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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Correlated Displacement of Dynamic Elastic Dipoles Produces Nonclassical Electrostriction in Zr-Doped Ceria

By combining experimental data with density functional theory-based ab initio molecular dynamics modeling, this work provides evidence that nonclassical electrostriction in isovalent Zr-doped ceria is due to the correlated anharmonic motion of dynamic elastic dipoles associated with multiple [ZrO 8 ]-local bonding units with a high Zr concentration (Zr 0.1 Ce 0.9 O 2 ). Introduction of 0.5 mol % trivalent or divalent codopants (Sc, Yb, La, or Ca) reduces the longitudinal electrostriction strain coefficient by more than a factor of 10, produces a 3-fold decrease in the relative dielectric permittivity, and increases the elastic modulus. Since these changes depend neither on the radius nor on the valency of the codopant, we conclude that the responsible species are charge-compensating oxygen vacancies (VO). For trivalent dopants (Do 0.005 Zr 0.1 Ce 0.895 O 1.9975 ), oxygen vacancies are present at a concentration ratio 1:40 with respect to Zr, giving, for random distribution, a characteristic interaction distance of ≤2.3 unit cells (1.2 nm). Oxygen vacancies participate in [ZrO 7 -V O ] local bonding units, disrupting the correlated dynamic displacements of the connected [ZrO 8 ]-local bonding units. Finally, such correlated motion of dynamic elastic dipoles may also explain the exponential increase in the longitudinal electrostriction strain coefficient with an increase in Zr concentration to <0.2 mole fraction and must be taken into account for further development of nonclassical electrostrictors based on Zr-doped ceria.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Vacancy-Driven Disorder and Elevated Dielectric Response in the Pyrochlore Pb 1.5 Nb 2 O 6.5

Lone pair-driven distortions are a hallmark of many technologically important lead (Pb)-based materials. Here, the role of Pb 2+ in polar perovskites is well understood and easily manipulated for applications in piezo- and ferroelectricity, but the control of ordered lone pair behavior in Pb-based pyrochlores is less clear. Crystallographically and geometrically more complex than the perovskite structure, the pyrochlore structure is prone to geometric frustration of local dipoles due to a triangular arrangement of cations on a diamond lattice. The role of vacancies on the O' site of the pyrochlore network has been implicated as an important driver for the expression and correlation of stereochemically active lone pairs in pyrochlores such as Pb 2 Ru 2 O 6.5 and Pb 2 Sn 2 O 6 . In this work we report on the structural, dielectric, and heat capacity behavior of the cation- and anion-deficient pyrochlore Pb 1.5 Nb 2 O 6.5 upon cooling. We find that local distortions are present at all temperatures that can be described by cristobalite-type cation ordering, and this ordering persists to longer length scales upon cooling. From a crystallographic perspective, the material remains disordered and does not undergo an observable phase transition. In combination with density function calculations, we propose that the stereochemical activity of the Pb 2+ lone pairs is driven by proximity to O' vacancies, and the crystallographic site disorder of the O' vacancies prohibits long range correlation of lone pair-driven distortions. This in turn prevents a low-temperature phase transition and results in an elevated dielectric permittivity across a broad temperature range.

