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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Naturally stable Sagnac–Michelson nonlinear interferometer

Interferometers measure a wide variety of dynamic processes by converting a phase change into an intensity change. Nonlinear interferometers, making use of nonlinear media in lieu of beamsplitters, promise substantial improvement in the quest to reach the ultimate sensitivity limits. Here we demonstrate a new nonlinear interferometer utilizing a single parametric amplifier for mode mixing conceptually, a nonlinear version of the conventional Michelson interferometer with its arms collapsed together. We observe up to 99.9% interference visibility and find evidence for noise reduction based on phase-sensitive gain. As a result, our configuration utilizes fewer components than previous demonstrations and requires no active stabilization, offering new capabilities for practical nonlinear interferometric-based sensors.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Gamma-radiation-induced negative nonlinear absorption in quartz glass

The effect of ionizing radiation on the nonlinear optical properties of materials needs to be considered for applications that employ high-power laser pulses in extreme radiation environments. The Heraeus Infrasil302 optical quartz glass was irradiated by gamma rays, and its nonlinear absorption was measured using the open-aperture Z-scan technique with nanosecond laser pulses. Irradiation results in a negative nonlinear absorption coefficient whose magnitude increases with irradiation dose. Nonlinear absorption coefficients of -0.78, -1.14, -1.29, and -1.88~ × ~10 -13 m/W are measured for gamma doses of 600 krad, 1.2 Mrad, 3.6 Mrad, and 10 Mrad, respectively. Thermal annealing restores the optical properties of quartz-glass to their unirradiated values. It is suggested that metallic impurities introduced by the manufacturing process have a role in inducing saturated absorption in irradiated quartz glass, which manifests as negative nonlinear absorption coefficient, and is demonstrated by comparing Infrasil302 quartz results to equivalent irradiated measurements for Spectrosil2000 quartz.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2024

Bayesian optimization of Fisher Information in nonlinear multiresonant quantum photonics gyroscopes

Abstract We propose an on-chip gyroscope based on nonlinear multiresonant optics in a thin film χ (2) resonator that combines high sensitivity, compact form factor, and low power consumption simultaneously. We theoretically analyze a novel holistic metric – Fisher Information capacity of a multiresonant nonlinear photonic cavity – to fully characterize the sensitivity of our gyroscope under fundamental quantum noise conditions. Leveraging Bayesian optimization techniques, we directly maximize the nonlinear multiresonant Fisher Information. Our holistic optimization approach orchestrates a harmonious convergence of multiple physical phenomena – including noise squeezing, nonlinear wave mixing, nonlinear critical coupling, and noninertial signals – all encapsulated within a single sensor-resonator, thereby significantly augmenting sensitivity. We show that ∼ 470 × $\sim 470{\times}$ improvement is possible over the shot-noise limited linear gyroscope with the same footprint, intrinsic quality factors, and power budget.

42 ENGINEERING↗
DOE OSTI2025

Nonlinearities in Magnetic Confinement, Ionospheric Physics, and Population Explosion Leading to Profile Resilience Нелінійності в магнетному утриманні, фізиці іоносфери та процесі демографічного вибуху, які приводять до стійкості профілю

Nonlinearities play an important role in many fields. In the field of thermonuclear fusion, they are involved in questions such as profile resilience and fluid closure. A nonlinear phenomenon common to both fusion and astrophysical planets is the generation of zonal flows. These flows play a significant role in determining the level of turbulence and fluid closure in fusion. The effects of resonance broadening and nonlinearities are investigated, specifically focusing on the case of nonlinear instability that has appeared in drift waves. Similarities and differences between our systems are discussed, with population explosion and the dynamics of nonlinear systems for drift waves by different states in profile resilience described with great precision. The aim of our study is to put our fluid model for drift waves in tokamaks within the wider framework of statistical physics principles. This reinforces our belief in the broad application of our drift wave model, which encompasses current tokamaks, ITER, and the fusion pilot plant.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Analysis of Nonlinear Dynamics by Square Matrix Method

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Data-driven Chaos Indicator for Nonlinear Dynamics and Applications on Storage Ring Lattice Design

A data-driven chaos indicator concept is introduced to characterize the degree of chaos for nonlinear dynamical systems. The indicator is represented by the prediction accuracy of surrogate models established purely from data. It provides a metric for the predictability of nonlinear motions in a given system. When using the indicator to implement a tune-scan for a quadratic Hénon map, the main resonances and their asymmetric stop-band widths can be identified. When applied to particle transportation in a storage ring, as particle motion becomes more chaotic, its surrogate model prediction accuracy decreases correspondingly. Therefore, the prediction accuracy, acting as a chaos indicator, can be used directly as the objective for nonlinear beam dynamics optimization. This method provides a different perspective on nonlinear beam dynamics and an efficient method for nonlinear lattice optimization. Applications in dynamic aperture optimization are demonstrated as real world examples.

