Nonlinear Bulk Research Articles

A synthetic moving-envelope metasurface antenna for independent control of arbitrary harmonic orders

Flexible frequency controls are crucial in many photonic and electronic applications, ranging from communications systems, spectroscopy, and metrology to quantum information processing. However, the state-of-the-art solutions based on nonlinear bulk media, electro-optic effect, and nonlinear metasurfaces incur very limited spectral controllability, and merely a couple of harmonic orders can be independently manipulated. Here, we theoretically propose and experimentally demonstrate synthetic moving-envelope metasurface antennas capable of simultaneously generating arbitrary harmonic orders and independently manipulating their wave properties in a software-defined manner. As proof-of-principle examples, we demonstrate unidirectional frequency transition, frequency comb generation, arbitrary harmonic orders independent control, and their applications in frequency-division multiplexing communications. All these complicated functionalities are achieved by the 1-bit spatiotemporally ON-OFF switching of meta-atoms of the waveguide-integrated metasurface antenna. Our proposed synthetic metasurface antenna solution greatly expands the frontiers of wave engineering and information manipulation, showing promising potential in wireless communications, spectroscopy, metrology, and quantum science.

High‐Order Nonlinear Frequency Conversion in Transparent Conducting Oxide Thin Films

AbstractThe study of conductive oxides has gained momentum within the photonics community due to their unique linear and nonlinear optical properties. Despite recent experiments reporting on high harmonic generation from thin films, the optical/electronic behavior of these compounds at the nanoscale is still not fully understood due to the lack of a suitable theoretical model. In the present work, aluminum zinc oxide is excited near its epsilon‐near‐zero crossing point using incident femtosecond pulses having peak power densities in the 1 TW cm−2 range. A relatively efficient frequency up‐conversion including even and odd harmonics up to the seventh order is observed. A hydrodynamic‐Maxwell theoretical approach is adopted, capable of simultaneously taking into account linear and nonlinear dispersions, nonlocal effects, surface, magnetic, and bulk nonlinearities in a spectral region that spans over two and a half octaves from the UV to the NIR region. The study enables a deeper understanding of the fundamental material parameters regulating optical nonlinearities, providing important insights to engineer this class of materials for applications in sensing, ultra‐fast physics, and spectroscopy.

Nonlinear elastic waves generated by surface wave interaction with local plasticity in thick-walled structures

Thick-walled structures (TWSs) are frequently utilized as primary load-bearing structures across diverse industrial sectors, illustrated by train axles. Proper health monitoring, particularly for early damage detection, is required to ensure the operational safety and structural integrity of such structures. Nonlinear elastic-wave-based structural health monitoring techniques present a potentially efficacious methodology, which relies heavily upon the understanding of nonlinear wave generation and propagation characteristics. Unfortunately, due to the complexity introduced by various wave modes in TWSs, a comprehensive understanding of nonlinear elastic waves is still lacking. Considering practical local plasticity on the surface of a TWS, this study investigates the characteristics of nonlinear elastic wave generation and propagation resulting from the fundamental surface wave-local plasticity interaction. Theoretical analyses were carried out to examine the scattering features of the generated nonlinear bulk waves based on Snell’s law. Finite element simulations were then performed to confirm the predicted scattering characteristics of the nonlinear bulk waves, with the introduction of a local material nonlinearity to replicate the plasticity in a TWS. Using the extrusion method, a local plastic zone was produced on an aluminum thick-walled beam. Experiments were finally carried out using a laser vibrometer to confirm the scattering features of nonlinear elastic waves. It was found that the nonlinear shear bulk waves are mainly generated due to the fundamental surface interaction with local plasticity. Furthermore, the generated nonlinear shear bulk waves propagate at a fixed angle towards the interior of the TWS, which can be measured on the opposite surface. The elucidation of the nonlinear elastic wave generation and propagation characteristics paves the way for an effective sensor arrangement in early damage detection applications.

Enormous and Tunable Bulk Charge/Spin Photovoltaic Effect in Piezoelectric Binary Materials T-IV-VI and T-V-V.