36 MATERIALS SCIENCE↗
DOE OSTI2024

CH 3 Radical Generation in Microplasmas for Up-Conversion of Methane

The conversion of methane, CH 4 , into higher value chemicals using low temperature plasmas is challenged by both improving efficiency and selectivity. One path towards selectivity is capturing plasma produced methyl radicals, CH 3 , in a solvent for aqueous processing. Due to the rapid reactions of methyl radicals in the gas phase, the transport distance from production of the CH 3 to its solvation should be short, which then motivates the use of microplasmas. The generation of CH 3 in Ar/CH 4 /H 2 O plasmas produced in nanosecond pulsed dielectric barrier discharge microplasmas is discussed using results from a computational investigation. The microplasma is sustained in the channel of a microfluidic chip in which the solvent flows along one wall or in droplets. CH 3 is primarily produced by electron-impact of and dissociative excitation transfer to CH 4 , as well as CH 2 reacting with CH 4 . CH 3 is rapidly consumed to form C 2 H 6 which, in spite of being subject to these same dissociative processes, accumulates over time, as do other stable products including C 3 H 8 and CH 3 OH. The gas mixture and electrical properties were varied to assess their effects on CH 3 production. CH 3 production is largest with 5% CH 4 in the Ar/CH 4 /H 2 O mixture due to an optimal balance of electron-impact dissociation, which increases with CH 4 percentage, and dissociative excitation transfer and CH 2 reacting with CH 4 , which decrease with CH 4 percentage. Design parameters of the microchannels were also investigated. Increasing the permittivity of the dielectrics in contact with the plasma increased the ionization wave intensity which increased CH 3 production. Increased energy deposition per pulse generally increased CH 3 production as does lengthening pulse length up to a certain point. The arrangement of the solvent flow in the microchannel can also affect the CH 3 density and fluence to the solvent. The fluence of CH 3 to the liquid solvent is increased if the liquid is immersed in the plasma as a droplet or is a layer on the wall where the ionization wave terminates. The solvation dynamics of CH 3 with varying numbers of droplets was also examined. Here, the maximum density of solvated methyl radicals CH 3aq occurs with a large number of droplets in the plasma. However, the solvated CH 3aq density can rapidly decrease due to desolvation, emphasizing the need to quickly react the solvated species in the solvent.

03 NATURAL GAS↗
DOE OSTI2020

Substrate-Dependent Exciton Diffusion and Annihilation in Chemically Treated MoS 2 and WS 2

Atomically thin semiconductors such as monolayer MoS 2 and WS 2 exhibit nonlinear exciton–exciton annihilation at notably low excitation densities (below ~10 excitons/μm 2 in exfoliated MoS 2 ). In this work, we show that the density threshold at which annihilation occurs can be tuned by changing the underlying substrate. When the supporting substrate is changed from SiO 2 to Al 2 O 3 or SrTiO 3 , the rate constant for second-order exciton–exciton annihilation, k XX [cm 2 /s], is reduced by 1 or 2 orders of magnitude, respectively. Using transient photoluminescence microscopy, we measure the effective room-temperature exciton diffusion coefficient in bis(trifluoromethane)sulfonimide-treated MoS 2 to be in the range D = 0.03–0.06 cm 2 /s, corresponding to a diffusion length of L D = 350 nm for an exciton lifetime of τ = 18 ns, which does not depend strongly on the substrate. We discuss possible mechanisms for the observed behavior, including substrate permittivity, long-range exciton–exciton or exciton–charge interactions, defect-mediated Auger recombination, and spatially inhomogeneous exciton populations arising from substrate-induced disorder. Exciton annihilation limits the overall efficiency of 2D semiconductor devices operating at high exciton densities; the ability to tune these interactions via the underlying substrate is an important step toward more efficient optoelectronic technologies featuring atomically thin materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Role of Solvent Rearrangement on Mg2+ Solvation Structures in Dimethoxyethane Solutions Using Multimodal NMR Analysis

One of the main impediments faced for predicting important emergent properties of a multivalent electrolyte (such as conductivity and electrochemical stability) is the lack of quantitative analysis of ion-ion and ion-solvent interactions, which manifest in solvation structures and dynamics. In particular, the role of ion-solvent interactions is still unclear in cases where the strong electric field from multivalent cations can influence structural evolution of lower permittivity organic solvent molecules on solvation structure. These influences are commonly refered to as electrostriction pheonmena. Using quantitative 1H, 19F, 17O, and 25Mg NMR together with 19F nuclear spin relaxation and diffusion measurments, we find an unusual correlation between ion concentration and solvation structure of Mg(TFSI)2 salt in dimethoxyethane (DME) solution. The domiant solvation structure evolves from contact ion pairs (i.e. [Mg(TFSI)(DME)1-2]+) to fully solvated clusters (i.e. [Mg(DME)3]2+) as salt concentration increases or as temperature decreases. This transition is coupled to a phase separation, which we study here between 0.06 M and 0.36 M. Subsequent analysis is based on an explanation of the electrostriction phenomena and the competion between solvent molecules and TFSI anions for cation coordination.

