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Redefining precision interferometry and spectroscopy with high-performance optical interference coatings

High-performance optical interference coatings have transformed precision interferometry and spectroscopy by enabling unparalleled control over light–matter interactions. This review explores recent innovations in ion-beam sputtered amorphous dielectric, as well as substrate-transferred crystalline coatings, and their impact on systems at the forefront of precision metrology. These state-of-the-art coating techniques generate multilayers with ultralow optical losses, yielding mirrors with exceptional reflectivity. Refinements in their noise performance push the ultimate limits of sensitivity, resolution, and stability in demanding laser-based metrology applications. These technologies underpin the most advanced timekeeping and spatial measurement tools, enabling high-finesse reference cavities for the world’s most precise optical atomic clocks and low-noise reflective test masses for km-baseline gravitational-wave detectors. Emerging hybrid designs combining these techniques expand access to the mid-infrared spectral region, enabling the first ultralow-optical-loss coatings in the 3000–5000 nm wavelength range for enhanced spectroscopy and trace-gas detection. We highlight how these technologies redefine coating performance metrics and set new benchmarks in quantum science, fundamental physics, and precision optical sensing.

Cole, Garrett D. [University of Arizona, Tucson, A↗

The ZBOT-NC Experiment - Effects of Non-Condensable Gases on Propellant Tank Pressurization and Pressure Control

Introduction Integral to all phases of NASA’s projected planetary expeditions is affordable and reliable cryogenic fluid storage for use in propellant or life support systems. It is greatly advantageous to develop innovative vent-less pressure control designs based on cooling/mixing of the bulk tank fluid to allow storage of the cryogenic fluid with zero or reduced boil-off. The presence of noncondensable gases, can interfere with the condensation at the interface impacting tank pressure control during subcooled jet mixing especially in microgravity. The Zero-Boil-Off Tank (ZBOT) Experiments are a series of small-scale experiments aboard the International Space Station (ISS) that use a transparent volatile simulant fluid in a transparent sealed tank to delineate various fundamental fluid flow, heat and mass transport, and phase change phenomena associated with storage tank pressurization and pressure control in microgravity. The ZBOT-1 experiment was performed on the ISS 2017-2018 timeframe and collected data to validate a state-of-the-art CFD model for tank pressurization and pressure control for a pure system. The ZBOT-NC Experiment is the second experiment in the series to be performed on the International Space Station (ISS) in 2025. Its goal is to investigate the effects of noncondensable gases on interfacial evaporation and condensation during self -pressurization and jet-mixing pressure control in microgravity for a two-component system. Materials & Methods In this work, we will describe the detailed features of the ZBOT-NC experimental hardware and Diagnostics that includes nonintrusive Quantum Dot Thermometry (QDT) for whole field temperature measurement. All microgravity pressurization and pressure control tests will be performed for both the pure and the two-components systems with Xenon and Neon as the two noncondensable gases spanning small and large molecular weights and sizes. The two-phase CFD model that is developed as part of the project will be also presented and discussed. Results Ground-based pressurization and jet mixing experiments and CFD simulation results are compared to each other to validate both the fidelity of the CFD model predictions and the accuracy of the QDT measurement. Model simulations for noncondensable gas effects will also be compared against large Cryogenic LH2-GHe experiments to indicate the noncondensable gas effects on tank pressure control during jet mixing in 1G. Finally, CFD results will be presented to predict the effects of the noncondensable gas during subcooled jet mixing during the ZBOT-NC in advance of the microgravity experiment in 2015.

Evaporation Condensation↗

The Zero-Boil-Off Tank Experiment: the Effects of Non-Condensable Gases on Pressurization and Pressure Control of Propellant Tanks in Microgravity

