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Massively parallel and universal approximation of nonlinear functions using diffractive processors

Nonlinear computation is essential for a wide range of information processing tasks, yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here, we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework, the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g., via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions, also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks, including the sigmoid, tanh, ReLU (rectified linear unit), and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore, we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation, paving the way for new capabilities in analog optical computing based on linear materials.

Rahman, Md Sadman Sakib [University of California,↗

Customizable wave tailoring nonlinear materials enabled by bilevel inverse design

Abstract Passive wave transformation via nonlinearity is ubiquitous in settings from acoustics to optics and electromagnetics. It is well known that different nonlinearities yield different effects on propagating signals, which raises the question of “what precise nonlinearity is the best for a given wave tailoring application?” In this work, considering a one-dimensional spring-mass chain connected by polynomial springs (a variant of the Fermi-Pasta-Ulam-Tsingou system), we introduce a bilevel inverse design method which couples the shape optimization of structures for tailored constitutive responses with reduced-order nonlinear dynamical inverse design. We apply it to two qualitatively distinct problems—minimization of peak transmitted kinetic energy from impact, and pulse shape transformation—demonstrating our method’s breadth of applicability. For the impact problem, we obtain two fundamental insights. First, small differences in nonlinearity can drastically change the dynamic response of the system, from severely under- to outperforming a comparative linear system. Second, the oft-used strategy of impact mitigation via “energy locking” bistability can be significantly outperformed by our optimal nonlinearity. We validate this case with impact experiments and find excellent agreement. This study establishes a framework for broader passive nonlinear mechanical wave tailoring material design, with applications to computing, signal processing, shock mitigation, and autonomous materials.

Science & Technology - Other Topics↗

Determining the tilt of the Raman laser beam using an optical method for atom gravimeters

The tilt of a Raman laser beam is a major systematic error in precision gravity measurement using atom interferometry. The conventional approach to evaluating this tilt error involves modulating the direction of the Raman laser beam and conducting time-consuming gravity measurements to identify the error minimum. In this work, we demonstrate a method to expediently determine the tilt of the Raman laser beam by transforming the tilt angle measurement into characterization of parallelism, which integrates the optical method of aligning the laser direction, commonly used in freely falling corner-cube gravimeters, into an atom gravimeter. A position-sensing detector (PSD) is utilized to quantitatively characterize the parallelism between the test beam and the reference beam, thus measuring the tilt precisely and rapidly. After carefully positioning the PSD and calibrating the relationship between the distance measured by the PSD and the tilt angle measured by the tiltmeter, we achieved a statistical uncertainty of less than 30 µrad in the tilt measurement. Furthermore, we compared the results obtained through this optical method with those from the conventional tilt modulation method for gravity measurement. The comparison validates that our optical method can achieve tilt determination with an accuracy level of better than 200 µrad, corresponding to a systematic error of 20 µGal in g measurement. This work has practical implications for real-world applications of atom gravimeters.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Defect Engineering in Large‐Scale CVD‐Grown Hexagonal Boron Nitride: Formation, Spectroscopy, and Spin Relaxation Dynamics

Recently, numerous techniques have been reported for generating optically active defects in exfoliated hexagonal boron nitride (hBN), which hold transformative potential for quantum photonic devices. However, achieving on-demand generation of desirable defect types in scalable hBN films remains a significant challenge. Here, it is demonstrated that formation of negative boron vacancy defects, V B − , in suspended, large-area CVD-grown hBN is strongly dependent on the type of bombarding particles (ions, neutrons, and electrons) and irradiation conditions. In contrast to suspended hBN, defect formation in substrate-supported hBN is more complex due to the uncontrollable generation of secondary particles from the substrate, and the outcome strongly depends on the thickness of the hBN. Different defect types are identified by correlating spectroscopic and optically detected magnetic resonance features, distinguishing boron vacancies (formed by light ions and neutrons and emitting at 800 nm) from other optically active defects emitting at 650 nm assigned to anti-site nitrogen vacancy (N B V N ) and reveal the presence of additional “dark” paramagnetic defects that influence spin-lattice relaxation time (T 1 ) and zero-field splitting parameters, all of which strongly depend on the defect density. These results underscore the potential for precisely engineered defect formation in large-scale CVD-grown hBN, paving the way for the scalable fabrication of quantum photonic devices.

