Transverse Coherence Length Research Articles

Generating bona fide twisted Gaussian Schell-model beams.

We experimentally realize bona fide twisted Gaussian Schell-model (TGSM) beams by converting an anisotropic GSM beam into a TGSM beam with a set of just three cylindrical lenses. In contrast to the previously reported experimental technique for generating TGSM beams, we are able to explicitly generate anisotropic GSM beams with simultaneously controlled beam widths and transverse coherence lengths along two mutually orthogonal directions, prior to converting them to genuine TGSM beams.

Pulsed electron gun for electron diffraction at surfaces with femtosecond temporal resolution and high coherence length.

We present a newly designed 30 kV pulsed electron gun for ultrafast electron diffraction suited for pump-probe setups driven by femtosecond laser pulses. The electron gun can be operated both in transmission and reflection geometry. A robust design with a back illuminated Au photocathode, extraction fields of 7.5 kV/mm, and a magnetic focus lens ensures reliable daily use. Magnetic deflectors allow for beam alignment and characterization. Focusing of the UV pulse on the photocathode results in a small source size of photoemitted electrons and thus a high transverse coherence length of more than 50 nm in diffraction. A low difference of ΔE = 0.1 eV between the work function of the 10 nm Au photocathode and photon energy of the frequency tripled UV laser pulses results in an instrumental temporal resolution of 330 fs full width at half maximum. This resolution is discussed with respect to the number of electrons per pulse.

Coupling characteristics and kurtosis parameter of partially coherent beams in turbulent atmosphere

ABSTRACTCoupling properties and kurtosis parameter (K parameter) of arbitrary beams propagating through atmospheric turbulence are investigated. A correlation factor (C4-factor) is introduced to describe the influence of turbulence on coupling characteristics. The general analytical expression for C4-factor of arbitrary beams in atmospheric turbulence is derived. It is shown that C4-factor of arbitrary beams in the turbulent atmosphere depends on the initial second-order moments and fourth-order moments and turbulence quantities. Taking the partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam as an example, we can obtain that C4-factor decreases as structure constant of the refractive index fluctuations and inner scale increase, and waist width and transverse coherence length decrease when z > 5 km. Moreover, K parameter of PCAEHG beam in turbulent atmosphere converges to 2 when propagation distance is large enough. It indicates that the profile of PCAEHG beams in turbulent atmosphere finally evolves into fundamental Gaussian distribution.

Transverse horizontal spatial coherence in shallow water

Since the advent of large-aperture array processing, more and more attention has been paid to the sound field correlation, which has fundamental limit to the array gain of spatial coherent signal processing. The two dominant mechanisms that degrade the spatial coherence are normal modes (or multi-paths) interference and the environmental variability caused by several relevant oceanographic processes. In the present study, the transverse horizontal spatial coherence of explosive signals has been studied experimentally by a bottom-mounted array in the Northern South China Sea. And the effects of normal mode interference on the transverse horizontal spatial coherence have been analyzed numerically. Expressed in terms of wavelengths, the coherence length is shown to be larger than 170λ/185λ at acoustic frequency 508-640Hz/80-101Hz in shallow water. It is much greater than Carey’s shallow-water result 30λ estimated from array signal gain after assuming a specific functional form for the coherence (The Journal of the Acoustical Society of America 104, 831 (1998)). It, however, is consistent with Rouseff’s modelling result of a coherence length larger than 100λ (The Journal of the Acoustical Society of America 138, 2256 (2015)). Both Carey and Rouseff argue that the transverse horizontal spatial coherence length depends only weakly on range, in direct. In the present study, however, the coherence length is shown to depend highly on source-receiver range, and it fluctuates synchronously with the sound-field intensity while range varies.

Coherence-Length Effects in Fast Atom Diffraction at Grazing Incidence

Coherence properties of projectiles, found relevant in ion-atom collisions, are investigated by analyzing the influence of the degree of coherence of the atomic beam on interference patterns produced by grazing-incidence fast-atom diffraction (GIFAD or FAD). The transverse coherence length of the projectiles, which depends on the incidence conditions and the collimating setup, determines the overall characteristics of GIFAD distributions. We show that for atoms scattered from a LiF(001) surface after a given collimation, we can modify the interference signatures of the angular spectra by varying the total impact energy, while keeping the normal energy as a constant. Also, the role played by the geometry of the collimating aperture is analyzed, comparing results for square and circular openings. Furthermore, we study the spot-beam effect, which is due to different focus points of the impinging particles. We show that when a region narrower than a single crystallographic channel is coherently illuminated by the atomic beam, the spot-beam contribution strongly affects the visibility of the interference structures, contributing to the gradual quantum-classical transition of the projectile distributions.