Introduction Integral to all phases of NASA’s projected planetary expeditions is affordable and reliable cryogenic fluid storage for use in propellant or life support systems. It is greatly advantageous to develop innovative vent-less pressure control designs based on cooling/mixing of the bulk tank fluid to allow storage of the cryogenic fluid with zero or reduced boil-off. The presence of noncondensable gases, can interfere with the condensation at the interface impacting tank pressure control during subcooled jet mixing especially in microgravity. The Zero-Boil-Off Tank (ZBOT) Experiments are a series of small-scale experiments aboard the International Space Station (ISS) that use a transparent volatile simulant fluid in a transparent sealed tank to delineate various fundamental fluid flow, heat and mass transport, and phase change phenomena associated with storage tank pressurization and pressure control in microgravity. The ZBOT-1 experiment was performed on the ISS 2017-2018 timeframe and collected data to validate a state-of-the-art CFD model for tank pressurization and pressure control for a pure system. The ZBOT-NC Experiment is the second experiment in the series to be performed on the International Space Station (ISS) in 2025. Its goal is to investigate the effects of noncondensable gases on interfacial evaporation and condensation during self -pressurization and jet-mixing pressure control in microgravity for a two-component system. Materials & Methods In this work, we will describe the detailed features of the ZBOT-NC experimental hardware and Diagnostics that includes nonintrusive Quantum Dot Thermometry (QDT) for whole field temperature measurement. All microgravity pressurization and pressure control tests will be performed for both the pure and the two-components systems with Xenon and Neon as the two noncondensable gases spanning small and large molecular weights and sizes. The two-phase CFD model that is developed as part of the project will be also presented and discussed. Results Ground-based pressurization and jet mixing experiments and CFD simulation results are compared to each other to validate both the fidelity of the CFD model predictions and the accuracy of the QDT measurement. Model simulations for noncondensable gas effects will also be compared against large Cryogenic LH2-GHe experiments to indicate the noncondensable gas effects on tank pressure control during jet mixing in 1G. Finally, CFD results will be presented to predict the effects of the noncondensable gas during subcooled jet mixing during the ZBOT-NC in advance of the microgravity experiment in 2015.

Evaporation Condensation↗

A spin-wave magnetometer with a positive feedback

In this work, we demonstrate experimentally the operation of a spin-wave magnetometer integrated into a circuit with a positive feedback. The circuit consists of the passive magnetic and active electric parts. The magnetic part includes a sensing element, which is a magnetic cross junction made of Y 3 Fe 2 (FeO 4 ) 3 . The electric part includes a non-linear amplifier and a phase shifter. The electric and magnetic parts are connected via micrometer size antennae. Spin waves are excited by two of these antennae while the output inductive voltage produced by the interfering spin waves is detected by the third antenna. Spin waves propagating in the orthogonal arms of the cross can accumulate significantly different phase shifts, depending on the direction and the strength of the external magnetic field. The output inductive voltage reaches its maximum in the case of constructive spin wave interference. The positive feedback provides further signal amplification. It appears possible to enhance the response function, compared to the passive circuits without a feedback, by a factor of ×100 without an increase in the noise level. The experimental data show a prominent response to the external magnetic field variation, exceeding 5 x 10 3 V/T. The intrinsic noise spectral density of the device can be as low as 10 -16 V 2 /Hz. The estimated sensitivity of the prototype device is 2 x 10 -12 T/√Hz at room temperature. We argue that spin-wave magnetometers can potentially be as sensitive as SQUIDs while operating at room temperature.

36 MATERIALS SCIENCE↗

Beyond 30% Conversion Efficiency in Silicon Solar Cells: A Numerical Demonstration

We demonstrate through precise numerical simulations the possibility of flexible, thin-film solar cells, consisting of crystalline silicon, to achieve power conversion efficiency of 31%. Our optimized photonic crystal architecture consists of a 15 μm thick cell patterned with inverted micro-pyramids with lattice spacing comparable to the wavelength of near-infrared light, enabling strong wave-interference based light trapping and absorption. Unlike previous photonic crystal designs, photogenerated charge carrier flow is guided to a grid of interdigitated back contacts with optimized geometry to minimize Auger recombination losses due to lateral current flow. Front and back surface fields provided by optimized Gaussian doping profiles are shown to play a vital role in enhancing surface passivation. We carefully delineate the drop in power conversion efficiency when surface recombination velocities exceed 100 cm/s and the doping profiles deviate from prescribed values. These results are obtained by exact numerical simulation of Maxwell’s wave equations for light propagation throughout the cell architecture and a state-of-the-art model for charge carrier transport and Auger recombination.