Chen, Ying↗
DOE OSTI2024

Colloidal Stability of PFSA-Ionomer Dispersions Part II: Determination of Suspension pH Using Single-Ion Potential Energies

Perfluorosulfonic acid (PFSA) ionomers serve a vital role in the performance and stability of fuel-cell catalyst layers. These properties, in turn, depend on the colloidal processing of precursor inks. Here, to understand the colloidal structure of fuel-cell catalyst layers, we explore the aggregation of PFSA ionomers dissolved in water/alcohol solutions and relate the predicted aggregation to experimental measurements of solution pH. Not all side chains contribute to measured pH because of burying inside particle aggregates. To account for the measured degree of dissociation, a new description is developed for how PFSA aggregates interact with each other. The developed single-counterion electrostatic repulsive pair potential from Part I is incorporated into the Smoluchowski collision-based kinetics of interacting aggregates with buried side chains. We demonstrate that the surrounding solvent mixture affects the degree of aggregation as well as the pH of the system primarily through the solution dielectric permittivity, which drives the strength of the interparticle repulsive energies. Successful pH prediction of Nafion ionomer dispersions in water/n-propanol solutions validates the numerical calculations. Nafion-dispersion pH measurements serve as a surrogate for Nafion particle-size distributions. The model and framework can be leveraged to explore different ink formulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Comparing Experimental Phase Behavior of Ion-Doped Block Copolymers with Theoretical Predictions Based on Selective Ion Solvation

The effects of salt-doping on the morphological behavior of block copolymers are well established but remain poorly understood, partially because of the challenge of resolving electrostatics in a heterogeneous medium with low average permittivity. By employing a recently developed field theory, we analyze the phase behavior of polystyrene-b-poly(ethylene oxide) (SEO) copolymers doped with lithium bis(trifluoromethanesulfonyl)imide salts (LiTFSI). Using a single fitting parameter, the ionic solvation radius, we obtain qualitative agreement between our theory and experimental data over a range of polymer molecular weights and copolymer compositions. Such agreement supports and highlights the need of solvation free energy to accurately describe the self-assembly of ion-doped block copolymers and demonstrates that experimentally observed dependence on molecular weight, not present in neutral block copolymers, can be rationalized by solvation effects. Overall, morphological variations are stronger than those predicted by the leading, linear order theory but can be captured by the full model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Mechanisms Controlling the Energy Barrier for Ion Hopping in Polymer Electrolytes

Here, the present work studies the mechanisms controlling the energy barrier for ion hopping in conducting polymers. Polymer electrolytes usually show Arrhenius-like temperature dependence of the conductivity relaxation time (characteristic time of local ion rearrangements) at temperatures below their glass transition T g . However, our analysis reveals that the Arrhenius fit of this regime leads to unphysically small prefactors, τ 0 $\ll$ 10 –13 s. Imposing a value of 10 –13 s for this parameter renders the fairly unexpected result that the energy barrier for charge transport in these polymers has strong temperature dependence even below T g . Our study also reveals significant temperature variations of the dielectric permittivity and the instantaneous shear modulus in the glassy state of these polymers. Using the Anderson and Stuart model, we demonstrate that these variations provide strong justifications for the temperature variation of energy barrier for ion hopping. Most importantly, the proposed approach reveals that the energy barrier controlling ion hopping in polymer electrolytes is significantly (~30–40%) lower than that estimated using traditional Arrhenius fit. These new insights call for revisions of many earlier results based on apparent Arrhenius fits, and the newly proposed approach can provide more accurate guidance for the design of solid-state electrolytes with enhanced ionic conductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Visible Out-of-plane Polarized Luminescence and Electronic Resonance in Black Phosphorus

