Nonlinear Material Response Research Articles

Anisotropic nonlinear optical response of nodal-loop materials

Nodal line semimetals have lately aroused much experimental and theoretical interest, with their gap closing along unconventional trajectories in the 3D Brillouin zone. These trajectories or nodal lines can close into loops and trace out intricate knotted or linked configurations with complicated topologies. In this work, we investigate the semi-classical optical response of two nodal loops in linked, unlinked and touching configurations, focusing particularly on the interplay of response anisotropy and non-linearity. We provide a geometric picture that unifies these aspects and sheds light on the effects of nodal topology and geometry. Based on a model abstracted from generic multi nodal loop scenarios, both with or without linkages, our findings will be applicable for a large class of nodal semimetal materials with multiple nodal lines or loops.

A two-stage design optimization framework for multifield origami-inspired structures

Different types of active materials have been used to actuate origami-inspired self-folding structures. To model the highly nonlinear deformation and material responses, as well as the coupled field equations and boundary conditions of such structures, high-fidelity models such as finite element (FE) models are needed but usually computationally expensive, which makes optimization intractable. In this paper, a computationally efficient two-stage optimization framework is developed as a systematic method for the multi-objective designs of such multifield self-folding structures where the deformations are concentrated in crease-like areas, active and passive materials are assumed to behave linearly, and low- and high-fidelity models of the structures can be developed. In Stage 1, low-fidelity models are used to determine the topology of the structure. At the end of Stage 1, a distance measure [Formula: see text] is applied as the metric to determine the best design, which then serves as the baseline design in Stage 2. In Stage 2, designs are further optimized from the baseline design with greatly reduced computing time compared to a full FEA-based topology optimization. The design framework is first described in a general formulation. To demonstrate its efficacy, this framework is implemented in two case studies, namely, a three-finger soft gripper actuated using a PVDF-based terpolymer, and a 3D multifield example actuated using both the terpolymer and a magneto-active elastomer, where the key steps are elaborated in detail, including the variable filter, metrics to select the best design, determination of design domains, and material conversion methods from low- to high-fidelity models. In this paper, analytical models and rigid body dynamic models are developed as the low-fidelity models for the terpolymer- and MAE-based actuations, respectively, and the FE model of the MAE-based actuation is generalized from previous work. Additional generalizable techniques to further reduce the computational cost are elaborated. As a result, designs with better overall performance than the baseline design were achieved at the end of Stage 2 with computing times of 15 days for the gripper and 9 days for the multifield example, which would rather be over 3 and 2 months for full FEA-based optimizations, respectively. Tradeoffs between the competing design objectives were achieved. In both case studies, the efficacy and computational efficiency of the two-stage optimization framework are successfully demonstrated.

Ultrafast optical switching and power limiting in intersubband polaritonic metasurfaces

Highly nonlinear optical materials with fast third-order nonlinear optical response are crucial for the operation of all-optical photonic devices, such as switches for signal processing and computation, power limiters, and saturable absorbers. The nonlinear response of traditional optical materials is weak, thus requiring large light intensities to induce significant changes in their properties. Here we show that optical control of the coupling rate in subwavelength patch antennas coupled to intersubband transitions in multi-quantum-well semiconductor heterostructures can provide a giant third-order nonlinear response, on the order of 3.4 × 10 − 13 m 2 / V 2 , with a response time < 2 p s . We utilize this effect to realize intersubband polaritonic metasurfaces and demonstrate their operation as highly nonlinear saturable and reverse saturable absorbers, enabling optical power limiters and other elements for all-optical modulation and control. Our approach enables a plethora of compact, low-power, highly nonlinear devices with spectral, temporal, and structured wavefront responses tailored by design.