CVD↗

Phase transitions of β-ZnTe(en) 0.5 under hydrostatic pressure

Organic–inorganic hybrid semiconductors have enhanced and distinctive material properties. β-ZnTe(en) 0.5 , which consists of alternating layers of two-monolayer-thick zinc telluride (ZnTe) and ethylenediamine (en), exhibits high crystallinity, stability, and tunable optical properties. Using x-ray diffraction (XRD) and Fourier transform infrared spectroscopy, this study investigated the structural response of β-ZnTe(en) 0.5 to applied hydrostatic pressure. Pressure-induced phase transitions were observed at 2.1 and 3.3 GPa. Shifts in the XRD peaks indicate substantial anisotropy in the pressure response, with the layer stacking direction ( b axis) exhibiting high compressibility. The a and b lattice parameters showed −0.55% strain/GPa and −2.26% strain/GPa, respectively, contradicting theoretical calculations that predicted a more isotropic response. IR spectroscopy revealed abrupt changes in NH 2 and CH 2 vibrational modes corresponding to the phase transitions.

Chemical compounds↗

Generative Physics-Informed Neural Network Solving Multi-Scale and Multi-Phase Plasma Chemical Flow Field

Low-temperature plasmas (LTPs) are non-equilibrium systems with near-room-temperature gas and highly energetic electrons. This makes them ideal for delicate applications in biomedicine and semiconductor manufacturing, enabling processes like wound healing, sterilization, etching, and plasma-enhanced chemical vapor deposition without thermal damage. However, LTPs involve complex chemistries, with hundreds of species and thousands of reactions, complicating their diagnosis, prediction, and control. Conventional diagnostics, such as Fourier-transform infrared spectroscopy (FTIR), laser-induced fluorescence (LIF), and optical emission spectroscopy (OES), offer limited species detection, while mass spectrometry (MS) struggles with low-sensitivity species. Additionally, LTP simulations face multi-scale challenges, as macroscopic fluid dynamics and microscopic particle collisions operate on vastly different timescales. To address these issues, we developed an artificial intelligence (AI) based diagnostic system: a generative physics-informed neural network (PINN-Gen) that can predict spatially resolved species concentrations and temperatures in LTPs by integrating experimental data from planar LIF with microscopic plasma chemical kinetics and macroscopic fluid mechanics, including plasma-liquid interactions at the interface between two phases. PINN-Gen solves no equations but checks the errors of physical laws by substituting the output from neural network, and the comparison with the experimental results. Thus, it naturally avoids the multi-scale difficulty of numerical simulations and predicts the results of conventionally unsolvable multi-scale and multi-phase problems. The real-time prediction will be robust due to the physical information used in the training of such a neural network, and only very limited input of condition required due to its generative feature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fast Fourier transform evaluation of the Fresnel integral for gravitational-wave lensing

Gravitational waves (GWs) exhibit wave-optics effects when their wavelength is comparable to the scale of the gravitational lens. This may occur in lensing from galactic subhalos in GWs emitted by binary black-hole mergers and is gaining interest as a novel probe of dark matter. Predictions for observables in these cases ultimately rely on evaluating a Fresnel integral that quantifies the effect of lensing on the amplitude of a GW at a given frequency. However, numerical evaluation of this Fresnel integral is tricky, and several algorithms and publicly available codes that implement it have been developed. Here, we show that the dependence of this integral on the lens position can be written as a two-dimensional Fourier transform. Modern FFT techniques then enable rapid evaluation at all-sky positions simultaneously for general lenses without symmetry. Vectorization of FFT routines allows for derivatives with respect to model parameters to be obtained with only incremental additional computational cost. If the lens is axisymmetric, further speedups can be achieved with recently developed techniques for nonuniform fast Hankel transforms. To demonstrate, we make available Fresnel Integral Optimization with Nonuniform Transforms (fiona), an efficient and accurate code that is significantly faster than current methods for dense source grids, reaching 2 orders of magnitude speedups for ∼10 6 GW-emitting points. As part of FIONA , we developed code that provides vectorized nonuniform fast Hankel transforms that may have other uses (e.g., calculation of cosmological two-point correlation functions) beyond those considered here.

