Full Spatial Coherence Research Articles

Acoustic error approximation due to Gouy phase in the sea

In order to estimate the statistical phase of underwater propagation for coherent acoustic systems, a calculation of background structure functions, based on wavespeeds, provides a wavefront distortion metric that excludes the phase due to focusing. In 1890, Gouy measured a phase change through the focus that differs for spherical vs cylindrical convergence by a factor of 2 from π/2. Statistics for the locations of the probable focus waist can use structure functions based on the measured sound speed profiles. Phase estimates are susceptible to errors in phase estimation unless results consider the Gouy phase while passing through focus waists. These foci may counteract or average with other errors of estimation, including scattering, type of spreading (cylindrical vs spherical foci), and reflections from the surface and bottom. Oceans have a sufficient range for the spatial derivatives of sound speed profiles to contribute persistently to foci that we show have coherence time and cross-sectional spatial (imaging) coherence. As an alternative, specular point theory can estimate deterministic pressure solutions. Convergence of these ray models that violate the stationary phase requires methods such as catastrophe theory to estimate the focal effects. Sommerfeld had an early comprehensive ray theory description that includes the Gouy phase. Using Flatté’s data, the foci are clearly time and length coherent. Statistically, the mutual coherence function for the Atlantic, Caribbean, and Gulf of Mexico regions shows that even distorted and out-of-phase convergence has full spatial coherence.

Modified Mach-Zehnder interferometer for spatial coherence measurement.

Spatial coherence of light sources is usually obtained by using the classical Young's interferometer. Although the original experiment was improved upon in successive works, some drawbacks still remain. For example, several pairs of points must be used to obtain the complex coherence degree (normalized first-order correlation function) of the source. In this work, a modified Mach-Zehnder interferometer which includes a pair of lenses and is able to measure the spatial coherence degree is presented. With this modified Mach-Zehnder interferometer, it is possible to measure the full 4D spatial coherence function by displacing the incoming beam laterally. To test it, we have measured only a 2D projection (zero shear) of the 4D spatial coherence, which is enough to characterize some types of sources. The setup has no movable parts, making it robust and portable. To test it, the two-dimensional spatial coherence of a high-speed laser with two cavities was measured for different pulse energy values. We observe from the experimental measurements that the complex degree of coherence changes with the selected output energy. Both laser cavities seem to have similar complex coherence degrees for the maximum energy, although it is not symmetrical. Thus, this analysis will allow us to determine the best configuration of the double-cavity laser for interferometric applications. Furthermore, the proposed approach can be applied to any other light sources.

Review of partially coherent diffraction imaging

Coherent diffraction imaging (CDI), a type of lensless imaging method, relies on the use of light source with high-degree coherence to compute highly resolved complex-valued objects. The coherence of light source consists of temporal coherence and spatial coherence. In practice, it is difficult to obtain a fully coherent source. Spatial decoherence can be generated in the following three scenarios: no synchronization mechanism for the whole radiation source, a finite (non-zero) point spread function of the detector, and the sample variation within exposure time. Partial temporal coherence means that the beam is not quasi-monochromatic, behaving as the energy spread of the illumination. The consequence of reduced degree of temporal and/or spatial coherence in CDI is the decrease of visibility in the measured diffraction intensity. A fundamental assumption of CDI is the full temporal and spatial coherence, and even a relatively small deviation from full coherence can prevent the phase retrieval algorithm from converging accurately. It is necessary to break the barrier of limited coherence by improving the experimental setups directly or optimizing the phase retrieval algorithms to mitigate decoherence. Based on the Wolf’s model of coherence-mode of light and the framework of CDI using partially coherent light proposed by Nugent et al., various methods have been proposed to solve the problems induced by low coherence. Those methods generally experience a similar development process, that is, from the requirement for measuring the spatial (coherent length or complex coherent factor) or temporal (spectrum distribution) coherence properties to without the need for such priori knowledge. Here in this work, the principles of partial coherent CDI, and the major progress of CDI with partial spatial- and temporal-coherent light are reviewed.

Single-shot large field of view Fourier transform holography with a picosecond plasma-based soft X-ray laser.