An efficient anisotropization technique to transform isotropic nonlinear materials into unidirectional and bidirectional composites

This work presents a procedure to transform an isotropic nonlinear and rate-dependent material model into orthotropic. This transformation relies on a fast computation modifying the material inelastic evolution along any desired direction. With this concept, the constitutive law of the pure isotropic, nonlinear and rate-dependent material is fully preserved. This paper shows a direct application to describe the nonlinear response of unidirectional (UD) or bidirectional (BD) fiber-reinforced polymer composites. Imposing one constraint leads to a UD composite, whilst imposing two orthogonal directions leads to a BD composite. The proposed methodology is implemented as user-defined material for Finite Element solvers. To prove the method, two different visco-plastic material models used to describe isotropic polymer resins are anisotropized to obtain their corresponding composite counterparts. The mechanical response of the simulations are compared qualitatively and quantitatively to experimental tests on a UD coupon under off-axis tensile test under different load directions. Consistency between the UD and BD anisotropization formulations is proved under tension, shear and different loading directions. Additionally, a complete study of computational performance is addressed to assess the anisotropization’s feasibility to be applied in modeling and design of new laminated and multilayer-based structures exhibiting nonlinear material response.

TFA and HS based homogenization techniques for nonlinear composites

The paper presents two reduced order homogenization techniques for studying the response of nonlinear composite materials. The first approach is based on Transformation Field Analysis, which considers the presence of eigenstrains to account for inelastic strains, while the second approach is derived from Hashin–Shtrikman variational principle, which introduces eigenstresses, namely polarization stresses, on a homogeneous elastic reference material to account for the heterogeneity and the inelastic response. In particular, the case of elasto-plastic periodic composites is investigated. A Unit Cell is identified and divided in subsets. In each subset, the eigenstrains or eigenstresses are assumed uniform. A very effective technique is derived for the Hashin–Shtrikman approach updating the elastic reference material properties during the inelastic strain evolution. Numerical procedures are implemented to derive the nonlinear response of composites with plastic constituents. Several numerical applications are carried out to assess the effectiveness of the two presented reduced order models. A deep investigation on the differences and similarities of the two approaches is presented, proving their equivalence under particular circumstances. Simple and complex loading histories are considered, comparing the results with a finite element solution, considered as the reference solution.

Simple Reservoir Computing Capitalizing on the Nonlinear Response of Materials: Theory and Physical Implementations

The potential of nonlinear dynamical systems serving as reservoirs has attracted much attention for the physical realization of reservoir computing (RC). Here, we propose a hardware system working as a reservoir with one simple form of nonlinearity that reflects the intrinsic characteristics of the materials. We show that insufficient dynamics in such physical systems can perform like complex dynamical systems with the assistance of external controls. Based on the idea of spatial multiplexing, this dynamical system is studied under two frameworks. The correlation between structural adjustments of the reservoir and system performance in processing various types of task is proposed. Our results are expected to enable the development of material-based devices for RC.

Decoding ultrafast polarization responses in lead halide perovskites by the two-dimensional optical Kerr effect

The ultrafast polarization response to incident light and ensuing exciton/carrier generation are essential to outstanding optoelectronic properties of lead halide perovskites (LHPs). A large number of mechanistic studies in the LHP field to date have focused on contributions to polarizability from organic cations and the highly polarizable inorganic lattice. For a comprehensive understanding of the ultrafast polarization response, we must additionally account for the nearly instantaneous hyperpolarizability response to the propagating light field itself. While light propagation is pivotal to optoelectronics and photonics, little is known about this in LHPs in the vicinity of the bandgap where stimulated emission, polariton condensation, superfluorescence, and photon recycling may take place. Here we develop two-dimensional optical Kerr effect (2D-OKE) spectroscopy to energetically dissect broadband light propagation and dispersive nonlinear polarization responses in LHPs. In contrast to earlier interpretations, the below-bandgap OKE responses in both hybrid CH3NH3PbBr3 and all-inorganic CsPbBr3 perovskites are found to originate from strong hyperpolarizability and highly anisotropic dispersions. In both materials, the nonlinear mixing of anisotropically propagating light fields results in convoluted oscillatory polarization dynamics. Based on a four-wave mixing model, we quantitatively derive dispersion anisotropies, reproduce 2D-OKE frequency correlations, and establish polarization-dressed light propagation in single-crystal LHPs. Moreover, our findings highlight the importance of distinguishing the often-neglected anisotropic light propagation from underlying coherent quasiparticle responses in various forms of ultrafast spectroscopy.