dark matter↗

Intercalation-Induced Topotactic Phase Transformation of Tungsten Disulfide Crystals

Recent research has demonstrated the potential for topological superconductivity, anisotropic Majorana bound states, optical nonlinearity, and enhanced electrochemical activity for transition metal dichalcogenides (TMDs) with a 2M structure. These unique TMD compounds exhibit metastability and, upon heating, undergo a transition to the thermodynamically stable 2H phase. The 2M phase is commonly made at high temperatures using traditional solid-state methods, and this metastability further complicates the growth of large 2M WS 2 crystals. Herein, a novel synthetic method was developed, focusing on a molten salt reaction to synthesize large 2H crystals and then inducing transformation to the 2M phase through intercalation and thermal treatment. The 2H crystals were intercalated via a room-temperature sodium naphthalenide solution, producing a previously unreported Na-intercalated 2H WS 2 phase. Thermal heating was required to facilitate the phase transition to the intercalated 2M crystal structure. This phase transition was studied by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), selected area electron diffraction (SAED), electron dispersive X-ray spectroscopy (EDS), and Raman spectroscopy, which confirmed the synthesis of the intercalated 2M phase. Upon deintercalation, crystal and powder samples showed superconductivity with a T c of 8.6–8.7 K, similar to previously reported values. The generality of this process was further demonstrated using alkali metal triethyl borohydride to intercalate 2H WS 2 and produced the desired 2M phase. This novel synthetic method has broad implications for discovering metastable phases in other TMD families and layered materials. Furthermore, separation of the intercalation and phase transition also has the potential to allow for large-scale synthesis of this technologically important phase with greater control over each step of the reaction.

36 MATERIALS SCIENCE↗

Design of a broadband, high-power, off-axis spiral polarization reflector

Spirally polarized beams are known to produce a strong longitudinal field under high numerical aperture focusing. Here, we report on the design of a reflective optical element with an off-axis geometry that is capable of transforming a uniformly polarized beam into a predominantly spirally polarized beam. By utilizing the retardance present in Fresnel reflection, our device can operate over a broad range of wavelengths. The output polarization and intensity structure of a beam passing through the reflector are calculated using polarization and scalar ray tracing. Vector diffraction is used to calculate the polarization and intensity structure under $f/0.656$ focusing. The off-axis reflective design is well-suited for high-power laser applications and could enable current and future laser-based particle accelerators to achieve strong longitudinal fields at focus.

Black, A. Nicholas [Univ. of Rochester, NY (United↗

Broadband rapid-scanning phase-modulated Fourier transform electronic spectroscopy

We present a phase-modulated approach for ultrabroadband Fourier transform electronic spectroscopy. To overcome the bandwidth limitations and spatial chirp introduced by acousto-optic modulators (AOMs), pulses from a 1 µm laser are modulated using AOMs prior to continuum generation. This phase modulation is transferred to the continuum generated in a yttrium aluminum garnet crystal. Separately generated phase-modulated continua in two arms of a Mach-Zehnder interferometer interfere with the difference of their modulation frequencies, enabling physical under-sampling of the signal and the suppression of low-frequency noise. By interferometrically tracking the relative time delay of the continua, we perform continuous, rapid-scanning Fourier transform electronic spectroscopy with a high signal-to-noise ratio and spectral resolution. As proof of principle, we measure the linear absorption and fluorescence excitation spectra of a laser dye and various biological samples.