It is challenging to obtain nanoscale resolution images in a single ultrafast shot because a large number of photons, greater than 1011, are required in a single pulse of the illuminating source. We demonstrate single-shot high resolution Fourier transform holography over a broad 7 µm diameter field of view with ∼ 5 ps temporal resolution. The experiment used a plasma-based soft X-ray laser operating at 18.9 nm wavelength with nearly full spatial coherence and close to diffraction-limited divergence implemented utilizing a dual-plasma amplifier scheme. A Fresnel zone plate with a central aperture is used to efficiently generate the object and reference beams. Rapid numerical reconstruction by a 2D Fourier transform allows for real-time imaging. A half-pitch spatial resolution of 62 nm was obtained. This single-shot nanoscale-resolution imaging technique will allow for real-time ultrafast imaging of dynamic phenomena in compact setups.

Diffraction based Hanbury Brown and Twiss interferometry at a hard x-ray free-electron laser

X-ray free-electron lasers (XFELs) provide extremely bright and highly spatially coherent x-ray radiation with femtosecond pulse duration. Currently, they are widely used in biology and material science. Knowledge of the XFEL statistical properties during an experiment may be vitally important for the accurate interpretation of the results. Here, for the first time, we demonstrate Hanbury Brown and Twiss (HBT) interferometry performed in diffraction mode at an XFEL source. It allowed us to determine the XFEL statistical properties directly from the Bragg peaks originating from colloidal crystals. This approach is different from the traditional one when HBT interferometry is performed in the direct beam without a sample. Our analysis has demonstrated nearly full (80%) global spatial coherence of the XFEL pulses and an average pulse duration on the order of ten femtoseconds for the monochromatized beam, which is significantly shorter than expected from the electron bunch measurements.

Babinet's principle for mutual intensity.

In classical diffraction theory, Babinet's principle relates the electromagnetic fields produced by complementary sources. This theorem was always formulated for single-point quantities, both intensities or field amplitudes, in conditions where the full spatial coherence is implicitly assumed. However, electromagnetic fields are, in general, partially coherent, and their spatial properties are described in terms of two-point field-field correlation functions. In this case, a generalized Babinet's principle can be derived that applies to the spatial coherence functions. We present both the derivation and the experimental demonstration of this generalized Babinet theorem.

Spectrally resolved modal characteristics of leaky-wave-coupled quantum cascade phase-locked laser arrays

The modal characteristics of nonresonant five-element phase-locked arrays of 4.7-μm emitting quantum cascade lasers (QCLs) have been studied using spectrally resolved near- and far-field measurements and correlated with results of device simulation. Devices are fabricated by a two-step metal-organic chemical vapor deposition process and operate predominantly in an in-phase array mode near threshold, although become multimode at higher drive levels. The wide spectral bandwidth of the QCL’s core region is found to be a factor in promoting multispatial-mode operation at high drive levels above threshold. An optimized resonant-array design is identified to allow sole in-phase array-mode operation to high drive levels above threshold, and indicates that for phase-locked laser arrays full spatial coherence to high output powers does not require full temporal coherence.

Dark–bright solitons in a superfluid Bose–Fermi mixture

The recent experimental realisation of Bose–Fermi superfluid mixtures of dilute ultracold atomic gases has opened new perspectives in the study of quantum many-body systems. Depending on the values of the scattering lengths and the amount of bosons and fermions, a uniform Bose–Fermi mixture is predicted to exhibit a fully mixed phase, a fully separated phase or, in addition, a purely fermionic phase coexisting with a mixed phase. The occurrence of this intermediate configuration has interesting consequences when the system is nonuniform. In this work we theoretically investigate the case of solitonic solutions of coupled Bogoliubov–de Gennes and Gross–Pitaevskii equations for the fermionic and bosonic components, respectively. We show that, in the partially separated phase, a dark soliton in Fermi superfluid is accompanied by a broad bosonic component in the soliton, forming a dark–bright soliton which keeps full spatial coherence.

Gain dynamics in a soft-X-ray laser amplifier perturbed by a strong injected X-ray field

Seeding soft-X-ray plasma amplifiers with high harmonics has been demonstrated to generate high-brightness soft-X-ray laser pulses with full spatial and temporal coherence. The interaction between the injected coherent field and the swept-gain medium has been modelled. However, no experiment has been conducted to probe the gain dynamics when perturbed by a strong external seed field. Here, we report the first X-ray pump–X-ray probe measurement of the nonlinear response of a plasma amplifier perturbed by a strong soft-X-ray ultra-short pulse. We injected a sequence of two time-delayed high-harmonic pulses (λ = 18.9 nm) into a collisionally excited nickel-like molybdenum plasma to measure with femtosecond resolution the gain depletion induced by the saturated amplification of the high-harmonic pump and its subsequent recovery. The measured fast gain recovery in 1.5–1.75 ps confirms the possibility to generate ultra-intense, fully phase-coherent soft-X-ray lasers by chirped pulse amplification in plasma amplifiers.

