Beam Spatial Coherence Research Articles

BEATS: BEAmline for synchrotron X-ray microTomography at SESAME.

The ID10 beamline of the SESAME (Synchrotron-light for Experimental Science and Applications in the Middle East) synchrotron light source in Jordan was inaugurated in June 2023 and is now open to scientific users. The beamline, which was designed and installed within the European Horizon 2020 project BEAmline for Tomography at SESAME (BEATS), provides full-field X-ray radiography and microtomography imaging with monochromatic or polychromatic X-rays up to photon energies of 100 keV. The photon source generated by a 2.9 T wavelength shifter with variable gap, and a double-multilayer monochromator system allow versatile application for experiments requiring either an X-ray beam with high intensity and flux, and/or a partially spatial coherent beam for phase-contrast applications. Sample manipulation and X-ray detection systems are designed to allow scanning samples with different size, weight and material, providing image voxel sizes from 13 µm down to 0.33 µm. A state-of-the-art computing infrastructure for data collection, three-dimensional (3D) image reconstruction and data analysis allows the visualization and exploration of results online within a few seconds from the completion of a scan. Insights from 3D X-ray imaging are key to the investigation of specimens from archaeology and cultural heritage, biology and health sciences, materials science and engineering, earth, environmental sciences and more. Microtomography scans and preliminary results obtained at the beamline demonstrate that the new beamline ID10-BEATS expands significantly the range of scientific applications that can be targeted at SESAME.

Evolution of coherence singularities in polarization singular beams.

The evolution of correlation singularities in partially coherent polarization singular beams (PC-PSBs) is investigated. Since PSBs are the superposition of two orthogonally polarized vortex beams, the occurrence of coherence singularities in PC-PSBs is strongly governed by the topological charge of the component vortex beams and the spatial coherence length. Coherence singularities appear in the form of ring dislocations in the modulus of the spectral degree of coherence (SDoC) profile, and the number of ring dislocations is equal to the higher value of the topological charge of the superposing vortex beam. Furthermore, the SDoC phase profile can be used to determine the polarity of a PC-PSB. The findings of the study could be valuable in various applications that rely on the spatial coherence of beams, such as free-space communication and imaging.

Light field analysis for modeling and transmission characteristics of partially coherent light-emitting diodes

When analyzing the transmission characteristics of LEDs for long-distance lighting and communication applications, the light field is commonly assumed to be fully incoherent. However, in reality, the LED light source emits partially coherent light with a spatial coherence length on the order of microns. This paper is based on the generalized higher-order Lambert model of LEDs and aims to construct a Gaussian-Schell model for the LED beam (LED-GSM) on the near-field source plane, with a half-power angle of no more than 10o. Utilizing the cross-spectral density function transmission theory for partially coherent light, this paper provides the LED-GSM model’s spatial coherence length and beam radius at different distances and designs an experiment for measuring the spatial coherence length of LED beams. Experimental measurements of the spatial coherence length and beam spot size of LED beams at different distances are carried out using a Thorlabs LED528EHP light source. The experimental results match well with the theoretical simulations of the LED-GSM model, thus validating its effectiveness. Then, the proposed LED-GSM model is utilized to investigate the long-distance transmission characteristics of partially coherent narrow-beam LED light. Simulation results indicate that the spatial coherence length of the LED light field can reach tens to hundreds of millimeters over transmission distances of several kilometers. The beam radius is much smaller than that of the beam radius based on the fully incoherent model, and the beam intensity distribution also displays distinct differences.

Experimental proof on the effect of beam width and spatial coherence on Goos-Hänchen shift

We have experimentally investigated the effect of beam width and spatial coherence on Goos-Hänchen (GH) shift of light in a double-prism structure. The beam width and spatial coherence of the incident light are well controlled and measured. The experimental results show that the GH shift is affected by both the beam width and spatial coherence of light, and this is qualitatively consistent with the prediction of coherence theory of light. The result can promote the application of controlling GH shifts of partially coherent finite beams in optical devices and sensors.