Javed, Ariba↗

Inverse design for waveguide dispersion with a differentiable mode solver

Inverse design of optical components based on adjoint sensitivity analysis has the potential to address the most challenging photonic engineering problems. However, existing inverse design tools based on finite-difference-time-domain (FDTD) models are poorly suited for optimizing waveguide modes for adiabatic transformation or perturbative coupling, which lies at the heart of many important photonic devices. Among these, dispersion engineering of optical waveguides is especially challenging in ultrafast and nonlinear optical applications involving broad optical bandwidths and frequency-dependent anisotropic dielectric material response. In this work, we develop gradient back-propagation through a general-purpose electromagnetic eigenmode solver and use it to demonstrate waveguide dispersion optimization for second harmonic generation with maximized phase-matching bandwidth. This optimization of three design parameters converges in eight steps, reducing the computational cost of optimization by ∼100x compared to exhaustive search and identifying new designs for broadband optical frequency doubling of laser sources in the 1.3–1.4 µm wavelength range. Furthermore, we demonstrate that the computational cost of gradient back-propagation is independent of the number of parameters, as required for optimization of complex geometries. This technique enables practical inverse design for a broad range of previously intractable photonic devices.

Gray, Dodd (ORCID:000000030469599X)↗

Reduction of Iron (III) Oxide in Microwaves Toward Gasification Studies

The purpose of this study is to reduce hematite (Fe2O3) using hydrogen (H2), carbon monoxide (CO), and methane (CH4) gases using microwave irradiation. Conventional temperature programmed reduction of iron phase transformation under H2, CO, and CH4 agree with the literature. Furthermore, the activation energy for the iron phase transformation in a conventional reactor was in the order of H2>CO>CH4, suggesting that CH4 was the best reductant to initiate the reduction at a much lower temperature than CO, and CO was significantly better than H2 atmosphere. Due to the uneven temperature distribution, the apparent activation energy of microwave reduction under H2 was approximately 1/4th when compared to the conventional reduction in H2. X-ray diffraction (XRD) analysis showed a mixed oxide phase in microwave reduction as opposed to the clear phase transformation in conventional studies. To combat the temperature measurement issues in microwave studies, fiber optic sensors and Forward Looking InfraRed (FLIR) sensors were used to acquire the actual temperature distribution in the catalyst bed. Therefore, a reasonably accurate activation energy estimation was achieved in the catalyst bed. Combining these with the characterization and quantification of the different iron phases in microwave reduction will provide a blueprint for future microwave-assisted gasification studies.

Aireddy, Divakar Reddy↗

Applying deep learning methods to develop new models of molecular charge transfer, nonadiabatic dynamics, and nonlinear spectroscopy in the condensed phase

Photon- and field-induced charge transfer has central importance in the generation and storage of electricity, the novel properties of materials, photo-induced catalysis, and electro-optic activity (e.g., photovoltaic cells, fuel cells, and organic chromophores for use in optical fibers and light-emission diodes). These non-equilibrium electronic and chemical transformations are probed by ultrafast, nonlinear spectroscopies. Accurate simulations play a crucial role in our ability to understand, optimize, and control these transformations. This project applies modern deep learning and machine learning (ML) methods to dramatically improve models of electronic dynamics, electronic-nuclear dynamics, and spectroscopic measurements for improved simulations of chemistry in complex environments, far from equilibrium phenomena, and processes in extreme environments, such as materials exposed to strong or resonant fields. This project develops accurate neural net models that go beyond predictive capability to also provide new insight into the fundamental physics underlying electron and nuclear dynamics. To achieve its objectives, this project explores and develops customized versions of high-capacity deep learning algorithms/models. These techniques are developed with an emphasis on fundamental chemical insight, not just predictive accuracy, to assist the development of the next generation of quantum simulation methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Collimated phase measuring deflectometry II: Re-design of the optical layout for high-curvature surfaces