Statistical properties of electromagnetic anomalous vortex beam with orbital angular momentum in atmospheric turbulence

Statistical properties of an electromagnetic anomalous vortex (EAV) beam with orbital angular momentum (OAM) through a turbulent atmosphere are studied. Analytical formulae for the average intensity (AI) and degree of polarization (DOP) of EAV beam in a strong turbulence are derived. Accurate analytical formulae (without any approximations) for M2-factor of EAV beam under all turbulence conditions are also derived based on the second-order moments of the Wigner distribution function. Numerical results show that the transverse distributions for AI of EAV beam depend mainly on topological charge, beam order and structure constant of turbulence. An anomalous result is found that the on-axis intensity is larger for an EAV beam in a stronger turbulence (i.e., larger structure constant and smaller inner scale). Inner scale effects of DOP of the EAV beam in strong turbulence are also investigated. Off-axis DOPs of an EAV beam will appear oscillation near the propagation axis. It can be also found that M2-factor of an EAV beam propagating through the strong and weak turbulence are smaller for smaller transverse coherent length and structure constant of turbulence, larger beam order, topological charge and inner scale of turbulence.

Rocking curve and spatial coherence properties ofalong X-ray compound refractive lens.

Semi-analytical theory of a long set of X-ray compound refractive lenses (CRLs) based on recurrence relations is developed further. The geometrical aperture, angular divergence of incident radiation and source size were accurately taken into account. Using this theory it is possible to calculate the width of the rocking curve of a long (40.7 cm) Be CRL which coincides with experimental data obtained earlier. By this approach the transverse coherence length for the X-ray beam after passing a set of CRLs of arbitrary complexity has been estimated. It is shown that at the focus this coherence length is equal to a diffraction-limited beam size (beam size in the case of a point source) and has minimal difference with the real beam size.

Transverse horizontal spatial coherence of explosive signals in northern South China sea

Transverse horizontal spatial cross-coherence was measured experimentally by bottom-mounted receiver arrays using explosive sources in Northern South China sea, where the water depth varies from 100 m to 1000 m in about 100 km ranges with a 200 m depth at about 75 km range. Expressed in terms of wavelengths, the coherence length is shown to be larger than 150λ at an acoustic frequency of 100 Hz in shallow water of 100 m depth. It is much greater than Carey’s shallow-water experimental result 30λ estimated from array signal gain (The Journal of the Acoustical Society of America 104, 831 (1998)), while it is consistent with Rouseff’s modeling result of a coherence length larger than 200λ (The Journal of the Acoustical Society of America 138, 2256 (2015)). In contrast to the good coherence in shallow water, the coherence length is measured to be only 5λ ~ 20λ at 100Hz in the transitional area with the array bottom-mounted at 1000m depth. Besides, both Carey and Rouseff argue that the transverse horizontal spatial coherence length depends only weakly on range. In the present study, however, the coherence length is shown to depend highly on range, and it fluctuates synchronously with the sound-field intensity while range varies.

Incoherent Nuclear Resonant Scattering from a Standing Spin Wave

We introduce a method to study the spatial profiles of standing spin waves in ferromagnetic microstructures. The method relies on Nuclear Resonant Scattering of 57Fe using a microfocused beam of synchrotron radiation, the transverse coherence length of which is smaller than the length scale of lateral variations in the magnetization dynamics. Using this experimental method, the nuclear resonant scattering signal due to a confined spin wave is determined on the basis of an incoherent superposition model. From the fits of the Nuclear Resonant Scattering time spectra, the precessional amplitude profile across the stripe predicted by an analytical model is reconstructed. Our results pave the way for studying non-homogeneous dynamic spin configurations in microstructured magnetic systems using nuclear resonant scattering of synchrotron light.

Intrinsic Orbital Angular Momentum States of Neutrons.

It has been shown that single-particle wave functions, of both photons and electrons, can be created with a phase vortex, i.e., an intrinsic orbital angular momentum (OAM). A recent experiment has claimed similar success using neutrons [C. W. Clark et al., Nature, 525, 504 (2015)NATUAS0028-083610.1038/nature15265]. We show that their results are insufficient to unambiguously demonstrate OAM, and they can be fully explained as phase contrast interference patterns. Furthermore, given the small transverse coherence length of the neutrons in the original experiment, the probability that any neutron was placed in an OAM state is vanishingly small. We highlight the importance of the relative size of the coherence length, which presents a unique challenge for neutron experiments compared to electron or photon work, and we suggest improvements for the creation of neutron OAM states.