43 PARTICLE ACCELERATORS↗
DOE OSTI2019

A Hamiltonian Surface-Shaping Approach for Control System Analysis and the Design of Nonlinear Wave Energy Converters

The dynamic model of Wave Energy Converters (WECs) may have nonlinearities due to several reasons such as a nonuniform buoy shape and/or nonlinear power takeoff units. This paper introduces the Hamiltonian Surface-Shaping (HSS) approach as a tool for the analysis and design of nonlinear control of WECs. The Hamiltonian represents the stored energy in the system and can be constructed as a function of the WEC’s system states, its position, and velocity. The Hamiltonian surface is defined by the energy storage, while the system trajectories are constrained to this surface and determined by the power flows of the applied non-conservative forces. The HSS approach presented in this paper can be used as a tool for the design of nonlinear control systems that are guaranteed to be stable. The optimality of the obtained solutions is not addressed in this paper. The case studies displayed here cover regular and irregular waves and demonstrate that a nonlinear control system can result in a multiple fold increase in the harvested energy.

16 TIDAL AND WAVE POWER↗
DOE OSTI2016

NONLINEAR REFLECTION PROCESS OF LINEARLY POLARIZED, BROADBAND ALFVÉN WAVES IN THE FAST SOLAR WIND

Using one-dimensional numerical simulations, we study the elementary process of Alfvén wave reflection in a uniform medium, including nonlinear effects. In the linear regime, Alfvén wave reflection is triggered only by the inhomogeneity of the medium, whereas in the nonlinear regime, it can occur via nonlinear wave–wave interactions. Such nonlinear reflection (backscattering) is typified by decay instability. In most studies of decay instabilities, the initial condition has been a circularly polarized Alfvén wave. In this study we consider a linearly polarized Alfvén wave, which drives density fluctuations by its magnetic pressure force. For generality, we also assume a broadband wave with a red-noise spectrum. In the data analysis, we decompose the fluctuations into characteristic variables using local eigenvectors, thus revealing the behaviors of the individual modes. Different from the circular-polarization case, we find that the wave steepening produces a new energy channel from the parent Alfvén wave to the backscattered one. Such nonlinear reflection explains the observed increasing energy ratio of the sunward to the anti-sunward Alfvénic fluctuations in the solar wind with distance against the dynamical alignment effect.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Generation of High Frequency Response in a Dynamically Loaded, Nonlinear Soil Column

Detailed guidance on linear seismic analysis of soil columns is provided in “Seismic Analysis of Safety-Related Nuclear Structures and Commentary (ASCE 4, 1998),” which is currently under revision. A new Appendix in ASCE 4-2014 (draft) is being added to provide guidance for nonlinear time domain analysis which includes evaluation of soil columns. When performing linear analysis, a given soil column is typically evaluated with a linear, viscous damped constitutive model. When submitted to a sine wave motion, this constitutive model produces a smooth hysteresis loop. For nonlinear analysis, the soil column can be modelled with an appropriate nonlinear hysteretic soil model. For the model in this paper, the stiffness and energy absorption result from a defined post yielding shear stress versus shear strain curve. This curve is input with tabular data points. When submitted to a sine wave motion, this constitutive model produces a hysteresis loop that looks similar in shape to the input tabular data points on the sides with discontinuous, pointed ends. This paper compares linear and nonlinear soil column results. The results show that the nonlinear analysis produces additional high frequency response. The paper provides additional study to establish what portion of the high frequency response is due to numerical noise associated with the tabular input curve and what portion is accurately caused by the pointed ends of the hysteresis loop. Finally, the paper shows how the results are changed when a significant structural mass is added to the top of the soil column.

nonlinear↗
DOE OSTI2017

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratio variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Nonlinearity in chorus waves during a geomagnetic storm on 1 November 2012

