Nonlinear Geometric Phase Gradient Metasurfaces beyond the Dipole Approximation.
Abstract not provided.
Gennaro, Sylvain Damien↗
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Polarization Control via Artificial Optical Nonlinearity in Dielectric Metasurfaces
Nonlinear optical phenomena are generally governed by geometry in matter systems, as they depend on the spatial arrangement of atoms within materials or molecules. Metasurfaces, through precisely designed geometries on a subwavelength scale, allow the optical response of a material to be tailored far beyond its natural properties. Therefore, metasurfaces are highly appealing for enabling the engineering of nonlinear optical interactions. Current studies of nonlinear metasurfaces predominantly focus on the phase control of the generated light. Nonetheless, investigating the tensorial nature of the nonlinearity of metasurfaces and its effect on the polarization of the generated light is critical to fully unlocking a range of applications, such as nonlinear vector beam generation and nonlinear polarization imaging. Here, we study the artificial optical nonlinearity of a dielectric metasurface originating from its meta-atom symmetry and describe the third-order nonlinear behavior by considering the polarization degree of freedom. We establish an effective nonlinear medium model that serves as a design toolbox for developing amorphous silicon-based geometric metasurfaces with customizable features for third-harmonic generation. We further extract quantitative values of the artificial nonlinear susceptibility tensor elements related to the investigated nonlinear process and geometry. The implemented functional devices demonstrate the versatility of dielectric metasurfaces in shaping the emitted light in terms of amplitude, phase, and polarization for the precise engineering of advanced nonlinear architectures targeting applications in nonlinear imaging and complex light generation.
Diffraction↗
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Lee, Kee-Joo↗
Antiferroelectric Ceramics for Energy–Efficient Capacitors by Theory–Guided Discovery
Antiferroelectric ceramics, via the electric-field-induced antiferroelectric (AFE)–ferroelectric (FE) phase transitions, show great promise for high-energy-density capacitors. Yet, currently, only 70–80% energy release is found during a charge–discharge cycle. Here, for PbZrO 3 -based oxides, geometric nonlinear theory of martensitic phase transitions is applied (first used to guide supercompatible shape-memory alloys) to predict the reversibility of the AFE–FE transition by using density-functional theory to assess AFE/FE interfacial lattice-mismatch strain that assures ultralow electric hysteresis and extended fatigue lifetime. A good correlation of mismatch strain with electric hysteresis, hence, with energy efficiency of AFE capacitors is observed. Here, guided by theory, high-throughput material search is conducted and AFE compositions with a near-perfect charge–discharge energy efficiency (98.2%), i.e., near-zero hysteresis are discovered. And the fatigue life of the capacitor reaches 79.5 million charge–discharge cycles, a factor of 80 enhancement over AFE ceramics with large electric hysteresis.
36 MATERIALS SCIENCE↗
Interlaminar fracture of random short-fiber SMC composite
In the experimental phase of the present study of the interlaminar fracture behavior of a randomly oriented short fiber sheet molding compound (SMC) composite, the double cantilever beam fracture test is used to evaluate the mode I interlaminar fracture toughness of different composite thicknesses. In the analytical phase of this work, a geometrically nonlinear analysis is introduced in order to account for large deflections and nonlinear load deflection curves in the evaluation of interlaminar fracture toughness. For the SMC-R50 material studied, interlaminar toughness is an order of magnitude higher than that of unreinforced neat resin, due to unusual damage mechanisms ahead of the crack tip, together with significant fiber bridging across crack surfaces. Composite thickness effects on interlaminar fracture are noted to be appreciable, and a detailed discussion is given on the influence of SMC microstructure.