Anisotropic spatial entanglement

The photon pairs generated through spontaneous parametric down-conversion (SPDC) possess strong correlations in their transverse position and momentum degrees of freedom. For such photon pairs, the transverse position correlation length depends on the crystal thickness and the pump wavelength. In contrast, the transverse momentum correlation length depends on the pump's beam waist and spatial coherence length. By controlling these parameters, it is possible to engineer spatial entanglement. Here, we utilize the circular asymmetry of the pump by using an elliptical-Gaussian beam to change the degree of entanglement in transverse directions, which we call anisotropic entanglement. We show the interrelation between the degree of anisotropic entanglement and the asymmetry in the beam width. In addition, we also show that for a highly asymmetric pump beam, the entanglement vanishes along the direction of the thinner beam width, while it remains intact in the direction of the broader beam width.

The singularity of the partially coherent beam in biological tissue

The singularity of the partially coherent beam propagating in biological tissue has been demonstrated, mainly including the properties of the normalized intensity distribution and phase evolution. It is shown that as the propagation distance increases, the evolution of the normalized intensity distribution undergoes several different stages, as well as the transformation of phase singularities takes place. Especially, the effect of the topological charge, the radial index, beam wave length and spatial coherence length on the beam singularity is analyzed, respectively.

Super cosh-Gauss nonuniformly correlated radially polarized beam and its propagation characteristics.

In this paper, a new kind of partially coherent vector beam termed as super cosh-Gauss nonuniformly correlated radially polarized (SCNRP) beam is introduced. Such beam source exhibits almost perfect coherence between two points that are within the beam center region or located on a ring concentric with the beam center. However, the coherence drops or even vanishes when the two points leave the central region and are located on the concentric rings with different radii. The second-order statistical properties, such as the spectral density, the state of polarization (SOP), and the degree of polarization (DOP) of such beam upon free-space propagation are studied through numerical examples. Our results reveal that the beam displays a self-focusing property during propagation. The focusing ability can be enhanced with increasing the beam index and decreasing the beam's spatial coherence width, whereas the DOP and SOP remain unchanged on propagation. Meanwhile, we establish an experimental system with the use of a radial polarization converter and a digital micro-mirror device to synthesize the SCNRP beam with controllable beam index and spatial coherence width. The spectral density and polarization properties of the synthesized beam during propagation are measured and analyzed in the experiment. The experimental results agree well with our theoretical predictions.

Influence of Kerr nonlinearity on propagation characteristics of twisted Gaussian Schell-model beams.

The analytical propagation formulae of twisted Gaussian Schell-model (TGSM) beams through nonlinear Kerr media are derived. It is found that a TGSM beam is less sensitive to Kerr nonlinearity than a Gaussian Schell-model (GSM) beam. Furthermore, the propagation characteristics of TGSM beams with stronger twist and worse spatial coherence are less affected by Kerr nonlinearity. The self-focusing effect enhances the beam twist, but degrades the beam spatial coherence. In the atmosphere (one kind of self-focusing media), a TGSM beam has greater resistance to self-focusing effects and atmospheric turbulence effects than a GSM beam or an ideal Gaussian beam.

Influence of biological tissue and spatial correlation on spectral changes of Gaussian-Schell model vortex beam

Based on the extended Huygens-Fresnel principle, the analytical expressions of the spectrum for Gaussian-Schell model vortex beam (GSMVB) propagating in biological tissues have been derived. The effects of the field point position, the species of the biological tissues, spatial correlation of beams on the relative spectral shift of GSMVB passing biological tissues have been investigated using the contour plots. It is shown that the spectral change is somewhat slow on the area near the z-axis, whereas the spectral redshift, blueshift and jump occur at far off-axis range. The stronger biological tissue turbulence can delay spectral jump, extend the space of observing the beam spectral jump, weaken the phenomenon of spectral jump on the propagation. Simultaneously, the results can well verify the scientificity and rationality of selecting the mouse as the experimental objects in biomedical research. The spatial coherence of beams can speed up the spectral change and slow the spectral jump down. Additionally, several physical explanations have been given to the above phenomena.