Aluminium alloy cross-sections under uniaxial bending and compression: A numerical study

The current study numerically investigates the structural behaviour of aluminium alloy square and rectangular hollow cross-sections under compression and uniaxial bending. Material and geometric nonlinear responses were carefully considered within finite element modelling. Geometric imperfections were also included through the execution of an initial eigenvalue buckling analysis. A thorough parametric study was carried out over a range of width-to-thickness ratios used in practice. Different initial loading eccentricities were examined generating various ratios of compressive axial load and bending moment at failure. The relatively new 6082-T6 heat-treated aluminium alloy, which is increasingly employed in structural applications owing to its high strength, was selected for this study. Based on the obtained numerical capacities, the EN 1999-1-1 design interaction curves were assessed providing rather conservative predictions, particularly for the stockiest cross-sections. The simplified Continuous Strength Method was, also, evaluated exhibiting slightly more accurate with less scattering strength provisions.

A method to quantify stiffness across the entire surface of a shoe‘s midsole

Quantifying the midsole material characteristics of athletic footwear is a standard task in footwear research and development. Current material testing protocols primarily focus on the determination of cushioning properties of the heel region or the quantification of the midsole properties as one assembly. However, midsoles possess different spatial material properties that have not been quantified from previous methodologies. Therefore, new material testing methods are required to quantify the local material response of athletic footwear. We developed a cyclical force-controlled material testing protocol for the determination of non-homogeneously distributed material stiffness with a high spatial resolution. In five prototype shoes varying in their stiffness distribution, we found that the material properties can be reliably measured across the midsole. Furthermore, we observed a characteristic non-linear material response regardless of the midsole location. We found that the material stiffness increased with an increase of the applied force and that this effect is further intensified by higher testing cycles. Additionally, the obtained midsole stiffness depends on the geometry of the midsole. We explored different approaches to reduce the measurement time of the testing protocol and found that the number of measurements can be reduced by 70% using 2 D-interpolation procedures. Determining the spatial material properties of midsoles needs to be considered to understand foot-shoe interactions. Furthermore, this measurement protocol can be used for quality control within the footwear and can be adapted for considering the effects of different running styles or speeds on ground force application characteristics.

Enhancing Reverse Saturable Absorption in SnS2 Nanosheets by Plasma Treatment.

The knowledge concerning the influence of defects on the nonlinear optical response of materials remains scarce so far. In this work, we have successfully introduced defects into SnS2 nanosheets by plasma treatment and shown that a defect generation is an effective approach to significantly improve the reverse saturable absorption of SnS2. The SnS2 nanosheets treated with Ar plasma for 40 s exhibit a nonlinear absorption coefficient (β0) as large as (2.9 ± 0.12) × 104 cm GW-1, which is nearly 9 times that of the untreated sample. The influence of Ar-plasma-treatment time, defect type, and defect number on the nonlinear absorption of SnS2 nanosheets are also studied. Structure and spectroscopy characterization confirms the introduction of S and Sn vacancies with Ar-plasma etching. Surface photovoltage spectroscopy and density functional theory calculation indicate that S vacancies can induce in-gap states in the band gap. These in-gap states act as intermediate states for the successive absorption of photons during femtosecond laser excitation (namely, excited-state absorption). In contrast, Sn defects cannot lead to in-gap states and have a limited contribution to nonlinear absorption. Our result would provide a promising way to improve optical nonlinearities.