Understanding the nonlinear response of light and materials is crucial for fundamental physics and next-generation electronic devices. In this work, we have investigated the second-order nonlinear bulk photovoltaic (BPV) and bulk spin photovoltaic (BSPV) effects in the piezoelectric binary materials T-IV-VI and T-V-V (IV = Ge, Sn; VI = S, Se; and V = P, As, Sb, Bi). The independent nonzero conductivity tensors of charge current are derived for these binaries through the symmetry analysis, along with the mechanism for generating pure spin current. These binaries, with their unique folded structure, exhibit significant charge and spin currents under illumination. Furthermore, we find that strain engineering can effectively modulate charge/spin currents by influencing charge density distribution and built-in electric field due to the piezoelectric effect. Our research suggests that the piezoelectric binary materials possess enormous and tunable charge/spin currents, underscoring their potential for applications in nonlinear flexible optoelectronics and spintronics.

Local plasticity-induced nonlinear surface wave scattering in thick-walled structures

Thick-walled structures (TWSs) are frequently utilized as primary load-bearing structures. The early detection of damage is crucial to ensure the operational safety and integrity of these structures. Nonlinear elastic-wave-based techniques provide a potential solution to the problem, which heavily relies on the good understanding of nonlinear wave generation and propagation characteristics. The task, however, is technically challenging due to the complex wave modes existing in a TWS. Targeting a meticulously manufactured local plasticized damage region on the surface of a TWS, which can be regarded as the precursor of incipient damage, this study investigates the scattering features of nonlinear elastic waves resulting from the interaction between the fundamental quasi-surface wave and the local plasticity. Finite element simulations and experiments show that, upon interacting with the nonlinear material zone, both nonlinear quasi-surface waves and shear bulk waves can be generated, with the latter scattered towards the opposite surface of the TWS. The scattered nonlinear shear waves exhibit a strong and predictable directivity with high nonlinear energy content, which is conducive to the detection and localization of the incipient surface damage of the TWS.

Advective Assembler‐Enhanced Support Bath Rotational Direct Ink Writing

AbstractManufacturing intricately controlled, hierarchically distributed structures poses significant fabrication challenges, but is crucial for enhancing functionality in synthetic systems. A 3D printing technique combining advective assembly with rotational direct ink writing is developed and exploited to build topologically complex, multimaterial structures with high precision. A modular advective assembler printhead is fabricated and employed in the process. This flow‐structuring device is designed with a complex network of internal channels that patterns flowing hydrogel‐based inks, creating multi‐layered filaments whose structures go well beyond conventional nozzle shape and size limitations. The composite filaments are extruded into a rotating support bath of Polyacrylic acid microgels. The rheology of the inks and support bath are critical to maintain print fidelity and integrity, and are characterized by linear and nonlinear bulk rheometry. Optimization of the materials creates a platform where curvilinear, multimaterial architectures are constructed without being constrained to slicing across X, Y, and Z axes. The versatility of this manufacturing platform is demonstrated by printing helical structures that undergo swelling‐induced actuation. This processing method has the potential to significantly enhance additive manufacturing by enabling the production of intricate, multiscale composite structures with broad applicability in fields such as bioengineering, soft robotics, and functional composite materials.

All-Solid-State Post-Compression of Low-Energy Pulses at High Repetition Rate

We demonstrate a proof of principle of a simple all-solid-state post-compression setup for low-energy, high-repetition-rate laser pulses, where spectral broadening was performed using a combination of highly nonlinear bulk materials in a simple single-pass geometry. The 75 fs, 210 nJ pulses from an amplified 76 MHz, 15.7 W Yb:KGW oscillator after sequential spectral broadening in ZnS and YAG samples of 2 mm and 15 mm thickness, respectively, were compressed to 37 fs by means of Gires–Tournois interferometric mirrors. The post-compressed pulses with an average power of 11.47 W demonstrated reasonable spatial-spectral homogeneity of the beam with the spectral overlap parameter V>83% and good beam quality with Mx2=1.28 and My2=1.14.

Programming mechanics in knitted materials, stitch by stitch

Knitting turns yarn, a 1D material, into a 2D fabric that is flexible, durable, and can be patterned to adopt a wide range of 3D geometries. Like other mechanical metamaterials, the elasticity of knitted fabrics is an emergent property of the local stitch topology and pattern that cannot solely be attributed to the yarn itself. Thus, knitting can be viewed as an additive manufacturing technique that allows for stitch-by-stitch programming of elastic properties and has applications in many fields ranging from soft robotics and wearable electronics to engineered tissue and architected materials. However, predicting these mechanical properties based on the stitch type remains elusive. Here we untangle the relationship between changes in stitch topology and emergent elasticity in several types of knitted fabrics. We combine experiment and simulation to construct a constitutive model for the nonlinear bulk response of these fabrics. This model serves as a basis for composite fabrics with bespoke mechanical properties, which crucially do not depend on the constituent yarn.