Generating electromagnetic Schell-model sources using complex screens with spatially varying auto- and cross-correlation functions

We present a method to generate any physically realizable electromagnetic Schell-model source. Our technique can be directly implemented on existing vector-beam generators that utilize spatial light modulators for coherence control, beam shaping, and relative phasing. This work significantly extends published research on the subject, where control over the partially coherent source’s cross-spectral density matrix was limited.We begin by presenting the statistical optics theory necessary to derive and implement our method. We then apply our technique, both analytically and in simulation, to produce two electromagnetic Schell-model sources from the literature. We demonstrate control over the full cross-spectral density matrices of both partially coherent beams. We compare the simulated results of these two sources to the corresponding theoretical or designed quantities to validate our approach. We find, through examination of the two-dimensional correlation coefficients, that both sources converge to their desired, ensemble (or by ergodicity, “long-time”) statistics within 500 random field instances.Our method and subsequent findings will be useful in any application where control over beam shape, polarization, and spatial coherence are important. These include but are not limited to free-space/underwater optical communications, directed energy, medicine, atomic optics, and optical tweezers.

Influence of optics vibration on synchrotron beam coherence.

Vibration of optics is one of the major limiting factors of the performance of state-of-the-art beamlines at low-emittance synchrotron facilities. We present a theoretical model with experimental data describing vibration-induced effects on x-ray beam coherence. Owing to the incoherent nature of vibration, the decrease in the beam spatial coherence perturbed by optics vibrations can be characterized by modeling the effective source profile of the vibrating beam. The measurements were carried out by using grating interferometry and a refractive lens with controlled vibration as test optics. The experimental results confirm the model and reveal the dependency of the measured beam spatial coherence on the acquisition time. The proposed method can be used to identify the eigenfrequency of the optical system as well as to optimize beamline operation and experimental conditions for coherence-related techniques.

Time Distribution of Reflected Light Signals from Partially Coherent Light Passing Through Complex Optical Systems with Multiple Apertures

Laser active detection technology scans and detects large target equipped with optoelectronic equipment by transmitting laser beam, converts the received reflected light signal into electrical signal, and obtains target information through various signal processing methods to achieve the goal of target detection. The laser beam output from the high power laser usually has multi-mode structure and partial coherence, and the optical reconnaissance equipment with complex optical structure is an equivalent system with multiple hard edge apertures. In the simulation of the coherent beams transmission through the multi aperture complex optical system, large matrix calculations are required in the spatial optical field computation, which consumes a lot of computation time. Furthermore, the size of the optical receiving lens is far less than the spot size after a long distance transmission, which results in the loss of optical information. To solve the problems, in this article, taking the Gauss Schell model (GSM) beam as a partially coherent light model, based on the Complex Gauss decomposition method for the hard edge diaphragm and ABCD optical transmission matrix, the recursive formula of the time series of the intensity distribution of the coherent GSM beams interference fringe field transmission through a multi aperture complex optical system is derived, and the influences of the spatial coherence of the GSM beam. The effects of the spatial coherence of GSM beams, the initial distance between coherent beams and the equivalent aperture size of complex optical systems on the time distribution of transmitted light intensity are analyzed. According to the results, the influence of the spatial coherence of the GSM beam on the spatial coherence of the beam itself is more obviously than that on the formation of two coherent GSM beam interference field. The interference fringe field spatial distribution and the aperture size are the main factors affecting the transmission of light time distribution. The conclusions obtained in this paper have important reference value for the application of partially coherent optical transmission through complex optical systems, and also provide a new idea for the target echo signal processing method of laser active detection.

Nonuniform self-imaging of achromatic Talbot lithography

Achromatic Talbot lithography (ATL) with high resolution has been demonstrated to be an excellent technique for large area periodic nano-fabrication. In this work, the uniformity of pattern distribution in ATL was studied in detail. Two ATL transmission masks with ∼50% duty cycle in a square lattice were illuminated by a spatial coherent broadband extreme ultraviolet beam with a relative bandwidth of 2.38%. Nonuniform dot size distribution was observed by experiments and finite-difference time-domain simulations. The sum of the two kinds of diffraction patterns, with different lattice directions (45° rotated) and different intensity distributions, results in the final nonuniform pattern distribution.

Controlling the Spatial Coherence of an Optical Source Using a Spatial Filter

This paper presents the theory for controlling the spectral degree of coherence via spatial filtering. Starting with a quasi-homogeneous partially coherent source, the cross-spectral density function of the field at the output of the spatial filter is found by applying Fourier and statistical optics theory. The key relation obtained from this analysis is a closed-form expression for the filter function in terms of the desired output spectral degree of coherence. This theory is verified with Monte Carlo wave-optics simulations of spatial coherence control and beam shaping for potential use in free-space optical communications and directed energy applications. The simulated results are found to be in good agreement with the developed theory. The technique presented in this paper will be useful in applications where coherence control is advantageous, e.g., directed energy, free-space optical communications, remote sensing, medicine, and manufacturing.