Effect of electron irradiation on the fluctuation conductivity in YBa2Cu3O7\u2212\u03b4 single crystals

In this work, the evolution of the excess conductivity of the YВа2Сu3О7−δ single crystals under electron irradiation is studied. It is shown that irradiation with electrons leads to a significant expansion of the temperature interval that excess conductivity exists. Therefore, the value of the transverse coherence length ξс(0) increases by a factor of 1.4 and the point of the 2D–3D crossover shifts with respect to the temperature.

Influence of annealing on the electrical resistance of YBCO single crystals

The effect of annealing on the basal-plane electrical resistivity of the YBa$_2$Cu$_3$O$_{7-\delta}$ single crystals is studied in a broad range of oxygen contents. Within the framework of s-d scattering of electrons by phonons, an increase in the oxygen deficit index, $\delta$, leads to a significant increase in the Debye temperature, $\theta$, which is associated with the isotropization of the phonon spectrum as the concentration of oxygen vacancies increases. Near the optimal doping, the role of the paraconductivity becomes crucial, whereas its contribution decreases with increasing $\delta$. At large values of $\delta$ some deviations from the s-d model of electron scattering by phonons are observed at room temperature, while no paraproductivity is observed. In the superconducting transition region, a 2D-3D crossover is observed, which shifts in the direction of $T_c$ with increasing $\delta$. The estimate for the transverse coherence length is about $1$\,\AA.

Fast interaction of atoms with crystal surfaces: coherent lighting

Quantum coherence of incident waves results essential for the observation of interference patterns in grazing incidence fast atom diffraction (FAD). In this work we investigate the influence of the impact energy and projectile mass on the transversal length of the surface area that is coherently illuminated by the atomic beam, after passing through a collimating aperture. Such a transversal coherence length controls the general features of the interference structures, being here derived by means of the Van Cittert-Zernike theorem. The coherence length is then used to build the initial coherent wave packet within the Surface Initial Value Representation (SIVR) approximation. The SIVR approach is applied to fast He and Ne atoms impinging grazingly on a LiF(001) surface along a low-indexed crystallographic direction. We found that with the same collimating setup, by varying the impact energy we would be able to control the interference mechanism that prevails in FAD patterns, switching between inter-cell and unit-cell interferences. These findings are relevant to use FAD spectra adequately as a surface analysis tool, as well as to choose the appropriate collimating scheme for the observation of interference effects in a given collision system.

Spatially modulated thermal light in atomic medium for enhanced ghost imaging

Recent years have seen vast progress in image modulation based on atomic media, with potential applications in both classical optical imaging and quantum imaging regions. However, there have been few investigations of how thermal light images interact with an electromagnetically induced transparent medium. In this letter, we experimentally demonstrate pseudo-thermal light modulation on coherent population trapping conditions in 87Rb vapor. By introducing the Laguerre-Gaussian beam as the control beam and the encoded speckle as the probe beam, we obtained sharper speckle patterns after the atom cell compared with that in free space. The spatially modulated thermal light was then used to enhance the image resolution in ghost imaging of which the resolution was enhanced by factor 3, since the ghost image resolution is heavily reliant on the speckle’s transverse coherent length. Our results are promising for potential applications in high resolution ghost imaging and image metrology, image processing and biomedical imaging.

Reconstructing mode mixtures in the optical near-field.

We propose a reconstruction scheme for hard x-ray inline holography, a variant of propagation imaging, which is compatible with imaging conditions of partial (spatial) coherence. This is a relevant extension of current full-field phase contrast imaging, which requires full coherence. By the ability to reconstruct the coherent modes of the illumination (probe), as demonstrated here, the requirements of coherence filtering could be relaxed in many experimentally relevant settings. The proposed scheme is built on the mixed-state approach introduced in [Nature494, 68 (2013)], combined with multi-plane detection of extended wavefields [Opt. Commun.199, 65 (2001), Opt. Express22, 16571 (2014)]. Notably, the diversity necessary for the reconstruction is generated by acquiring measurements at different defocus positions of the detector. We show that we can recover the coherent mode structure and occupancy numbers of the partial coherent probe. Practically relevant quantities as the transversal coherence length can be computed from the reconstruction in a straightforward way.

Reduction of Intrinsic Electron Emittance from Photocathodes Using Ordered Crystalline Surfaces.

The generation of intense electron beams with low emittance is key to both the production of coherent x rays from free electron lasers, and electron pulses with large transverse coherence length used in ultrafast electron diffraction. These beams are generated today by photoemission from disordered polycrystalline surfaces. We show that the use of single crystal surfaces with appropriate electronic structures allows us to effectively utilize the physics of photoemission to generate highly directed electron emission, thus reducing the emittance of the electron beam being generated.