Motion Control of Electro-Hydrostatic Actuators With Modeling and Compensation of Nonlinear Bulk Modulus

Motion Control of Electro-Hydrostatic Actuators With Modeling and Compensation of Nonlinear Bulk Modulus

Calculation and Measurement of Dielectric Parameters of Ceramic and Ferroelectric Materials in the Microwave Range

Introduction. Determination of the electrophysical parameters of linear and nonlinear dielectric materials for use in microwave technology represents an important direction. Linear dielectrics are used as a basis for the substrates of microwave circuits, as well as volumetric elements for the construction of frequency selective or resonant structures that operate across a wide temperature range. Therefore, the issue of stabilizing the electrical parameters of such structures from temperature influences appears relevant. A possible solution lies in the use of a multilayer combination of dielectrics, both with linear and nonlinear properties. Due to their nonlinear properties, ferroelectrics find application in functional units with an electrical rearrangement of frequency and phase characteristics. Therefore, it is important to determine not only the relative permittivity of the material, but also the control coefficient in the RF– microwave wavelength ranges.Aim. Construction of computational mathematical models for layered bulk and film structures to determine the relative permittivity of linear and nonlinear dielectrics in the ultrahigh frequency range.Materials and methods. The construction of computational mathematical models for the analysis of complex layered structures was carried out on the basis of Maxwell’s equations and the Galerkin method using boundary conditions for electromagnetic field components.Results. An electrodynamic analysis of a two-layer volumetric disk resonator was performed, and numerical results of calculating the resonant frequency were obtained. A numerical analysis of a multielectrode half-wave resonator with a ferroelectric film (FEF) was carried out.Conclusion. The mathematical models created and the experiment performed made it possible to numerically evaluate the properties of linear and nonlinear dielectric bulk and film materials in the microwave range.

Numerical model of nonlinear elastic bulk wave propagation in solids for non-destructive evaluation

Nonlinear ultrasonic techniques can be difficult and non-intuitive to understand due to the range of wave mixing combinations available between similar or different wave modes. To overcome this, a numerical model that uses a Finite Difference Time Domain (FDTD) scheme, without a staggered grid system, to solve the nonlinear elastic bulk wave equations in two dimensions is proposed in this paper, with the purpose of better understanding nonlinear ultrasonic techniques. Both material and geometrical nonlinearities are considered and a stress-type boundary condition is used to model the excitation. The energy transfer between frequency bands is shown and the amplitude trend of the harmonics are validated against available theories. It is then used to simulate the nonlinear ultrasonic field generated by a finite-size element of an array in a solid to better understand its behaviour. An array-element directivity at the second harmonic frequency is shown. Since the FDTD model does not account for attenuation, a correction using a ray-based approach is applied to the simulated result for direct comparison against experimental measurements. The field obtained from a typical array used in non-destructive testing is then simulated to characterise its behaviour. Experimental comparison of the nonlinear displacement fields for different focal positions showed good agreement, further validating the FDTD model. This FDTD model opens opportunities to virtually experiment and design appropriate nonlinear ultrasonic array inspections whilst isolating and understanding contribution from material nonlinearity.

Amplitude-dependent edge states and discrete breathers in nonlinear modulated phononic lattices

We investigate the spectral properties of one-dimensional spatially modulated nonlinear phononic lattices, and their evolution as a function of amplitude. In the linear regime, the stiffness modulations define a family of periodic and quasiperiodic lattices whose bandgaps host topological edge states localized at the boundaries of finite domains. With cubic nonlinearities, we show that edge states whose eigenvalue branch remains within the gap as amplitude increases remain localized, and therefore appear to be robust with respect to amplitude. In contrast, edge states whose corresponding branch approaches the bulk bands experience de-localization transitions. These transitions are predicted through continuation studies on the linear eigenmodes as a function of amplitude, and are confirmed by direct time domain simulations on finite lattices. Through our predictions, we also observe a series of amplitude-induced localization transitions as the bulk modes detach from the nonlinear bulk bands and become discrete breathers that are localized in one or more regions of the domain. Remarkably, the predicted transitions are independent of the size of the finite lattice, and exist for both periodic and quasiperiodic lattices. These results highlight the co-existence of topological edge states and discrete breathers in nonlinear modulated lattices. Their interplay may be exploited for amplitude-induced eigenstate transitions, for the assessment of the robustness of localized states, and as a strategy to induce discrete breathers through amplitude tuning.