A novel multi-scale large deformation approach for modelling of granular collapse

Collapse of granular material is usually accompanied by long run-out granular flows in natural hazards, e.g. rock/debris flow and snow avalanches. This paper presents a novel multi-scale approach for modelling granular column collapse with large deformation. This approach employs the smoothed particle hydrodynamics (SPH) method to solve large deformation boundary value problems, while using a micromechanical model to derive the nonlinear material response required by the SPH method. After examining the effect of initial cell size, the proposed approach is subsequently applied to simulate the flow of granular column in a rectangular channel at a low water content by varying the initial aspect ratio. The numerical results show good agreement with various experimental observations on both collapse process and final deposit morphology. Furthermore, the meso-scale behaviour is also captured owing to the advantages of the micromechanical model. Finally, it was demonstrated that the novel multi-scale approach is helpful in improving the understanding of granular collapse and should be an effective computational tool for the analysis of real-scale granular flow.

Data‐driven solvers for strongly nonlinear material response

AbstractThis work presents a data‐driven magnetostatic finite‐element solver that is specifically well suited to cope with strongly nonlinear material responses. The data‐driven computing framework is essentially a multiobjective optimization procedure matching the material operation points as closely as possible to given material data while obeying Maxwell's equations. Here, the framework is extended with heterogeneous (local) weighting factors—one per finite element—equilibrating the goal function locally according to the material behavior. This modification allows the data‐driven solver to cope with unbalanced measurement data sets, that is, data sets suffering from unbalanced space filling. This occurs particularly in the case of strongly nonlinear materials, which constitute problematic cases that hinder the efficiency and accuracy of standard data‐driven solvers with a homogeneous (global) weighting factor. The local weighting factors are embedded in the distance‐minimizing data‐driven algorithm used for noiseless data, likewise for the maximum entropy data‐driven algorithm used for noisy data. Numerical experiments based on a quadrupole magnet model with a soft magnetic material show that the proposed modification results in major improvements in terms of solution accuracy and solver efficiency. For the case of noiseless data, local weighting factors improve the convergence of the data‐driven solver by orders of magnitude. When noisy data are considered, the convergence rate of the data‐driven solver is doubled.

Microfluidic tuning of linear and nonlinear absorption in graphene oxide liquid crystals.

Manipulation of the nonlinear optical response of materials plays a significant role in photonics applications; however, it may be irreversible, untunable, and uncontrollable, which makes it difficult. In this Letter, we present a mechanical-hydrodynamical approach through a microchannel to tune the nonlinear absorption response of graphene oxide liquid crystals. In this material, the optical properties depend on the flake orientation. This feature has helped us to study empirically the dependency of the nonlinear absorption coefficients to external hydrodynamical force by employing the Z-scan technique. The experimental results show that increasing the flow rate in the microchannel enhances both linear and nonlinear absorption coefficients and, as a result, reduces the laser beam transmission through the sample. It has been observed that the percentage change in the nonlinear absorption coefficient of the sample is significant due to the flow rate.

Enhanced nonlinear optical effects based on strong coupling between epsilon-near-zero mode and gap surface plasmons