Wang, S. S.↗
Phase Matching of Diverse Modes in a WGM Resonator
Phase matching of diverse electromagnetic modes (specifically, coexisting optical and microwave modes) in a whispering-gallery-mode (WGM) resonator has been predicted theoretically and verified experimentally. Such phase matching is necessary for storage of microwave/terahertz and optical electromagnetic energy in the same resonator, as needed for exploitation of nonlinear optical phenomena. WGM resonators are used in research on nonlinear optical phenomena at low optical intensities and as a basis for design and fabrication of novel optical devices. Examples of nonlinear optical phenomena recently demonstrated in WGM resonators include low-threshold Raman lasing, optomechanical oscillations, frequency doubling, and hyperparametric oscillations. The present findings regarding phase matching were made in research on low-threshold, strongly nondegenerate parametric oscillations in lithium niobate WGM resonators. The principle of operation of such an oscillator is rooted in two previously observed phenomena: (1) stimulated Raman scattering by polaritons in lithium niobate and (2) phase matching of nonlinear optical processes via geometrical confinement of light. The oscillator is partly similar to terahertz oscillators based on lithium niobate crystals, the key difference being that a novel geometrical configuration of this oscillator supports oscillation in the regime. The high resonance quality factors (Q values) typical of WGM resonators make it possible to achieve oscillation at a threshold signal level much lower than that in a non-WGM-resonator lithium niobate crystal.
Savchenkov, Anatoliy↗
Characterization of nonlinear ultrasonic waves behavior while interacting with poor interlayer bonds in large-scale additive manufactured materials
Over the past decades, researchers have developed several nonlinear ultrasonic techniques for quality control of materials commonly used in different applications. Owing to the superior sensitivity of nonlinear ultrasound waves to small defects such as micro-cracks, their applicability in different nondestructive testing (NDT) problems has been investigated in numerous studies. These studies utilize frequency domain analysis to detect the generation of higher harmonics because of the formation of defects in the inspected medium. Frequency domain analysis based on the Fourier transform is a significant approach used in linear systems; however, it may not perform adequately on nonlinear systems. Hence, studies on nonlinear dynamics and physics consider analyzing systems' behavior in the phase-space domain. In contrast to the frequency domain analysis, which can result in information loss, analysis in the phase-space domain retains all the information regarding a system's states. Here, we investigate the nonlinearities induced by poor interlayer bonding in polymer-based additive manufactured parts in the phase-space domain. It is convenient to characterize the nonlinearity in the phase-space domain because it provides a geometrical representation of a system's states. Two types of low quality interlayer bond are considered. The first type is simulated artificially while the second type is manufactured by reducing the bond quality during the printing process. The analysis verified that the received ultrasonic signals exhibit classical nonlinear behavior in the phase-space domain while interacting with simulated poor interlayer bonds. In addition, the results showed that the behavior of ultrasonic waves is amplitude-dependent and evolves into models that have not been previously reported. Furthermore, Largest Lyapunov Exponent (LLE) is used to quantify the behavior of nonlinear ultrasonic waves while interacting with poor interlayer bonds. Using LLE, it was observed that the divergence rate of the phase-space trajectories depends on the amplitude of the excitation. This observation quantitatively proves that nonlinear behavior of ultrasound while interacting with poor interlayer bonds can be amplitude-dependent. The results of both simulated and inherent poor interlayer bond cases showed that LLE can be used as a reliable quantitative damage-sensitive feature to detect and potentially characterize weak bonds, which are difficult to detect using conventional approaches. Additionally, the reported results in the phase-space domain provide a basis for proposing a new mathematical model for ultrasonic waves interacting with poor interlayer bonds.
36 MATERIALS SCIENCE↗
Nonlocal Metasurface with Resonance-Selective Nonlinear Wavefront Shaping
We demonstrate a nonlinear nonlocal metasurface supporting quasi-trapped modes that enable helicity-dependent wavefront shaping at third-harmonic wavelengths. The geometric phase is selectively modified near resonance, revealing a mechanism for polarization-dependent nonlinear phase control.
Sedeh, Hooman [Duke University]↗
A tutorial on high-order harmonic generation in atoms, molecules, and condensed matter
This tutorial introduces strong-field-driven high-order harmonics, their experimental generation and characterization techniques, and their main applications including attosecond pulse generation and ultrafast spectroscopy of the target material. We begin from the use of atomic targets, where the first high-order harmonic generation (HHG) experiments were realized in the late 1980s. Then, we briefly discuss the basics of the microscopic generation mechanism and how various steps of the mechanism were exploited in applications such as generating isolated attosecond pulses and probing molecular orbitals. We introduce and describe the standard experimental approaches for condensed phase HHG, where we discuss unique technical challenges of the use of solid-state materials, such as the mitigation of plasma formation and laser damage. We cover the fundamentals of high-harmonic spectroscopy in condensed matter systems, such as wide bandgap dielectrics, semiconductors, liquid media, and 2D-crystals. We provide some examples of rapidly emerging spectroscopic capabilities, such as for probing crystal symmetries, Berry phases, and associated non-trivial topological properties of the source material. Finally, we provide an overview of the research field, including some of the challenges, opportunities, and open questions.