Controllable optical bistability in a Fabry–Pérot cavity with a nonlinear three-dimensional Dirac semimetal

Optical bistability (OB) is capable of rapidly and reversibly transforming a parameter of an optical signal from one state to another, and homologous nonlinear optical bistable devices are core components of high-speed all-optical communication and all-optical networks. In this paper, we theoretically investigated the controllable OB from a Fabry–Pérot (FP) cavity with a nonlinear three-dimensional Dirac semimetal (3D DSM) in the terahertz band. The OB stems from the third-order nonlinear bulk conductivity of the 3D DSM and the resonance mode has a positive effect on the generation of OB. This FP cavity structure is able to tune the OB because the transmittance and the reflectance can be modulated by the Fermi energy of the 3D DSM. We believe that this FP cavity configuration could provide a reference concept for realizing tunable bistable devices.

Manipulation of nonlinear optical responses in layered ferroelectric niobium oxide dihalides

Realization of highly tunable second-order nonlinear optical responses, e.g., second-harmonic generation and bulk photovoltaic effect, is critical for developing modern optical and optoelectronic devices. Recently, the van der Waals niobium oxide dihalides are discovered to exhibit unusually large second-harmonic generation. However, the physical origin and possible tunability of nonlinear optical responses in these materials remain to be unclear. In this article, we reveal that the large second-harmonic generation in NbOX2 (X = Cl, Br, and I) may be partially contributed by the large band nesting effect in different Brillouin zone. Interestingly, the NbOCl2 can exhibit dramatically different strain-dependent bulk photovoltaic effect under different polarized light, originating from the light-polarization-dependent orbital transitions. Importantly, we achieve a reversible ferroelectric-to-antiferroelectric phase transition in NbOCl2 and a reversible ferroelectric-to-paraelectric phase transition in NbOI2 under a certain region of external pressure, accompanied by the greatly tunable nonlinear optical responses but with different microscopic mechanisms. Our study establishes the interesting external-field tunability of NbOX2 for nonlinear optical device applications.

Control of nonlinear bulk deformation and large shear strain on first-order phase transformation kinetics

Phase transformations play a key role in numerous coupled natural processes, and they are important for many industrial applications. However, the kinetics of phase transformations in coupled chemo-mechanical systems undergoing large mechanical deformations still needs to be better quantified. Here, we study the phase transformation kinetics of a two-phase binary mixture using the diffuse interface approach. We couple a Cahn–Hilliard type model with a mechanical model for a compressible viscous flow. The bulk compressibility is a nonlinear function of the pressure, and the shear viscosity is a nonlinear function of the concentration. The mechanical coupling is achieved by employing a pressure-dependent mechanical mixing term in the equation for the Gibbs energy. We derive a dimensionless system of equations which we solve numerically with a pseudo-transient method using conservative finite differences for discretization. We perform numerical simulations in 1D and 2D model setups considering far-field simple shear and pure shear. For a chemo-mechanically coupled system, we show that the velocity of the phase boundary is a linear function of the degree of metastability and, hence, confirm the hypothesis of “normal growth.” A stronger mechanical coupling and a larger volumetric effect of the chemical reaction result in lower phase boundary velocities. The 2D results show a significant impact of the mechanical coupling and the far-field deformation on the orientation and kinetics of the phase transformations. Under far-field simple shear and pure shear in 2D, the phase transformations generate string-like patterns. The orientation of these patterns is controlled by the applied far-field deformation and orientations differ by 45 degrees between simple shear and pure shear.

A versatile model with three-dimensional triangular lattice for unconventional transport and various topological effects.