Black phosphorus (BP) is unique among layered materials because of its homonuclear lattice and strong structural anisotropy. While recent investigations on few-layer BP have extensively explored the in-plane (a, c) anisotropy, much less attention has been given to the out-of-plane direction (b). Here, the optical response from bulk BP is probed using polarization-resolved photoluminescence (PL), photoluminescence excitation (PLE), and resonant Raman scattering along the zigzag, out-of-plane, and armchair directions. An unexpected b-polarized luminescence emission is detected in the visible, far above the fundamental gap. PLE indicates that this emission is generated through b-polarized excitation at 2.3 eV. The same electronic resonance is observed in resonant Raman with the enhancement of the A g phonon modes scattering efficiency. These experimental results are fully consistent with DFT calculations of the permittivity tensor elements and demonstrate the remarkable extent to which the anisotropy influences the optical properties and carrier dynamics in black phosphorus.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Phase-Exchange-Driven Wake-Up and Fatigue in Ferroelectric Hafnium Zirconium Oxide Films

Ferroelectric hafnium zirconium oxide holds great promise for a broad spectrum of complementary metal–oxide–semiconductor (CMOS) compatible and scaled microelectronic applications, including memory, low-voltage transistors, and infrared sensors, among others. An outstanding challenge hindering the implementation of this material is polarization instability during field cycling. Herein, the nanoscale phenomena contributing to both polarization fatigue and wake-up are reported. Using synchrotron X-ray diffraction, the conversion of non-polar tetragonal and polar orthorhombic phases to a non-polar monoclinic phase while field cycling devices comprising noble metal contacts is observed. This phase exchange accompanies a diminishing ferroelectric remanent polarization and provides device-scale crystallographic evidence of phase exchange leading to ferroelectric fatigue in these structures. A reduction in the full width at half-maximum of the superimposed tetragonal (101) and orthorhombic (111) diffraction reflections is observed to accompany wake-up in structures comprising tantalum nitride and tungsten electrodes. Combined with polarization and relative permittivity measurements, the observed peak narrowing and a shift in position to lower angles is attributed, in part, to a phase exchange of the non-polar tetragonal to the polar orthorhombic phase during wake-up. These results provide insight into the role of electrodes in the performance of hafnium oxide-based ferroelectrics and mechanisms driving wake-up and fatigue, and demonstrate a non-destructive means to characterize the phase changes accompanying polarization instabilities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Achieving Flat-on Primary Crystals by Nanoconfined Crystallization in High-Temperature Polycarbonate/Poly(vinylidene fluoride) Multilayer Films and Its Effect on Dielectric Insulation

To meet the stringent requirements of next-generation film capacitors for power electronics, multilayer films (MLFs) are fabricated with the advantage of achieving high temperature rating, high energy density, and reasonably low loss simultaneously. In this study, a high permittivity polar polymer, poly(vinylidene fluoride) (PVDF), is multilayered with a linear, low loss dielectric polymer such as high-temperature polycarbonate (HTPC). However, the dielectric loss of these MLFs was still high as compared with current state-of-the-art biaxially oriented polypropylene (BOPP) films. The goal of this work is to decrease the dielectric loss and enhance dielectric insulation by achieving flat-on primary PVDF crystals in MLFs via nanoconfined melt-recrystallization. Based on simultaneous small- and wide-angle X-ray scattering experiments, edge-on lamellar crystals were observed for all as-extruded MLFs, regardless of different PVDF layer thicknesses. However, after melting at 180 °C followed by recrystallization, flat-on primary crystals were successfully achieved when the PVDF layer thickness was below 39 nm. Above 78 nm for the PVDF layer, major edge-on primary crystals with minor flat-on secondary crystals were observed. Furthermore, from leakage current, breakdown, lifetime, and electric displacement-electric field loop studies, MLFs with the flat-on primary crystals exhibited reduced loss and enhanced dielectric insulation as compared to as-extruded MLFs and those with edge-on primary/flat-on secondary crystals. This was attributed to the effective blockage of charge carriers by the flat-on PVDF primary crystals and their reduced ferroelectric switching.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Revisiting the Role of Mobile Ion Size for the Activation Barrier of Charge Transport in Single Ion Conducting Polymers