14 SOLAR ENERGY↗

Gradient Field Detection Using Interference of Stimulated Microwave Optical Sidebands

Here, we demonstrate that stimulated microwave optical sideband generation using parametric frequency conversion can be utilized as a powerful technique for coherent state detection in atomic physics experiments. The technique has advantages over traditional absorption or polarization rotation-based measurements and enables the isolation of signal photons from probe photons. We outline a theoretical framework that accurately models sideband generation using a density matrix formalism. Using this technique, we demonstrate a novel intrinsic magnetic gradiometer that detects magnetic gradient fields between two spatially separated vapor cells by measuring the frequency of the beat note between sidebands generated within each cell. The sidebands are produced with high efficiency using parametric frequency conversion of a probe beam interacting with 87 Rb atoms in a coherent superposition of magnetically sensitive hyperfine ground states. Interference between the sidebands generates a low-frequency beat note whose frequency is determined by the magnetic field gradient between the two vapor cells. In contrast to traditional gradiometers the intermediate step of measuring the magnetic field experienced by the two vapor cells is unnecessary. We show that this technique can be readily implemented in a practical device by demonstrating a compact magnetic gradiometer sensor head with a sensitivity of 25 fT/cm/ √ Hz with a 4.4 cm baseline, while operating in a noisy laboratory environment unshielded from Earth’s field.

74 ATOMIC AND MOLECULAR PHYSICS↗

Fluorescence Studies of Protein Crystallization Interactions

We are investigating protein-protein interactions in under- and over-saturated crystallization solution conditions using fluorescence methods. The use of fluorescence requires fluorescent derivatives where the probe does not markedly affect the crystal packing. A number of chicken egg white lysozyme (CEWL) derivatives have been prepared, with the probes covalently attached to one of two different sites on the protein molecule; the side chain carboxyl of ASP 101, within the active site cleft, and the N-terminal amine. The ASP 101 derivatives crystallize while the N-terminal amine derivatives do not. However, the N-terminal amine is part of the contact region between adjacent 43 helix chains, and blocking this site does would not interfere with formation of these structures in solution. Preliminary FRET data have been obtained at pH 4.6, 0.1M NaAc buffer, at 5 and 7% NaCl, 4 C, using the N-terminal bound pyrene acetic acid (PAA, Ex 340 nm, Em 376 nm) and ASP 101 bound Lucifer Yellow (LY, Ex 425 nm, Em 525 nm) probe combination. The corresponding Csat values are 0.471 and 0.362 mg/ml (approximately 3.3 and approximately 2.5 x 10 (exp 5) M respectively), and all experiments were carried out at approximately Csat or lower total protein concentration. The data at both salt concentrations show a consistent trend of decreasing fluorescence yield of the donor species (PAA) with increasing total protein concentration. This decrease is apparently more pronounced at 7% NaCl, consistent with the expected increased intermolecular interactions at higher salt concentrations (reflected in the lower solubility). The estimated average distance between protein molecules at 5 x 10 (exp 6) M is approximately 70 nm, well beyond the range where any FRET can be expected. The calculated RO, where 50% of the donor energy is transferred to the acceptor, for the PAA-CEWL * LY-CEWL system is 3.28 nm, based upon a PAA-CEWL quantum efficiency of 0.41.

Pusey, Marc L.↗

Self referencing attosecond interferometer with zeptosecond precision

In this work we demonstrate the generation of two intense, ultrafast laser pulses that allow a controlled interferometric measurement of higher harmonic generation pulses with 12.8 attoseconds in resolution (half the atomic unit of time) and a precision as low as 680 zeptoseconds (10–21 seconds). We create two replicas of a driving femtosecond pulse which share the same optical path except at the focus where they converge to two foci. An attosecond pulse train emerges from each focus through the process of high harmonic generation. The two attosecond pulse trains from each focus interfere in the far field producing a clear interference pattern in the extreme ultraviolet region. By controlling the relative optical phase (carrier envelope phase for pulsed fields) between the two driving laser pulses we are able to actively influence the delay between the pulses and are able to perform very stable and precise pump-probe experiments. Because of the phase shaping operation occurs homogeneously across the entire spatial profile, we effectively create two indistinguishable intense laser pulses or a common path interferometer for attosecond pulses. Commonality across the two beams means that they are extremely stable to environmental and mechanical fluctuations up to a Rayleigh range from the focus. In our opinion this represents an ideal source for homodyne and heterodyne spectroscopic measurements with sub-attosecond precision.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Photon-odderon interference in exclusive χ c charmonium production at the Electron-Ion Collider