Collimated phase measuring deflectometry (CPMD) is an optical metrology technique developed to improve upon traditional phase measuring deflectometry (PMD). CPMD utilizes telecentric imaging and collimated structured light illumination to eliminate the height-slope ambiguity present in traditional PMD measurements. After the publication of the first CPMD paper, efforts began to optimize the optical layout of the CPMD system. The first proposed change, and the one detailed in this work, was to move the Fourier transform (FT) lens closer to the surface under test (SUT). Moving the FT lens closer to the SUT meant that for a given FT lens diameter, a larger range of surface slopes on the SUT could be measured. This change to the optical layout was not trivial and introduced at least two concerns that had to be addressed: telecentricity in the imaging path and possible ghost reflections from the re-located FT lens. Here, in this work, we examine how these concerns were addressed and present results showing that the revised optical layout is capable of measurement results at least as good as the original CPMD optical layout. We also demonstrate the increased slope measuring range of the revised optical layout.

47 OTHER INSTRUMENTATION↗

Carbon doping in GeTe drives differences in local structure and properties

Advances in low-power, energy-efficient information storage and computing require understanding and controlling the atomic and nanoscale structures of functional materials, such as phase-change materials. Phase-change memory technology enables nonvolatile, low-power memory in devices by storing information through reversible changes in a phase-change material's atomic structure (i.e., transformations between amorphous and crystalline phases) that have corresponding changes in properties, including electronic resistivity and optical reflectivity. Here, we apply complementary X-ray absorption spectroscopy and X-ray pair distribution function analyses to experimentally identify the local- and medium-range atomic structure differences of GeTe and C-doped GeTe thin films. Upon controlled heating, composition- and temperature-dependent atomic structure evolution in GeTe and C-doped GeTe films shows differences in bonding behavior and local structure that directly influence crystallization onset temperature. We find that the introduction of C interrupts Ge–Ge bonds in amorphous GeTe, altering the as-deposited structure to be more similar to the distorted rocksalt structure of crystalline α–GeTe. The change alters the response of the amorphous atomic structure to heating and also lowers the crystallization onset temperature, from 230 °C in GeTe to 220 °C in the C-doped film. The combined insights from both X-ray techniques provide understanding of structural transformations that enables the development and optimization of next-generation memory and computing materials.

36 MATERIALS SCIENCE↗

Pb:Sn Ratio-Driven Polytypism and Band Modulation in Photoresponsive Hexagonal Perovskitoids

Three-dimensional (3D) perovskites of the formula AMX 3 are known for their excellent optoelectronic properties, but their design is limited by the narrow range of A-site cations that can template the 3D corner-sharing structure, and many of the viable options have already been explored. These materials also face structural instability under environmental conditions. In contrast, 3D hexagonal perovskitoids, with the same chemical formula, may offer enhanced stability and richer structural diversity through a range of corner- and face-sharing octahedral configuration options, providing greater opportunities for structural design; however, challenges such as synthesis complexity and wide band gaps have hindered optoelectronic performance achieved to date. Herein, we synthesized a structural homologous series of mixed-metal hexagonal perovskitoids with the formula APb 1-x Sn x I 3 (x = 0, 0.25, 0.50, 0.75, 1; A = ethylammonium, guanidinium) and identified three polytypes (9R, 12R, 6H) using single-crystal X-ray diffraction (SCXRD). These structures exhibited increasing corner-sharing connectivity with higher Sn content, revealing a previously unobserved relationship between metal composition and structural evolution in perovskitoid materials. The incorporation of Sn reduced the band gap (tunable from 2.51 eV to 1.87 eV) and drove structural transformations, a trend seen also in density functional theory (DFT) calculations, which suggest a thermodynamic preference for Pb at face-sharing sites and Sn at corner-sharing sites. DFT band structure calculations and optical spectroscopy also reveal an anomalous behavior in these materials, which we term polytypic band modulation. This phenomenon combines conventional band bowing with the structural transformations that occur as Sn content increases, as observed in the band gap and in photoluminescence spectra. Photodiodes fabricated from thin films of these materials exhibited stable and pronounced photoresponses across various light intensities over time. Furthermore, the combination of templating 3D perovskitoids with multiple cations and alloying Pb and Sn, suggests a vastly underexplored phase space that offers new parameters to tune perovskitoids.