Interplay between multiple scattering and optical nonlinearity in liquid crystals.

We discuss the role played by time-dependent scattering on light propagation in liquid crystals. In the linear regime, the effects of the molecular disorder accumulate in propagation, yielding a monotonic decrease in the beam spatial coherence. In the nonlinear case, despite the disorder-imposed Brownian-like motion to the self-guided waves, self-focusing increases the spatial coherence of the beam by inducing spatial localization. Eventually, a strong enhancement in the beam oscillations occurs when power is strong enough to induce self-steering, i.e., in the non-perturbative regime.

Spatial and temporal coherence in optical parametric devices pumped with multimode beams

We investigate the emergence of spatial and temporal coherence for the fields in the noncritical nondegenerate parametric second-order down-conversion process pumped with low spatial and temporal coherence beams. It is shown that in this scenario, which is of considerable practical importance, the parametric gain in the near field breaks down into an ensemble of mutually incoherent beamlets containing parametric waves. The field generated in a single beamlet is fully spatially coherent. The size of such coherent parametric gain regions is governed by the near-field spatial coherence radius of the pump, which also acts as a parameter, restraining the linear diffraction of the parametric waves generated in the nonlinear interaction. Furthermore, we experimentally demonstrate how the spatial and temporal coherence can be substantially enhanced by manipulating the spatial field correlation of the multilongitudinal and multi-transversal mode pump.

Precise method for measuring spatial coherence in TEM beams using Airy diffraction patterns.

We have developed a method to precisely measure spatial coherence in electron beams. The method does not require an electron biprism and can be implemented in existing analytical transmission electron microscopes equipped with a post-column energy filter. By fitting the Airy diffraction pattern of the selector aperture, various parameters such as geometric aberrations of the lens system and the point-spread function of the diffraction blurring are precisely determined. From the measurements of various beam diameters, components that are attributed to the partial spatial coherence are successfully separated from the point-spread functions. A linear relationship between the spatial coherence length and beam diameter is revealed, thus indicating that a wide range of coherence lengths can be determined by our proposed method as long as the coherence length remains >80% of the aperture diameter. A remarkable feature of this method is its ability to simultaneously determine diffraction blurring and lens aberrations. Possible applications of this method are also discussed.

Polarization-entangled photon generation using partial spatially coherent pump beam

The generation of two photon fields, to date, has been demonstrated utilizing a fully coherent pump beam. In this paper we demonstrate, the theoretical and experimental generation of polarization entangled single photon pairs by varying the spatial coherence of the pump beam. The effect of the pump beam spatial coherence on the visibility of a polarization-entangled single photon source is investigated. A comparison of the visibility measurements using a fully coherent and partially coherent pump beam is performed. It is shown that the partial coherence of the pump beam contributes to an increase in the visibility. The coherence properties of the beam are significant for free-space optical transmission in particular for long range free-space quantum communication.

Speckle reduction in laser projection using microlens-array screens.

We report on a novel speckle reduction scheme using microlens arrays as screen material for application in laser-based projection systems. The scheme is based on properly adjusting the coherence properties on the screen: when the coherence area on the microlens-array screen is smaller than the microlens footprint, there is no interference between the fields emitted by the different microlenses and as a result no speckle is formed. We measured and modelled the speckle properties of microlens arrays with regular and irregular structure and lens sizes, and also a paper screen for comparison. In the experiments, we tune the laser beam's spatial coherence by sending it through a rotating diffuser. We show the amount of speckle reduction that can be achieved, which mechanisms influence the observed speckle contrast and we discuss the limitations due to increased non-uniformity in the projected image.

Generation of Vector Partially Coherent Optical Sources Using Phase-Only Spatial Light Modulators

Partially coherent beams (PCBs) of light can be highly directional, as from lasers, yet resistant to speckle and scintillation, as from LEDs. Generating PCBs with separate optical components for beam shaping and spatial coherence is complicated, and fundamentally limited. The authors control both shape and coherence using liquid-crystal spatial light modulators, and can produce two different classes of PCBs using the same simple optical setup. This work is immediately applicable in such diverse fields as medicine, directed energy, free-space optical communication, and manufacturing.