The finite Berry curvature in topological materials can induce many subtle phenomena, such as the anomalous Hall effect (AHE), spin Hall effect (SHE), anomalous Nernst effect (ANE), non-linear Hall effect (NLHE) and bulk photovoltaic effects. To explore these novel physics as well as their connection and coupling, a precise and effective model should be developed. Here, we propose such a versatile model-a 3D triangular lattice with alternating hopping parameters, which can yield various topological phases, including kagome bands, triply degenerate fermions, double Weyl semimetals and so on. We reveal that this special lattice can present unconventional transport due to its unique topological surface states and the aforementioned topological phenomena, such as AHE, ANE, NLHE and the topological photocurrent effect. In addition, we also provide a number of material candidates that have been synthesized experimentally with this lattice, and discuss two materials, including a non-magnetic triangular system for SHE, NLHE and the shift current, and a ferromagnetic triangular lattice for AHE and ANE. Our work provides an excellent platform, including both the model and materials, for the study of Berry-curvature-related physics.

Estimation of fat content in soft tissues using dual frequency ultrasound—A phantom study

This paper presents an initial investigation into the use of dual frequency pulse-echo ultrasound, second order ultrasound field (SURF) imaging, to measure the fat content of soft tissues. The SURF imaging method was used to measure the non-linear bulk elasticity (NBE) of several fatty phantoms that were created by mixing different mass fractions of soybean oil uniformly into agar phantoms. The median of the measured NBE within the estimation region was found to increase linearly with fat mass fraction (R2 = 0.99), from 1.7 GPa-1 at 9.6% fat to 2.52 GPa-1 at 63.6% fat, thus, showing promise as a sensitive parameter for fat content measurement. Comparisons to mixture laws in earlier literature are made, and the most important error sources that need to be considered for the in vivo applications of the method are discussed.

A competition–species model for water vapour-aerosol-cloud-rain interactions

In this paper, a non-linear bulk model inspired from species competition dynamics is proposed in order to describe the physics of water vapour-aerosol-cloud-rain interactions. Despite the complexity of such interactions, certain non-trivial aspects of the macro behavior of a cloud are predictable without concerning the full complexity of the dynamical system. The model is for warm clouds (no ice) and it consists in a set of three non-linear differential equations. This species-competition model is confronted with in situ measurements in different situations: for pristine environments (1) at the high-altitude Maïdo Observatory (Indian Ocean, Reunion Island) and (2) in a pure oceanic context around the Reunion Island (aeromarine field campaign) and for a continental urban context (3) in Lille (North of France). Compared with observations (radar, radiometric measurements), it is shown that, whatever the situation considered, the model reproduces efficiently the macro features of clouds, like cloud occurrences, cloud water content magnitudes, and cloud-rain links. The model is adapted to a two-dimensional (horizontal) grid and its predictions are compared with the era5 reanalyses above the Hauts-de-France region and in the pristine Southwest Indian Ocean (around Reunion Island). Furthermore, satellite data enable to corroborate that the model clearly shows promising results for the horizontal cloud field organization. The spatiotemporal resolution of this model is adaptable according to the needs and it can be used in any region and at the desired altitude provided that data be available for implementation. In this paper, it is also suggested that the model may be fruitful to derive from measurements, by means of an optimization scheme, different theoretical parameters not easy to determine. The model runs on a laptop with a relatively short time (of the order of the minute); it is not intended to supplant comprehensive models, but it may be fruitful to understand the essential mechanisms in warm cloud formation.

Local Three-Dimensional Characterization of Nonlinear Grain Boundary Length within Bulk ZnO Using Nanorobot in SEM

Aiming at the problems of lack of data on the nonlinear morphology to divide uneven grain boundary in bulk ceramics, a unique approach of nanorobot-based characterization of three-dimensional nonlinear structure length can be creatively proposed under scanning electron microscope to quantify the actual morphology of local micro-area grain boundary in bulk ZnO. Contour shapes of the targeted grain boundaries in plane X-Y can be imaged using SEM. Z-directional relative height differences at different positions can be sequentially probed by nanorobot. Experiments demonstrate that it is effective to characterize three-dimensional length structures of nonlinear grain boundaries in bulk materials. By quantifying Z-directional relative height differences, it can be verified to show that irregular characteristics exist in three-dimensional grain boundary length, which can extend the depth effect on nonlinear bulk conductance. Furthermore, this method can also obtain nonlinear quantitative topographies to divide grain boundaries to uneven structure in the analysis of bulk polycrystalline materials.

Thermal Stability and Luminescence Quenching of Working Color Centers in Nonlinear Bulk Photographic Materials Based on KCl–TlNO3 Compound

Thermal Stability and Luminescence Quenching of Working Color Centers in Nonlinear Bulk Photographic Materials Based on KCl–TlNO3 Compound