Attosecond pulses↗
An Analysis of the Macroscopic Tensile Behavior of a Nonlinear Nylon Reinforced Elastomeric Composite System Using MAC/GMC
A special class of composite laminates composed of soft rubbery matrices and stiff reinforcements made of steel wires or synthetic fibers is examined, where each constituent behaves in a nonlinear fashion even in the small strain domain. Composite laminates made of piles stacked at alternating small orientation angles with respect to the applied axial strain are primarily dominated by the nonlinear behavior of the reinforcing fibers. However; composites with large ply orientations or those perpendicular to the loading axis, will approximate the behavior of the matrix phase and respond in even a more complex fashion for arbitrarily stacked piles. The geometric nonlinearity due to small cord rotations during loading was deemed here to have a second order effect and consequently dropped from any consideration. The user subroutine USRMAT within the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC), was utilized to introduce the constituent material nonlinear behavior. Stress-strain behavior at the macro level was experimentally generated for single and multi ply composites comprised of continuous Nylon-66 reinforcements embedded in a carbon black loaded rubbery matrix. Comparisons between the predicted macro composite behavior and experimental results are excellent when material nonlinearity is included in the analysis. In this paper, a brief review of GMC is provided, along with a description of the nonlinear behavior of the constituents and associated constituent constitutive relations, and the improved macro (or composite) behavior predictions are documented and illustrated.
Assaad, Mahmoud↗
Uncertainty Analysis of Composite Structures
A two-phase approach and a computational procedure are presented for predicting the variability in the nonlinear response of composite structures associated with variations in the geometric and material parameters of the structure. In the first phase, hierarchical sensitivity analysis is used to identify the major parameters, which have the most effect on the response quantities of interest. In the second phase, the major parameters are taken to be fuzzy parameters, and a fuzzy set analysis is used to determine the range of variation of the response, associated with preselected variations in the major parameters. The effectiveness of the procedure is demonstrated by means of a numerical example of a cylindrical panel with four T-shaped stiffeners and a circular cutout.
Noor, Ahmed K.↗
Topology and geometry under the nonlinear electromagnetic spotlight
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this Review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. Furthermore, we give an overview of the field by discussing theoretical ideas, experiments and the materials that drive them. We conclude by discussing how these techniques can be combined with device architectures to uncover, probe and ultimately control quantum phases with emergent topological and correlated properties.
36 MATERIALS SCIENCE↗
Time-series forecasting using manifold learning, radial basis function interpolation, and geometric harmonics
We address a three-tier numerical framework based on nonlinear manifold learning for the forecasting of high-dimensional time series, relaxing the “curse of dimensionality” related to the training phase of surrogate/machine learning models. At the first step, we embed the high-dimensional time series into a reduced low-dimensional space using nonlinear manifold learning (local linear embedding and parsimonious diffusion maps). Then, we construct reduced-order surrogate models on the manifold (here, for our illustrations, we used multivariate autoregressive and Gaussian process regression models) to forecast the embedded dynamics. Finally, we solve the pre-image problem, thus lifting the embedded time series back to the original high-dimensional space using radial basis function interpolation and geometric harmonics. The proposed numerical data-driven scheme can also be applied as a reduced-order model procedure for the numerical solution/propagation of the (transient) dynamics of partial differential equations (PDEs). In conclusion, we assess the performance of the proposed scheme via three different families of problems: (a) the forecasting of synthetic time series generated by three simplistic linear and weakly nonlinear stochastic models resembling electroencephalography signals, (b) the prediction/propagation of the solution profiles of a linear parabolic PDE and the Brusselator model (a set of two nonlinear parabolic PDEs), and (c) the forecasting of a real-world data set containing daily time series of ten key foreign exchange rates spanning the time period 3 September 2001–29 October 2020.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A survey of the core-congruential formulation for geometrically nonlinear TL finite elements
This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.