The development of polymer electrolytes for energy storage and conversion technologies requires a fundamental understanding of the material parameters controlling the energy barriers for ion transport. In glassy polymers, these activation barriers are usually extracted by using Arrhenius procedures. However, our recent studies of single ion conducting polymers reveal that this traditional Arrhenius description provides anomalously small prefactors, an issue that is widely disregarded in the literature. Here, to address it, an alternative approach was introduced for extracting the effective activation barrier E by imposing a physically valid limit (∼10 –13 s) for the ion hopping attempt time. Two consequences of this recent approach are that in polymer electrolytes (i) E is significantly (∼30–40%) lower than the barrier estimated using traditional Arrhenius fits and (ii) E displays significant temperature dependence even in the glassy state. Under these circumstances, we are revisiting the role of ion size, glass transition temperature T g , and dielectric and elastic constants of the polymer matrix on the effective activation barriers for ion transport as extracted using the recently proposed approach and highlight the differences from the picture that previously emerged based on simplistic apparent Arrhenius analysis. To this end, we investigate cation transport in three families of single ion conducting trifluoromethane sulfonimide-based polyanions with varied T g . Our results indicate that E decreases with mobile cation size and is highly sensitive to changes in the dielectric permittivity of the matrix, even for large cations. These insights call for revisions of many earlier results based on apparent Arrhenius fits as the proposed approach can provide more accurate guidance for the design of polymer electrolytes with enhanced ionic conductivity.

energy barrier↗
DOE OSTI2020

Quantifying Single-Ion Transport in Percolated Ionic Aggregates of Polymer Melts

Single-ion conducting polymers such as ionomers are promising battery electrolyte materials, but it is critical to understand how rates and mechanisms of free cation transport depend on the nanoscale aggregation of cations and polymer-bound anions. We perform coarse-grained molecular dynamics simulations of ionomer melts to understand cation mobility as a function of polymer architecture, background relative permittivity, and corresponding ionic aggregate morphology. In systems exhibiting percolated ionic aggregates, cations diffuse via stepping motions along the ionic aggregates. These diffusivities can be quantitatively predicted by calculating the lifetimes of continuous association between oppositely charged ions, which equal the time scales of the stepping (diffusive) motions. In contrast, predicting cation diffusivity for systems with isolated ionic aggregates requires another time scale. Finally, our results suggest that to improve conductivity the Coulombic interaction strength should be strong enough to favor percolated aggregates but weak enough to facilitate ion dissociation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Large-Area, Highly Crystalline DNA-Assembled Metasurfaces Exhibiting Widely Tunable Epsilon-Near-Zero Behavior

Metasurfaces prepared via bottom-up nanoparticle assembly enable the deliberate manipulation of light in the optical regime, resulting in media with unprecedented optical responses. Here, we report a scalable method to grow highly crystalline 2D metasurfaces comprised of colloidal gold nanocubes, over macroscopic areas, using DNA-mediated assembly under equilibrium conditions. Using an effective medium description, we predict that these plasmonic metasurfaces behave as dielectric media with high refractive indices that can be dynamically tuned by tuning DNA length. Furthermore, we predict that when coupled with an underlying thin gold film, the real permittivity of these metasurfaces exhibits a crossover region between positive and negative values, known as the epsilon-near-zero (ENZ) condition, which can be tuned between 1.5 - 2.6 μm by changing DNA length. Optical characterization performed on the DNA-assembled metasurfaces reveals that the predicted optical properties agree well with measured response. Overall, we propose an efficient method for realizing large-area plasmonic metasurfaces that enable dynamic control over unique optical characteristics. High-index and ENZ metasurfaces operating in the telecommunications regime could have significant implications in high-speed optical computing, optical communications, optical imaging, and other areas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Remote-Contact Catalysis for Target-Diameter Semiconducting Carbon Nanotube Arrays