Cations↗

Quantitative Infrared-to-Terahertz Nanospectroscopy of Semiconductors

Semiconductor technology now employs few-nanometer features, necessitating tools probing electronic properties on the same length scale. While the concentration of free charge carriers is routinely measured, the scattering rate remains challenging to access at the nanoscale. Here, we present ultrabroadband (5–50 THz) synchrotron infrared nanospectroscopy as a quantitative metrology tool for semiconductors. This technique can determine both the charge carrier concentration and scattering rate with percent-level accuracy, and it is inherently capable of ∼10 nm spatial resolution. We study silicon with different doping levels and confirm the method’s accuracy by statistical analysis and comparison with established far-field infrared spectroscopy. Near-field measurements systematically reveal charge-carrier concentrations ∼30% lower than far-field values, consistent with increased surface sensitivity and surface depletion. Our work establishes synchrotron infrared nanospectroscopy as a precise tool for quantitative nanoscale semiconductor characterization and paves the way toward all-optical characterization of surface depletion effects.

36 MATERIALS SCIENCE↗

Metal ion dopant-induced famatinite to chalcostibite phase transformation of copper antimony sulphide colloidal nanostructures: effect on photophysical and pseudocapacitance properties

Here, the strategic doping of transition metal ions into copper antimony sulphide (CAS) semiconducting nanostructures can significantly influence their photophysical and pseudocapacitive properties, for which there are few reports and therefore is the focus of this study. Accordingly, highly crystalline metal ion (Mn 2+ , Fe 2+ , Co 2+ , Ni 2+ and Zn 2+ ) doped off-stoichiometric copper rich/poor, antimony-rich/poor, and sulphur-poor CAS nanostructures (10–23 nm) were grown via colloidal (hot-injection) synthesis using metal diethyldithiocarbamate precursors. Importantly, metal ion doping significantly influences the structure and composition of the off-stoichiometric CAS nanostructures. Data from powder X-ray diffraction, Raman spectroscopy, high-resolution scanning/transmission electron microscopy, and energy dispersive X-ray spectroscopy confirm that the heavier metal ion dopants induce a novel phase transformation from famatinite (fCAS) to chalcostibite (cCAS) nanostructures. The influence of the metal ion dopants is also observed in the optical properties of as-synthesized nanostructures. This involves blue-shifted ultraviolet-visible absorption, reduced Urbach tailing, and tunable bandgaps between 2.17 and 2.38 eV. Also, the doped nanostructures display broad visible-near infrared photoluminescence via a triple radiative pathway with relatively short decay lifetimes between 0.2 and 6.1 ns. This is mediated by electronic transitions involving intrinsic (copper/antimony/sulphur interstitial) and extrinsic (metal ion interstitial) defect states. Additionally, electrodes prepared from Mn 2+ -doped fCAS nanostructures show enhanced pseudocapacitance via Na+ surface adsorption and intercalation relative to undoped fCAS electrodes, while Zn 2+ -doped cCAS electrodes exhibit pseudocapacitance via a combination of Na+ surface adsorption, intercalation, and redox reactions. These electrodes exhibit reduced charge transfer resistance, improved electronic conductivity and notably enhanced specific capacitance (∼222 F g −1 ), and charge transport, as measured in 1 M Na 2 SO 4 electrolyte via cyclic voltammetry and electrochemical impedance spectroscopy. To this end, the discovery of the metal ion-induced phase transformation presents a new avenue for optimizing the functional properties of fCAS and cCAS nanostructures, highlighting the critical role of metal ion-related defects in controlling the optical and electrochemical properties, towards potential solar absorption and energy storage applications.

25 ENERGY STORAGE↗