Exclusive C = + 1 scalar, axial-vector, and tensor quarkonium production in high-energy electron-proton scattering requires a C -odd t -channel exchange of a photon or a three-gluon ladder. We derive the expressions for the corresponding amplitudes. The relative phase of the photon vs three-gluon exchange amplitudes is determined by the sign of the light-front matrix element of the eikonal color current operator d a b c J + a J + b J + c at moderate x , and is not affected by small- x QCD evolution. Model calculations predict constructive interference, which is particularly strong for momentum transfer | t | ∼ 1 GeV 2 where the cross section for χ c J production exceeds that for pure photon exchange by up to a factor of 4. Exclusive χ c J electroproduction at the high luminosity Electron-Ion Collider occurs with well measurable rates and measurements of these processes should find evidence for the perturbative odderon exchange. We also compute the total electroproduction cross section as a function of energy and provide first estimates of the number of χ c J events per month at the Electron-Ion Collider design luminosity. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Numerical and perturbative computations of the fuzzy dark matter model

We investigate nonlinear structure formation in the fuzzy dark matter (FDM) model using both numerical and perturbative techniques. On the numerical side, we examine the virtues and limitations of a Schrödinger-Poisson solver (wave formulation) versus a fluid dynamics solver (Madelung formulation). On the perturbative side, we carry out a computation of the one-loop mass power spectrum, i.e. up to third order in perturbation theory. We find that (1) in many situations, the fluid dynamics solver is capable of producing the expected interference patterns, but it fails in situations where destructive interference causes the density to vanish—a generic occurrence in the nonlinear regime. (2) The Schrödinger-Poisson solver works well in all test cases, but it is demanding in resolution: suppose one is interested in the mass power spectrum on large scales, it is not sufficient to resolve structure on those same scales; one must resolve the relevant de Broglie scale which is often smaller. The fluid formulation does not suffer from this issue. (3) We compare the one-loop mass power spectrum from perturbation theory against the mass power spectrum from the Schrödinger-Poisson solver, and find good agreement in the mildly nonlinear regime. We contrast fluid perturbation theory with wave perturbation theory; the latter has a more limited range of validity. (4) As an application, we compare the Lyman-alpha forest flux power spectrum obtained from the Schrödinger-Poisson solver versus one from an N-body simulation (the latter is often used as an approximate method to make predictions for FDM). At redshift 5, the two, starting from the same initial condition, agree to better than 10% on observationally relevant scales as long as the FDM mass exceeds 2 × 10 –23 eV. Furthermore, we emphasize that the so called quantum pressure is capable of both enhancing and suppressing fluctuations in the nonlinear regime—which dominates depends on the scale and quantity of interest.

79 ASTRONOMY AND ASTROPHYSICS↗

Macroscopic Violation of Three Cauchy-Schwarz Inequalities Using Correlated Light Beams From an Infra-Red Emitting Semiconductor Diode Array

We briefly review quantum mechanical and semi-classical descriptions of experiments which demonstrate the macroscopic violation of the three Cauchy-Schwarz inequalities: g(sup 2)(sub 11)(0) greater than or equal to 1; g(sup 2)(sub 11)(0) greater than or equal to g(sup 2)(sub 11)(t), (t approaches infinity); (the absolute value of g(sup 2)(sub 11)(0))(exp 2) less than or equal to g(sup 2)(sub 11)(0) g(sup 2)(sub 11)(0). Our measurements demonstrate the violation, at macroscopic intensities, of each of these inequalities. We show that their violation, although weak, can be demonstrated through photodetector current covariance measurements on correlated sub-Poissonian Poissonian, and super Poissonian light beams. Such beams are readily generated by a tandem array of infrared-emitting semiconductor junction diodes. Our measurements utilize an electrically coupled array of one or more infrared-emitting diodes, optically coupled to a detector array. The emitting array is operated in such a way as to generate highly correlated beams of variable photon Fano Factor. Because the measurements are made on time scales long compared with the first order coherence time and with detector areas large compared with the corresponding coherence areas, first order interference effects are negligible. The first and second inequalities are violated, as expected, when a sub-Poissonian light beam is split and the intensity fluctuations of the two split beams are measured by two photodetectors and subsequently cross-correlated. The third inequality is violated by bunched (as well as anti-bunched) beams of equal intensity provided the measured cross correlation coefficient exceeds (F - 1)/F, where F is the measured Fano Factor of each beam. We also investigate the violation for the case of unequal beams.