Quantitative phase imaging with broadband fields

Recently, Wolf has shown that the phase measurement associated with fields that are not monochromatic, which is relevant for all x-ray structure investigations, must be properly defined via a cross-spectral density function under full spatial coherence conditions; otherwise, the problem is meaningless and has no solution [E. Wolf, Phys. Rev. Lett. 103, 075501 (2009)]. We propose an experimental realization for retrieving the phase across the entire field of an image. The demonstration is performed using broadband optical fields, but can be extended to other electromagnetic radiation, including x-rays.

Diffractive Imaging Using Partially Coherent X Rays

The measured spatial coherence characteristics of the illumination used in a diffractive imaging experiment are incorporated in an algorithm that reconstructs the complex transmission function of an object from experimental x-ray diffraction data using 1.4 keV x rays. Conventional coherent diffractive imaging, which assumes full spatial coherence, is a limiting case of our approach. Even in cases in which the deviation from full spatial coherence is small, we demonstrate a significant improvement in the quality of wave field reconstructions. Our formulation is applicable to x-ray and electron diffraction imaging techniques provided that the spatial coherence properties of the illumination are known or can be measured.

Spatially coherent, phase matched, high-order harmonic EUV beams at 50 kHz

By focusing a high repetition rate (50 kHz), compact, femtosecond laser system with low pulse energy (25 muJ) using a tight-focusing geometry, we demonstrate fully phase matched high-order harmonic generation for the first time at very high repetition rates, resulting in EUV light with full spatial coherence. The result is a practical, single-box, coherent source useful for applications in metrology, ultrafast spectroscopy, imaging and microscopy. The soft x-ray flux can be improved further by increasing the laser pulse energy and/or repetition rate.

A fully coherent electron beam from a noble-metal covered W(111) single-atomemitter

In quantum mechanics, a wavefunction contains two factors: the amplitude and the phase.Only when the probing beam is fully phase coherent, can complete information be retrievedfrom a particle beam based experiment. Here we use the electron beam field emitted from anoble-metal covered W(111) single-atom tip to image single-walled carbon nanotubes(SWNTs) in an electron point projection microscope (PPM). The interferencefringes of an SWNT bundle exhibit a very high contrast and the fringe patternextends throughout the entire beam width. This indicates good phase correlation atall points transverse to the propagation direction. Application of these sourcescan significantly improve the performance and expand the capabilities of currentelectron beam based techniques. New instrumentation based on the full spatialcoherence may allow determination of the three-dimensional atomic structuresof nonperiodic nanostructures and make many advanced experiments possible.

Phase-coherent, injection-seeded, table-top soft-X-ray lasers at 18.9 nm and 13.9 nm

There is keen interest in generating intense, coherent, soft-X-ray beams for scientific and measurement applications1. Here, we report the demonstration of soft-X-ray lasers with essentially full spatial and temporal coherence operating at wavelengths below 20 nm, and in particular within the 13-nm spectral region, which is important for the manufacturing of computer chips using extreme uv lithography. Gain-saturated pulses were produced in dense laser-created plasmas by amplifying high-harmonic seed pulses in the 18.9-nm and 13.9-nm transitions of nickel-like molybdenum and silver ions, respectively. These results, obtained using an injection seeding technique that can also be applied to improve the temporal coherence of free-electron lasers, extend our ability to generate bright phase-coherent laser beams to significantly shorter wavelengths. Moreover, the experiments were conducted using a practical table-top laser2. These compact soft-X-ray lasers offer new scientific opportunities, such as high-resolution coherent imaging and phase-coherent probing of atomic and molecular systems, in small laboratory environments.

Structural characterization of a novel spatially coherent crystalline nanocomposite obtained from a melt of KBr, RbCl, RbBr, KI and RbI salts

Large transparent bulks, grown by a pulling technique from a melt prepared by mixing equal molar fractions of KBr, RbCl, RbBr, KI and RbI salts, are characterized by X-ray diffractometry, Laue photography and low-current-field-emission high-resolution electron microscopy. The bulks consist of a multiphase crystalline material made of nanocrystallites (with a size distribution range of 5–60 nm) of three different fcc-phases. One of these phases is identified as single RbBr while the other two are discussed to be binary KI(39%):RbI(61%) and ternary KBr(47%):RbCl(39%):RbBr(14%), respectively, with unit-cell sizes of 6.889 ± 0.007, 7.234 ± 0.025 and 6.631 ± 0.005 A, respectively. The lattices of the crystallites, no matter the particular phase they belong to, are spatially coherent to each other so that the normal vectors to a lattice (HKL)-plane, in different crystallites, are confined in the space within a narrow circular cone around the lattice [HKL]-direction. For this cone, the semi-apical angle was determined for the cases of HKL equal to 301, 411, 331, 401, 311, 511, 221 and 321. The ternary phase crystallites contribute mainly to the observed departure of the composite crystallographic texture from a condition of full spatial coherence.