In this study, we investigate the possibility of nonlinearity in chorus waves during a geomagnetic storm on 1 November 2012. The data we use were measured by the Van Allen Probe B. Wave data and plasma sheet electron data are analyzed. Chorus waves were frequently measured in the morning side during the main phase of this storm. Large–amplitude chorus waves were seen of the order of ~0.6 nT and >7 mV/m, which are similar to or larger than the typical ULF waves. The waves quite often consist of rising tones during the burst sampling. Since the rising tone is known as a signature of nonlinearity, a large portion of the waves are regarded as nonlinear at least during the burst sampling periods. These results underline the importance of nonlinearity in the dynamics of chorus waves. We further compare the measurement and the nonlinear theories, based on the inhomogeneity ratio, our own calculation derived from the field equation and the backward wave oscillator model. The wave quantities examined are frequency, amplitude, frequency drift rate, and duration. Furthermore, this type of study is useful to more deeply understand wave-particle interactions and hence may lead to predicting the generation and loss of radiation belt electrons in the future.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Giant Nonlinear Optical Response via Coherent Stacking of In-Plane Ferroelectric Layers

Thin ferroelectric materials hold great promise for compact nonvolatile memory and nonlinear optical and optoelectronic devices. Herein, an ultrathin in-plane ferroelectric material that exhibits a giant nonlinear optical effect, group-IV monochalcogenide SnSe, is reported. Nanometer-scale ferroelectric domains with ≈90°/270° twin boundaries or ≈180° domain walls are revealed in physical-vapor-deposited SnSe by lateral piezoresponse force microscopy. Atomic structure characterization reveals both parallel and antiparallel stacking of neighboring van der Waals ferroelectric layers, leading to ferroelectric or antiferroelectric ordering. Ferroelectric domains exhibit giant nonlinear optical activity due to coherent enhancement of second-harmonic fields and the as-resulted second-harmonic generation was observed to be 100 times more intense than monolayer WS 2 . This work demonstrates in-plane ferroelectric ordering and giant nonlinear optical activity in SnSe, which paves the way for applications in on-chip nonlinear optical components and nonvolatile memory devices.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Difference‐Frequency Generation in Polaritonic Intersubband Nonlinear Metasurfaces

Abstract A nonlinear intersubband polaritonic metasurface designed for difference‐frequency generation that provides a practical level of nonlinear response under continuous wave illumination is reported. An effective nonlinear susceptibility of up to 340 nm V −1 is measured experimentally. Approximately 0.3% of λ = 5.4 µm photons are downconverted to λ = 12.9 µm photons at the focal spot in the experiment. This work indicates that the ultrathin metasurface devices may provide a versatile nonlinear element for frequency down‐ and upconversion in a relatively broad spectral range and without phase‐matching constrains of traditional bulk nonlinear crystals.

Liu, Yingnan↗
DOE OSTI2025

First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs

ABSTRACT We present a model reduction approach for the real‐time solution of time‐dependent nonlinear partial differential equations (PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced‐order models for nonlinear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methods to deal with nonlinear terms. Furthermore, we introduce a first‐order empirical interpolation method (EIM) to provide an efficient approximation of the nonlinear terms in time‐dependent PDEs. We demonstrate the effectiveness of our approach on the Allen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two‐phase fluid flow in porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with both the Galerkin–Newton approach and hyper‐reduced models using the standard EIM.

Nguyen, Ngoc Cuong [Center for Computational Engin↗
DOE OSTI2023

Denoising diffusion algorithm for inverse design of microstructures with fine-tuned nonlinear material properties

Here we introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually denoise images and generate realistic synthetic samples. By learning the reverse of a Markov diffusion process, we design an artificial intelligence to efficiently manipulate the topology of microstructures to generate a massive number of prototypes that exhibit constitutive responses sufficiently close to designated nonlinear constitutive behaviors. To identify the subset of microcstructures with sufficiently precise fine-tuned properties, a convolutional neural network surrogate is trained to replace high-fidelity finite element simulations to filter out prototypes outside the admissible range. Results of this study indicate that the denoising diffusion process is capable of creating microstructures of fine-tuned nonlinear material properties within the latent space of the training data. More importantly, this denoising diffusion algorithm can be easily extended to incorporate additional topological and geometric modifications by introducing high-dimensional structures embedded in the latent space. Numerical experiments are conducted on the open-source mechanical MNIST data set (Lejeune, 2020). Consequently, this algorithm is not only capable of performing inverse design of nonlinear effective media, but also learns the nonlinear structure–property map to quantitatively understand the multiscale interplay among the geometry, topology, and their effective macroscopic properties.