Edwards, P. J.↗

Optical measure of disorder: Why Urbach analysis works for amorphous silicon but fails for amorphous carbon

We investigate the basis for the Paradox where the Urbach-slope disorder parameter disagrees with the Raman width in amorphous diamond-like carbon (DLC) materials (lower Urbach-Eo yet greater Raman width). We examined the bandgap and Urbach-slope measurement issues. While significant errors are identified, ultimately these cannot resolve the Paradox. This resolution involves large changes in shape of DLC's absorption band resulting from large energy shifts. To solidify the understanding of band energy shifts, we examined their properties using a-Si:H, well known for its agreement between Raman and Urbach-slope disorder parameters. Using Tauc-Lorentz (T-L) dispersion functions, the Urbach method works for a-Si:H because small changes in shape occur, as measured by (i) peak position, (ii) peak width, (iii) peak amplitude, and (iv) and gap energies. Moreover, for a-Si:H, a 5th condition (v) there is no other feature below the principal band to interfere with its fall. All 5 of these conditions fail for DLCs. Because T-L dispersions accommodate asymmetry, we traced the Paradox to a steepening of the band shape as it pushes toward lower energy. This steepening is unrelated to disorder, but to a boundary value problem where energy cannot be negative. We conclude that Urbach analysis is invalid for DLC materials, but the T-L width is a good measure instead. We also examined another disorder measure, where π bonds should be considered as disorder relative to the σ bonds in an idealized “amorphous diamond” sp 3 network: superconvergence can be used to quantify these π transitions. Finally, further molecular orbital calculations are needed to properly interpret the changes in T-L widths.

36 MATERIALS SCIENCE↗

Absorption of transverse spin current in ferromagnetic NiCu: Dominance of bulk dephasing over spin-flip scattering

In ferromagnetic metals, transverse spin currents are thought to be absorbed via dephasing—i.e., destructive interference of spins precessing about the strong exchange field. Yet, due to the ultrashort coherence length of ≈1 nm in typical ferromagnetic thin films, it is difficult to distinguish dephasing in the bulk from spin-flip scattering at the interface. Here, to assess which mechanism dominates, we examine transverse spin-current absorption in ferromagnetic NiCu alloy films with reduced exchange fields. We observe that the coherence length increases with decreasing Curie temperature, as weaker dephasing in the film bulk slows down spin absorption. Moreover, nonmagnetic Cu impurities do not diminish the efficiency of spin-transfer torque from the absorbed spin current. Our findings affirm that the transverse spin current is predominantly absorbed by dephasing inside the nanometer-thick ferromagnetic metals, even with high impurity contents.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Integration of Highly Luminescent Lead Halide Perovskite Nanocrystals on Transparent Lead Halide Nanowire Waveguides through Morphological Transformation and Spontaneous Growth in Water

The integration of highly luminescent CsPbBr 3 quantum dots on nanowire waveguides has enormous potential applications in nanophotonics, optical sensing and quantum communications. On the other hand, CsPb 2 Br 5 nanowires have also attracted a lot of attention due to their unique water stability and controversial luminescent property. Here we first report the growth of CsPbBr 3 nanocrystals on CsPb 2 Br 5 nanowires by simply immersing CsPbBr 3 powder into pure water, CsPbBr 3-γ X γ (X = Cl, I) nanocrystals on CsPb 2 Br 5-γ X γ nanowires are then synthesized for tunable light sources. Systematic structure and morphology studies, including in-situ monitoring, revealed that CsPbBr 3 powder was first converted to CsPb 2 Br 5 microplatelets in water, followed by a morphological transformation from CsPb 2 Br 5 microplatelets to nanowires, which is a kinetic dissolution-recrystallization process controlled by electrolytic dissociation and supersaturation of CsPb 2 Br 5 . CsPbB r3 nanocrystals are spontaneously formed on CsPb 2 Br 5 nanowires when nanowires are collected from the aqueous solution. Raman spectroscopy, combined photoluminescence and SEM imaging confirm that the bright emission originates from CsPbBr 3-γ X γ nanocrystals while CsPb 2 Br 5-γ X γ nanowires are transparent waveguides. In conclusion, the intimate integration of nanoscale light sources with a nanowire waveguide is demonstrated through the observation of the wave guiding of light from nanocrystals and Fabry-Perot interference modes of the nanowire cavity.