Speckle Reduction Based on Ultrashort Laser Pulse

In this paper, a method to reduce spatial coherence of the emission and improve intensity distribution by ultrashort laser pulses has been proposed. The spatial decoherence manifests itself in the formation of a Gaussian far field intensity distribution. For lasers with a high Fresnel number, the loss of full spatial coherence is usually due to the coemission of multiple mutually incoherent transverse modes, which are individually fully spatially coherent. That is to say, it is due to breakdown of the modal emission of these lasers.

High-Brightness Injection-Seeded Soft-X-Ray-Laser Amplifier Using a Solid Target

We demonstrate the generation of an intense soft-x-ray-laser beam by saturated amplification of high harmonic seed pulses in a dense transient collisional soft-x-ray-laser plasma amplifier created by heating a titanium target. Amplification in the 32.6 nm line of Ne-like Ti generates laser pulses of subpicosecond duration that are measured to approach full spatial coherence. The peak spectral brightness is estimated to be approximately 2 x 10(26) photons/(s mm(2) mrad(2) 0.01% bandwidth). The scheme is scalable to produce extremely bright lasers at very short wavelengths with full temporal and spatial coherence.

Effect of the spatial coherence of ultraviolet radiation (255 nm) on the fabrication efficiency of phase mask based fiber Bragg gratings

In this paper, we present a comparative study on fiber Bragg gratings fabrication efficiency namely the peak reflectivity and rate of growth in non-hydrogenated boron/germanium co-doped fiber for three writing UV beams (255 nm) of spatial coherence width varying from 30% to 100% of the full beam cross-section. All other UV-beam parameters viz. fluence, average power, spot size as well as the phase mask to fiber distance of 0.8 mm and grating length of 1 cm were kept same. The maximum reflectivity of about 31 dB was achieved, in about 210 s, for the UV beam having full spatial coherence. To the best of our knowledge, this is one of the best results for UV copper vapor laser (CVL) based system for non-hydrogenated FBGs writing. This high reflectivity is observed at about five times lower UV fluence than that normally reported. It is attributable to the vastly improved spatial coherence of UV beam, generated from the high spatial coherence, generalized diffraction filtered resonator based CVL.

Demonstration of a Fully Spatial Coherent X-Ray Laser at 13.9 nm

We have recently reported the successful development of a fully coherent X-ray laser (XRL) at 13.9 nm by an oscillator-amplifier configuration with two targets. In the experiment, a seed XRL beam from the first target is injected into a plasma amplifier at the second target. The observed XRL beam has full spatial coherence and 0.2 mrad of nearly diffraction-limited divergence. In order to improve the output fluence, the amplification properties of the XRL beam have been investigated using various plasma lengths of the second amplifier target. The output energy has been improved by a factor of ten, increasing the length of the gain region to 10 mm, resulting in about 0.2 /spl mu/J of output energy.

Coherence properties of a quasi-Gaussian submilliradiant divergence soft-x-ray laser pumped by capillary discharges

The coherence properties of a $46.9\text{\ensuremath{-}}\mathrm{nm}$ soft-x-ray laser beam produced in a capillary discharge plasma have been investigated. The beam is produced in a regime that is free from the effect of refraction defocusing, with a divergence of only $0.5--0.6\phantom{\rule{0.3em}{0ex}}\mathrm{mrad}$. The discharge plasma is produced in capillary channels with length of $45\phantom{\rule{0.3em}{0ex}}\mathrm{cm}$, where the Fresnel number of the gain medium is of the order of unity. The full laser energy is about $300\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{J}$. The spatial coherence of the laser has been experimentally investigated using a Young's double-slit interferometer and analyzed assuming a Gaussian Schell-model source and the generalized Van Cittert--Zernike theorem. We demonstrate the achievement of almost full spatial coherence and a near-Gaussian intensity distribution.