Compression of high-density 0.16 pC electron bunches through high field gradients for ultrafast single shot electron diffraction: The Compact RF Gun.

We present an RF gun design for single shot ultrafast electron diffraction experiments that can produce sub-100 fs high-charge electron bunches in the 130 keV energy range. Our simulations show that our proposed half-cell RF cavity is capable of producing 137 keV, 27 fs rms (60 fs FWHM), 106 electron bunches with an rms spot size of 276 μm and a transverse coherence length of 2.0 nm. The required operation power is 9.2 kW, significantly lower than conventional rf cavity designs and a key design feature. This electron source further relies on high electric field gradients at the cathode to simultaneously accelerate and compress the electron bunch to open up new space-time resolution domains for atomically resolved dynamics.

Propagation characteristics of partially coherent flat-topped beams propagating through inhomogeneous atmospheric turbulence.

M2-factor and root-mean-square (rms) angular width of partially coherent flat-topped (PCFT) beams propagating through inhomogeneous atmospheric turbulence are studied based on the extended Huygens-Fresnel principle and the Wigner distribution function (WDF). It is shown that the effect of turbulence on the PCFT beams can be neglected as the vertical height increases, which is different from the homogeneous turbulence. Analytical formulae of the M2-factor and rms angular width of PCFT beams have been given. The saturation propagation distances (SPDs) increase with increasing zenith angle. It can be seen that the SPDs of the M2-factor and rms angular width of PCFT beams propagating through inhomogeneous atmospheric turbulence are about 30 km and 0.5 km, respectively, when the zenith angle is π/4. It can be found that the M2-factor increases with increasing beam order and zenith angle, and with decreasing waist width, inner scale, wavelength, and transverse coherence length. The rms angular width increases with increasing beam order, wavelength, and zenith angle, and decreasing waist width, inner scale, and transverse coherence length.

Multiobjective optimization design of an rf gun based electron diffraction beam line

Multiobjective genetic algorithm optimizations of a single-shot ultrafast electron diffraction beam line comprised of a $100\text{ }\text{ }\mathrm{MV}/\mathrm{m}$ 1.6-cell normal conducting rf (NCRF) gun, as well as a nine-cell $2\ensuremath{\pi}/3$ bunching cavity placed between two solenoids, have been performed. These include optimization of the normalized transverse emittance as a function of bunch charge, as well as optimization of the transverse coherence length as a function of the rms bunch length of the beam at the sample location for a fixed charge of $1{0}^{6}$ electrons. Analysis of the resulting solutions is discussed in terms of the relevant scaling laws, and a detailed description of one of the resulting solutions from the coherence length optimizations is given. For a charge of $1{0}^{6}$ electrons and final beam sizes of ${\ensuremath{\sigma}}_{x}\ensuremath{\ge}25\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ and ${\ensuremath{\sigma}}_{t}\ensuremath{\approx}5\text{ }\text{ }\mathrm{fs}$, we found a relative coherence length of ${L}_{c,x}/{\ensuremath{\sigma}}_{x}\ensuremath{\approx}0.07$ using direct optimization of the coherence length. Additionally, based on optimizations of the emittance as a function of final bunch length, we estimate the relative coherence length for bunch lengths of 30 and 100 fs to be roughly 0.1 and $0.2\text{ }\text{ }\mathrm{nm}/\ensuremath{\mu}\mathrm{m}$, respectively. Finally, using the scaling of the optimal emittance with bunch charge, for a charge of $1{0}^{5}$ electrons, we estimate relative coherence lengths of 0.3, 0.5, and $0.92\text{ }\text{ }\mathrm{nm}/\ensuremath{\mu}\mathrm{m}$ for final bunch lengths of 5, 30 and 100 fs, respectively.

Retrieval of Cn2 profile from differential column image motion lidar using the regularization method

We develop a regularization-based algorithm for reconstructing the Cn2 profile using the profile of Fried’s transverse coherent length (r0) of differential column image motion (DCIM) lidar. This algorithm consists of fitting the set of measured data to a spline function and a two-stage inversion method based on regularized least squares QR-factorization (LSQR) in combination with an adaptive selection method. The performance of this algorithm is analyzed by a simulated profile generated from the HV5/7 model and experimental DCIM lidar data. Both the simulation and experiment support the presented approach. It is shown that the algorithm can be applied to estimate a reliable Cn2 profile from DCIM lidar.