42 ENGINEERING↗
DOE OSTI2013

Investigation on the structural and nonlinear optical properties of Pt doped TiO{sub 2} nanoparticles

Graphical abstract: The open aperture Z-scan traces of Pt doped TiO{sub 2} nanoparticles at different Pt concentrations were carried out at an irradiation wavelength of 532 nm. It was numerically found that, two photon absorption (TPA) type process gives the best fit to the obtained open aperture Z-scan data. The nonlinear transmission was found to be of third order as it fits to a two-photon absorption. The optical limiting performances of nanoparticles were greatly enhanced with increased volume ratio of Pt. Increasing particle size reduced the limiting threshold and enhanced the optical limiting performance. - Highlights: • Pt doped TiO{sub 2} nanoparticles with different concentrations of Pt have been synthesized by sol–gel method. • The average fluorescence lifetime decreases as the volume fraction of Pt dopant increases. • The effects of Pt content on the optical limiting property were investigated by open aperture Z-scan measurements done at 532 nm using 5 ns laser pulses. • The values of the third-order nonlinearities of nanoparticles are interesting from the application point of view which could be used as a potential candidate for the application of nonlinear optical device. - Abstract: Pt doped TiO{sub 2} nanoparticles with different concentrations of Pt were prepared by sol–gel method. X-ray diffraction (XRD) study reveals that the samples have a homogeneous anatase phase tetragonal system and the lattice parameter analysis indicates that Pt ions substitute into the lattice of TiO{sub 2}. The addition of dopant increases the growth of TiO{sub 2} grains, agglomerates them and shifts the absorption band of TiO{sub 2} from ultraviolet to visible region. The incorporation of Pt in TiO{sub 2} is also confirmed by fluorescence quenching and the fluorescence lifetime decreases as the volume fraction of Pt dopant increases. Open aperture Z-scan measurements done at 532 nm using 7 ns laser pulses show nonlinear absorption which arises from an effective two photon absorption process. The nonlinear optical properties are characterized by using fluence dependent transmittance measurements in order to reveal the optical limiting effects. It is found that the optical limiting performances of nanoparticles were greatly enhanced with increased concentration of Pt.

36 MATERIALS SCIENCE↗
DOE OSTI2019

A high precision calibration of the nonlinear energy response at Daya Bay

A high precision calibration of the nonlinearity in the energy response of the Daya Bay Reactor Neutrino Experiment’s antineutrino detectors is observed. The energy nonlinearity originates from the particle-dependent light yield of the scintillator and charge-dependent electronics response. The nonlinearity model is constrained by γ calibration points from deployed and naturally occurring radioactive sources, the β spectrum from 12 B decays, and a direct measurement of the electronics nonlinearity with a new flash analog-to-digital converter readout system. With this beind said, less than 0.5% uncertainty in the energy nonlinearity calibration is achieved for positrons of kinetic energies greater than 1 MeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. The nonlinear interaction between counterpropagating Alfvén waves, denoted Alfvén wave collisions, drives this turbulent energy cascade, as recognized by early work with incompressible magnetohydrodynamic (MHD) equations. Recent work employing analytical calculations and nonlinear gyrokinetic simulations of Alfvén wave collisions in an idealized periodic initial state have demonstrated the key properties that strong Alfvén wave collisions mediate effectively the transfer of energy to smaller perpendicular scales and self-consistently generate current sheets. For the more realistic case of the collision between two initially separated Alfvén wavepackets, we use a nonlinear gyrokinetic simulation to show here that these key properties persist: strong Alfvén wavepacket collisions indeed facilitate the perpendicular cascade of energy and give rise to current sheets. Furthermore, the evolution shows that nonlinear interactions occur only while the wavepackets overlap, followed by a clean separation of the wavepackets with straight uniform magnetic fields and the cessation of nonlinear evolution in between collisions, even in the gyrokinetic simulation presented here which resolves dispersive and kinetic effects beyond the reach of the MHD theory.

Physics↗