nonresonance fields, the Zeeman coherences on two adjacent allowed Δm = 1 transitions. Under the action of an RF transverse field these coherences induce further a coherence on a forbidden Δm = 2 transition. The resonance behavior of such coherence was earlier observed experimentally when the RF-field frequency coincided with the Δm = 2 transition frequency. The theoretical conclusions are in quantitative agreement with the experiment.     

随机电磁涡旋光束的深聚焦特性

基于德拜矢量积分理论,研究了随机电磁涡旋光束经过大数值孔径透镜之后的聚焦特性及透镜的数值孔径、入射光束的偏振度、拓扑荷以及横向相干长度对焦平面附近聚焦光束的光强分布和相干度的影响.结果表明:适当地选择相关参量,可在焦平面上得到椭圆形光斑的光强分布以及平顶光强分布.随机电磁涡旋光束在焦平面上同一点处两个相互垂直分量之间的相干度,不同两点处两个相同分量之间的相干度以及不同两点处两个相互垂直分量之间的相干度研究表明,入射光束的拓扑荷和横向相干长度对聚焦光束的相干性有着十分明显的影响.     

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.     

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 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.     

Transverse spectra of waves in random media

We consider the statistics of the transverse spectra of forward-propagating waves in a stationary random medium. A short-range perturbation solution is used to derive the difference equations that govern the long-range evolution of the ensemble-averaged transverse wave spectrum and coherence. The conditions under which these equations may be approximated by differential and integro-differential equations are given, and it is shown that the approximation is valid for the treatment of beam propagation provided that the transverse dimension of the beam is sufficiently large, and at ranges where the transverse coherence length of the beam remains larger than a wavelength. The equations that are derived are not limited by the parabolic approximation, and are amenable to numerical solution by marching techniques. We use the equation that governs the spectral density of the total energy flux, and also the propagation of waves which are statistically homogeneous in transverse planes, to show the conditions under which previously studied approximations derive from the present formulation, and to illustrate the numerical solution of the problem.     

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.     

Transverse spectra of waves in random media

Abstract

We consider the statistics of the transverse spectra of forward-propagating waves in a stationary random medium. A short-range perturbation solution is used to derive the difference equations that govern the long-range evolution of the ensemble-averaged transverse wave spectrum and coherence. The conditions under which these equations may be approximated by differential and integro-differential equations are given, and it is shown that the approximation is valid for the treatment of beam propagation provided that the transverse dimension of the beam is sufficiently large, and at ranges where the transverse coherence length of the beam remains larger than a wavelength. The equations that are derived are not limited by the parabolic approximation, and are amenable to numerical solution by marching techniques. We use the equation that governs the spectral density of the total energy flux, and also the propagation of waves which are statistically homogeneous in transverse planes, to show the conditions under which previously studied approximations derive from the present formulation, and to illustrate the numerical solution of the problem.     

非相干空间孤子的自陷行为

用相干密度法研究了一维非相干光束在饱和对数型光折变介质中的自陷行为,发现在传输过程中孤子的形态可具有稳态和周期性振荡的特点,具体取决于入射光束的初始宽度、相干特性和材料的非线性响应;研究了构成非相干光束的相干组份的传播行为,发现各相干组份的强度和光束宽度沿纵向发生周期性变化,峰值位置沿横向发生周期性变化.另外,利用横向相干宽度研究了非相干光束在各种传输状态下相干特性的变化,从而进一步解释了非相干光束在不同传播状态下的演化特性.     

Direct measurement of transverse coherence length of hard X rays from interference fringes

We propose a simple interferometric technique for hard x-ray spatial coherence characterization, recording a Fresnel interference pattern produced by a round fiber or a slit. We have derived analytical formulas that give a direct relation between a visibility of interference fringes and either the source size or the transverse coherence length. The technique is well suited to third-generation synchrotron radiation sources and was experimentally applied to determine the spatial coherence length and the source size at the European Synchrotron Radiation Facility.     

What type of coherence of the optical field is observed in the Michelson interferometer

The types and corresponding coherence functions of the optical field are considered depending on the frequency and angular spectra of the field. The main concepts of the theory of coherence effects in the interference experiment with the amplitude splitting of the initial field are discussed. It is shown that, in strict correspondence with the theory of coherence of the random wave fields, the Michelson interferometer reveals manifestations of the transverse and longitudinal spatial (rather than temporal, as it is commonly adopted) coherence of the optical field; the purely temporal coherence of the optical field is revealed only under special conditions of the interference experiment. Beyond these conditions, either spatial or spatiotemporal coherence is revealed.     

Influence of the frequency spectrum width on the transverse coherence of optical field

Transverse spatial coherence of the optical field depending on parameters of angular and frequency spectra is considered. Expressions for the function and length of the transverse coherence in relation to the widths of the angular and frequency spectra are obtained. Experimental studies with a modified high-power Young interferometer that prove theoretical results are performed.     

Quantitative evaluation of spatial coherence of the electron beam from low temperature field emitters

By using multiwalled carbon nanotubes as an element of a nanobiprism, we evaluated quantitatively the coherence of electrons emitted from tungsten tips at room temperature and 78 K, and found an enhancement of coherence at 78 K. The increase of the transverse coherence length of the electron beam agreed well with that of the inelastic mean free path of electrons in solids, demonstrating the direct relationship between the coherences of the electron beam and the original electronic states. On the basis of this experimental fact, we comment on the interpretation of recent Hanbury Brown-Twiss type experiments for electrons reported by Kiesel et al. [Nature (London) 418, 392 (2002)]].     

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.     

Detection of a semirough target in turbulent atmosphere by a partially coherent beam

The inverse problem of the interaction of an isotropic Gaussian Schell-model beam with a semirough target in turbulent atmosphere is investigated. It is found that we can determine the target size and the transverse correlation width of the target by measuring the transverse beam widths and the transverse coherence widths of the beams at the source plane and the receiver plane. Our results are useful for remote sensing and bistatic LIDAR system.     

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.     

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.