Electrostatic catalysis has been an exciting development in chemical synthesis (beyond enzymes catalysis1 ) in recent years, boosting reaction rates and selectively producing certain reaction products2 . Most of the studies to date have been focused on using external electric field (EEF) to rearrange the charge distribution in small molecule reactions such as Diels-Alder addition3 , carbene reaction4 , etc. However, in order for these EEFs to be effective, a field on the order of 1 V/nm (10 MV/cm) is required, and the direction of the EEF has to be aligned with the reaction axis5 . Such a large and oriented EEF will be challenging for large-scale implementation, or materials growth with multiple reaction axis or steps. Here, we demonstrate that the energy band at the tip of an individual single-walled carbon nanotube6 (SWCNT) can be spontaneously shifted in a high-permittivity growth environment, with its other end in contact with a low-work function electrode (e.g., hafnium carbide or titanium carbide7 ). By adjusting the Fermi level at a point where there is a substantial disparity in the density of states (DOS) between semiconducting (s-) and metallic (m-) SWCNTs8 , we achieve effective electrostatic catalysis for s-SWCNT growth assisted by a weak EEF perturbation (200V/cm). This approach enables the production of high-purity (99.92%) s-SWCNT horizontal arrays with narrow diameter distribution (0.95±0.04 nm), targeting the requirement of advanced SWCNT-based electronics for future computing9-11. These findings highlight the potential of electrostatic catalysis in precise materials growth, especially for s-SWCNTs, and pave the way for the development of advanced SWCNT-based electronics12.

Wang, Jiangtao↗
DOE OSTI2022

Surface plasmons induce topological transition in graphene/α-MoO3 heterostructures

Abstract Polaritons in hyperbolic van der Waals materials—where principal axes have permittivities of opposite signs—are light-matter modes with unique properties and promising applications. Isofrequency contours of hyperbolic polaritons may undergo topological transitions from open hyperbolas to closed ellipse-like curves, prompting an abrupt change in physical properties. Electronically-tunable topological transitions are especially desirable for future integrated technologies but have yet to be demonstrated. In this work, we present a doping-induced topological transition effected by plasmon-phonon hybridization in graphene/α-MoO 3 heterostructures. Scanning near-field optical microscopy was used to image hybrid polaritons in graphene/α-MoO 3 . We demonstrate the topological transition and characterize hybrid modes, which can be tuned from surface waves to bulk waveguide modes, traversing an exceptional point arising from the anisotropic plasmon-phonon coupling. Graphene/α-MoO 3 heterostructures offer the possibility to explore dynamical topological transitions and directional coupling that could inspire new nanophotonic and quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Johnson-noise-limited cancellation-free microwave impedance microscopy with monolithic silicon cantilever probes

Abstract Microwave impedance microscopy (MIM) is an emerging scanning probe technique for nanoscale complex permittivity mapping and has made significant impacts in diverse fields. To date, the most significant hurdles that limit its widespread use are the requirements of specialized microwave probes and high-precision cancellation circuits. Here, we show that forgoing both elements not only is feasible but also enhances performance. Using monolithic silicon cantilever probes and a cancellation-free architecture, we demonstrate Johnson-noise-limited, drift-free MIM operation with 15 nm spatial resolution, minimal topography crosstalk, and an unprecedented sensitivity of 0.26 zF/ √ Hz. We accomplish this by taking advantage of the high mechanical resonant frequency and spatial resolution of silicon probes, the inherent common-mode phase noise rejection of self-referenced homodyne detection, and the exceptional stability of the streamlined architecture. Our approach makes MIM drastically more accessible and paves the way for advanced operation modes as well as integration with complementary techniques.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Optical analogues to the equatorial Kerr–Newman black hole

Optical analogues to black holes allow the investigation of general relativity in a laboratory setting. Previous works have considered analogues to Schwarzschild black holes in an isotropic coordinate system; the major drawback is that required material properties diverge at the horizon. We present the dielectric permittivity and permeability tensors that exactly reproduce the equatorial Kerr–Newman metric, as well as the gradient-index material that reproduces equatorial Kerr–Newman null geodesics. Importantly, the radial profile of the scalar refractive index is finite along all trajectories except at the point of rotation reversal for counter-rotating geodesics. Construction of these analogues is feasible with available ordinary materials. A finite-difference frequency-domain solver of Maxwell’s equations is used to simulate light trajectories around a variety of Kerr–Newman black holes. For reasonably sized experimental systems, ray tracing confirms that null geodesics can be well-approximated in the lab, even when allowing for imperfect construction and experimental error.

79 ASTRONOMY AND ASTROPHYSICS↗