42 ENGINEERING↗

Orbital-resolved calculations of two-center interferences in linear triatomic molecules

In this report we perform ab initio calculations of high-harmonic spectroscopy (HHS) of two-center interference phenomena in oriented carbon-dichalcogen molecules, using time-dependent density functional theory (TDDFT). We show that by resolving the harmonic response into contributions from individual Kohn-Sham orbitals, we can extract target-specific characteristics for both the spectral amplitude and phase. We also discuss that this extraction is predicated on a careful analysis and normalization of the harmonic spectrum. Finally, we present field-free scattering calculations that mimic the recollision step in high-order-harmonic generation and allow the calculation of recombination dipole matrix elements without explicitly calculating the scattering states of a molecule. We show that the orbital-resolved TDDFT HHS results and results based on our field-free scattering calculations are in very good agreement with each other.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

$t\bar{t}b\bar{b}$ at the LHC: on the size of corrections and b -jet definitions

We report on the calculation of the next-to-leading order QCD corrections to the production of a $t\bar t$ pair in association with two heavy-flavour jets. We concentrate on the di-lepton $t\bar t$ decay channel at the LHC with $\sqrt{s}$ = 13 TeV. The computation is based on pp → $e^+ν_eμ^-\bar{ν}_μb\bar{b}b\bar{b}$ matrix elements and includes all resonant and non-resonant diagrams, interferences and off-shell effects of the top quark and the W gauge boson. As it is customary for such studies, results are presented in the form of inclusive and differential fiducial cross sections. We extensively investigate the dependence of our results upon variation of renormalisation and factorisation scales and parton distribution functions in the quest for an accurate estimate of the theoretical uncertainties. We additionally study the impact of the contributions induced by the bottom-quark parton density. Results presented here are particularly relevant for measurements of $t\bar{t}H(H → b\bar{b})$ and the determination of the Higgs coupling to the top quark. In addition, they might be used for precise measurements of the top-quark fiducial cross sections and to investigate top-quark decay modelling at the LHC.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators

We address the challenge of acoustic simulations in three-dimensional (3D) virtual rooms with parametric source positions, which have applications in virtual/augmented reality, game audio, and spatial computing. The wave equation can fully describe wave phenomena such as diffraction and interference. However, conventional numerical discretization methods are computationally expensive when simulating hundreds of source and receiver positions, making simulations with parametric source positions impractical. To overcome this limitation, we propose using deep operator networks to approximate linear wave-equation operators. This enables the rapid prediction of sound propagation in realistic 3D acoustic scenes with parametric source positions, achieving millisecond-scale computations. By learning a compact surrogate model, we avoid the offline calculation and storage of impulse responses for all relevant source/listener pairs. Our experiments, including various complex scene geometries, show good agreement with reference solutions, with root mean squared errors ranging from 0.02 to 0.10 Pa. Notably, our method signifies a paradigm shift as—to our knowledge—no prior machine learning approach has achieved precise predictions of complete wave fields within realistic domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Small-angle scattering interferometry with neutron orbital angular momentum states

Methods to prepare and characterize neutron helical waves carrying orbital angular momentum (OAM) were recently demonstrated at small-angle neutron scattering (SANS) facilities. These methods enable access to the neutron orbital degree of freedom which provides new avenues of exploration in fundamental science experiments as well as in material characterization applications. However, it remains a challenge to recover phase profiles from SANS measurements. We introduce and demonstrate a novel neutron interferometry technique for extracting phase information that is typically lost in SANS measurements. An array of reference beams, with complementary structured phase profiles, are put into a coherent superposition with the array of object beams, thereby manifesting the phase information in the far-field intensity profile. We demonstrate this by resolving petal-structure signatures of helical wave interference for the first time: an implementation of the long-sought recovery of phase information from small-angle scattering measurements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