Optical nonlinear effect plays an important role in optical communication, optical detection, quantum information and other areas. However, it is constrained by the weakness of the nonlinear optical response of the common materials. The enhancement of the optical nonlinear response on a nanoscale becomes a critical challenge. Over the years, several ways to enhance the optical nonlinear effects have been suggested. In fact, these technologies can slightly enhance the optical nonlinear response. Recently, some research groups focused on the materials with vanished permittivity, which is called epsilon-near-zero (ENZ) material, showing that it can exhibit large optical nonlinearity due to the field enhancement in the material of this type. However, the ENZ material only holds a large optical nonlinear response in a limited spectral range. In order to overcome this limitation, here in this paper we report the ENZ mode which is excited by the ITO film and strongly coupled to the gap surface plasmons excited by the metal-dielectric-metal structure. To acquire the nonlinear refractive index <i>n</i><sub>2</sub>, we first calculate the ITO permittivity through the Drude-Lorentz model and find the wavelength of the ENZ material. Then we calculate the time-dependent electron temperature and lattice temperature of ITO by the two-temperature model. According to the elevated electron temperature, we can calculate the plasma frequency <inline-formula><tex-math id="M1">\begin{document}${\omega _{\rm p}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M1.png"/></alternatives></inline-formula>, and by taking it into the Drude-Lorentz model, we can obtain a new permittivity of ITO compared with the initial one. Finally, we can calculate the variation of the refractive index <inline-formula><tex-math id="M2">\begin{document}$ \Delta n $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M2.png"/></alternatives></inline-formula>, and the nonlinear refractive index <inline-formula><tex-math id="M3">\begin{document}$ {n_2} = \Delta n/{I_0} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210290_M3.png"/></alternatives></inline-formula>. In this paper, our coupled structure exhibits a broadband (～1000 nm bandwidth) enhancement of the nonlinear optical effect in the near-infrared spectrum, a maximum nonlinear refractive index <i>n</i><sub>2</sub> as large as 3.02 cm<sup>2</sup>·GW<sup>–1</sup>, which is nearly 3 orders larger than the previously reported nonlinear refractive index of bare ITO film. As a result, it is possible to realize a dramatically large variation of nonlinear refractive index under a low-power optical field. It is expected to be used in the nano photonic devices such as optical storage, all-optical switches, etc.

Refining rheological model for description of linear and nonlinear viscoelasticity of polymer systems

The article reviews the current mesoscopic modeling of flows for polymer solutions and melts of various structures. It also demonstrates the unified structure of the rheological constitutive relation, up to a certain dissipative function. Linear and nonlinear effects are considered for the simple shear and uniaxial tension of polymer melts based on the modified Vinogradov and Pokrovskii rheological model. The model can describe with adequate accuracy the linear viscoelasticity of fluid polymer systems, as well as transient processes at the shear flow and uniaxial elongation. It was compared with other experimental data for the melt of an industrial polyethylene sample. The nonlinear viscoelastic response of a polymer material was modeled at large periodic deformations. The calculation results were obtained via the Runge-Kutta approach with in-line subprograms of MATLAB IT environment. They were later compared with the experimental data for the solution of polyethylene oxide in dimethyl sulfoxide. The nonlinear behavior of the polymer sample manifested itself in the distortion of the viscoelastic response of the material at sinusoidal oscillations. In this case the shear stresses are no longer the correct harmonics and a "step" appears at the leading edge of the response. Besides, their amplitude is not proportional to the amplitude of the shift. The paper also considers the superposition of the oscillating shear flow on the simple shear. The distortion of the viscoelastic response is observed here though, unlike the high-amplitude periodic deformation, the curvatures of the upper and lower half-waves of the response differ. Since there is still no experimental data for this case, this work expects to encourage the researchers working in the field of nonlinear viscoelastic properties of polymer solutions and melts for further endeavors.

Mechanical properties of cell- and microgel bead-laden oxidized alginate-gelatin hydrogels.

3D-printing technologies, such as biofabrication, capitalize on the homogeneous distribution and growth of cells inside biomaterial hydrogels, ultimately aiming to allow for cell differentiation, matrix remodeling, and functional tissue analogues. However, commonly, only the mechanical properties of the bioinks or matrix materials are assessed, while the detailed influence of cells on the resulting mechanical properties of hydrogels remains insufficiently understood. Here, we investigate the properties of hydrogels containing cells and spherical PAAm microgel beads through multi-modal complex mechanical analyses in the small- and large-strain regimes. We evaluate the individual contributions of different filler concentrations and a non-fibrous oxidized alginate-gelatin hydrogel matrix on the overall mechanical behavior in compression, tension, and shear. Through material modeling, we quantify parameters that describe the highly nonlinear mechanical response of soft composite materials. Our results show that the stiffness significantly drops for cell- and bead concentrations exceeding four million per milliliter hydrogel. In addition, hydrogels with high cell concentrations (≥6 mio ml-1) show more pronounced material nonlinearity for larger strains and faster stress relaxation. Our findings highlight cell concentration as a crucial parameter influencing the final hydrogel mechanics, with implications for microgel bead drug carrier-laden hydrogels, biofabrication, and tissue engineering.