Felippa, Carlos A.↗
Optofluidic memory and self-induced nonlinear optical phase change for reservoir computing in silicon photonics
Nanophotonics allows to employ light-matter interaction to induce nonlinear optical effects and realize non-conventional memory and computation capabilities, however to date, light-liquid interaction was not considered as a potential mechanism to achieve computation on a nanoscale. Here, we experimentally demonstrate self-induced phase change effect which relies on the coupling between geometric changes of thin liquid film to optical properties of photonic waveguide modes, and then employ it for neuromorphic computing. In our optofluidic silicon photonics system we utilize thermocapillary-based deformation of thin liquid film capable to induce nonlinear effect which is more than one order of magnitude higher compared to the more traditional heat-based thermo-optical effect, and allowing operation as a nonlinear actuator and memory element, both residing at the same compact spatial region. The resulting dynamics allows to implement Reservoir Computing at spatial region which is approximately five orders of magnitude smaller compared to state-of-the-art experimental liquid-based systems.
42 ENGINEERING↗
A phase-field model for non-isothermal phase transformation and plasticity in polycrystalline yttria-stabilized tetragonal zirconia
Here we propose an elastoplastic phase-field (PF) model to investigate the mechanics of tetragonal-to-monoclinic phase transformation (TMPT) and elastoplastic deformation of polycrystalline yttria-stabilized tetragonal zirconia (YSTZ). A Landau polynomial with non-vanishing chemical energy at the equilibrium temperature is introduced to account for the actual formation energies of the phases. The effects of different grain orientations, latent heat, and temperature on TMPT and deformation mechanisms are considered. The suppressive transformation effects of the grain boundaries (GBs) is modeled using an inhomogeneous kinetic coefficient in the bulk and GBs. The simulation results for single crystals demonstrate the capability of the model to reproduce the orientation-dependent compressive deformation of YSTZ similar to atomistic simulations and micropillar experiments. The single crystal with [100] crystallographic orientation along the loading direction (SC[100]) displays both TMPT and plasticity, SC[101] experiences only phase transformation, while SC[001] undergoes only plastic yielding. The TMPT induced by compressive loading exhibits shape memory effect (SME) below the equilibrium transformation temperature and pseudoelasticity above it, while the critical transformation stress increases with increasing loading temperature. The irrecoverable plastic strain is found to trap a part of the monoclinic phase, which prevents a complete reverse transformation. The polycrystalline cases also display SME and PE at low and high temperatures, respectively. Due to the orientation differences between grains and the stress concentrations at geometric nonlinearities, plastic deformation occurs in polycrystalline YSTZ for an applied load less than the yield stress. The results suggest a possible limitation of plasticity and an improvement of the shape recovery of YSTZ if one can control the orientation of the grains and/or increase the density of stacking faults at the GBs during material processing.
36 MATERIALS SCIENCE↗
WINCLR: a Computer Code for Heat Transfer and Clearance Calculation in a Compressor
One of the concerns during inclement weather operation of aircraft in rain and hail storm conditions is the nature and extent of changes in compressor casing clearance. An increase in clearance affects efficiency while a decrease may cause blade rubbing with the casing. The change in clearance is the result of geometrical dimensional changes in the blades, the casing and the rotor due to heat transfer between those parts and the two-phase working fluid. The heat transfer interacts nonlinearly with the performance of the compressor, and, therefore, the determination of clearance changes necessitates a simultaneous determination of change in performance of the compressor. A computer code the WINCLR has been designed for the determination of casing clearance, that is operated interactively with the PURDU-WINCOF I code designed previously for determining the performance of a compressor. A detailed description of the WINCLR code is provided in a companion report. The current report provides details of the code with an illustrative example of application to the case of a multistage compressor. It is found in the example case that under given ingestion and operational conditions, it is possible for a compressor to undergo changes in performance in the front stages and rubbing in the back stages.
Bose, T. K.↗
Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration
Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.
Siclari, Michael J.↗