Modulation of the second-harmonic generation in MoS2 by graphene covering* *Project supported by Beijing Natural Science Foundation, China (Grant No. JQ19004), Beijing Excellent Talents Training Support, China (Grant No. 2017000026833ZK11), the National Natural Science Foundation of China (Grant Nos. 52025023, 51991340, and 51991342), the National Key Research and Development Program of China (Grant Nos. 2016YFA0300903 and 2016YFA0300804), the Key R&D

Nonlinear optical frequency mixing, which describes new frequencies generation by exciting nonlinear materials with intense light field, has drawn vast interests in the field of photonic devices, material characterization, and optical imaging. Investigating and manipulating the nonlinear optical response of target materials lead us to reveal hidden physics and develop applications in optical devices. Here, we report the realization of facile manipulation of nonlinear optical responses in the example system of MoS2 monolayer by van der Waals interfacial engineering. We found that, the interfacing of monolayer graphene will weaken the exciton oscillator strength in MoS2 monolayer and correspondingly suppress the second harmonic generation (SHG) intensity to 30% under band-gap resonance excitation. While with off-resonance excitation, the SHG intensity would enhance up to 130%, which is conjectured to be induced by the interlayer excitation between MoS2 and graphene. Our investigation provides an effective method for controlling nonlinear optical properties of two-dimensional materials and therefore facilitates their future applications in optoelectronic and photonic devices.

Nanoscale Engineering of Optical nonlinearity Based on a Metal Nitride/Oxide Heterostructure.

The abilities to modulate linear and nonlinear optical response of materials in the nanoscale are of central importance in the design and fabrication of photonic devices for applications like optical modulators. Here, based on a simple transition metal oxide/nitride (TiO2/TiN) system, we show that it is possible to tune the optical properties by controlling the nanoscale architecture. Through controlled oxidation of the plasmonic TiN nanoparticle surfaces, we observe a continuous change of linear and nonlinear optical (NLO) properties with the increase of the thickness of the oxide layer in the TiN/TiO2 heterogeneous architecture. The NLO response is manifested by the strong saturable absorption with a structurally tunable negative NLO absorption coefficient. The variation in the NLO absorption coefficient by up to 7-fold can be connected to the relative change in the volume fraction of the metallic core and the dielectric shell. We demonstrate further that the optimized TiN-TiO2 heterostructures can be used to drive an optical switch for pulse laser generation in the 1.5 μm wavelength region. Our results delineate a topochemical process for optimization of the NLO properties of common plasmonic materials for photonic applications based on simple materials chemistry.

Transient perturbative nonlinear responses of plasmonic materials

Recent investigations on optical nonlinearities of plasmonic materials suggest their responses may be even beyond the usual perturbative description. To better understand these surprisingly strong responses, we develop here a simple but general approach to describe the nonlinear optical response of plasmonic materials up to $n$th perturbation order. We apply the approach to understand spectral broadening occurring in resonant metasurfaces and investigate the enhancement of high-harmonic generation from multiply-resonant metasurfaces, predicting an over million-fold enhancement of higher harmonics.

Direct Reading of the Nonlinear Optical Response via Spatial Mapping

We propose and demonstrate a scheme for spatial mapping and direct reading of the nonlinear response of optical materials from the propagation of self-accelerating beam profiles. Through a single evolution measurement, a two-dimensional compact Airy beam is able to directly map the nonlinear response of a medium into spatial profiles. The most efficient mapping takes place along some particular transverse directions rather than the direction of the beam acceleration, depending on both the Airy intensity pattern and the type of nonlinearity. Our work may herald a simple yet effective way for measuring the nonlinear optical response, in contrast to the conventional Z-scan technique.