Large Nonlinearity Research Articles

Large third-order optical nonlinearities of two-dimensional CsPbBr3 nanoplatelets

Metal halide perovskites show considerable optical nonlinearity and could be used for cost-effective nonlinear optical devices if their nonlinear susceptibilities can be improved. Here, we report large optical nonlinearity, including third-order nonlinear absorption, refraction, and two-photon absorption excited luminescence, of CsPbBr3 nanoplatelets with a thickness of two or three atomic layers and a plane size of about 60 nm. Specifically, the nonlinear absorption was mainly induced by two-photon absorption at low incident powers, and the nonlinear absorption cross section reached 2.15 × 107 GM. It is two orders of magnitude larger than that of CsPbBr3 nanocrystals, which makes them an ideal optical limiting material. Furthermore, the nanoplatelets exhibited large self-phase modulation-induced nonlinear refraction, and the figures of merit W and T satisfied W >1 and T <1, which allow for optical switching. The large optical nonlinearity of CsPbBr3 nanoplatelets provides a basis for multifunctional applications in nonlinear optical devices.

Seismic and failure behavior simulation for RC shear walls under cyclic loading based on vector form intrinsic finite element

Seismic performance and failure mode simulations for reinforced concrete (RC) structures are impeded by large deformations and material nonlinearity particularly when subjected to the combined action of compression, bending and shear. Structural deformation and failure analysis based on traditional finite element (FE) often fails for the small–deformation assumption and global equilibrium. Moreover, it remains difficult to obtain convergence results for the existing FE methods by applying general concrete constitutive models for the complicity of anisotropic materials. To simulate the hysteretic performance and the damage development process of the RC shear wall under cyclic loading, the vector form intrinsic finite element (VFIFE) method with independent particles was adopted and combined with the two-directional concrete constitutive model considering the loading and unloading rules to perform large deformation and damage estimations. Concrete planar triangular element and fiber element for steel bar equipped with the hysteretic constitutive models were used to model six RC shear walls with different design parameters. Owing to the merits of avoiding repeated accumulation of the global stiffness matrix for vector mechanics, the planar structural behaviors involving biaxial stress–strain and loading–unloading behavior were numerically demonstrated. The simulated results were in close agreement with the experimental tests, including the hysteretic loop, skeleton curve, bending–shear deformation, and damage mode. This research also provides successive evidence for damage process simulation by VFIFE for RC structures under seismic loading considering a comprehensive constitutive relation.

Linearization for Microwave Photonic OFDM Transmission Systems Using an Iterative Algorithm Based on FEC Mechanism

A digital linearization algorithm is proposed to reduce the third-order intermodulation distortion (IMD3) for the microwave photonic (MWP) orthogonal frequency-division multiplexing (OFDM) transmission system with intensity modulation and direct detection. Forward error correction (FEC) is added to the OFDM signal to suppress the IMD3 in conjunction with an iterative operation. The distorted OFDM signal from the MWP system goes through iterative operations including fast Fourier transform, demodulation, error correction, signal reconstruction, and interference cancellation until the output converges. Compared with the non-iterative method and the iterative method without FEC mechanism, the proposed method has a significant advantage in linearizing signals with large nonlinearity and low signal-to-noise ratio. 200-Msym/s 64 quadrature-amplitude modulation (64-QAM) OFDM signals with a large peak-to-peak voltage of 650 mV are amplified by a power amplifier and then input to the MWP link and linearized by the FEC-based iterative method. The results show that the error vector magnitudes (EVMs) of the OFDM signals can be optimized from 13.1% to 2.9% and from 13.4% to 6.3% when the output <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_b/N₀</i> from the MWP link is about 35 dB and 13.5 dB, respectively. Besides, a 3-GHz 64-QAM OFDM signal is successfully transmitted through a 25-km standard single-mode fiber with an EVM of 3.9% after linearization.

Al2O3 tailored La0.8Sr0.2FeO3 crystallization in heavy metal oxide glass: Synthesis, structure, and enhanced linear &amp; nonlinear properties

Glass containing magnetic nanocrystals are attractive to provide high optical linear and nonlinearity properties. In this study, we reported the synthesis of perovskite La 0.8 Sr 0.2 FeO 3 nanocrystals in heavy metal oxide glass under the Al 2 O 3 tailoring. The influence of Al 2 O 3 amount to the formation of La 0.8 Sr 0.2 FeO 3 nanocrystals and the influence of nanocrystals to glass structure, optical linear& nonlinear properties were thoroughly investigated. The 10 nm-nanocrystals of orthogonal La 0.8 Sr 0.2 FeO 3 were synthesized by melting quenching followed with subsequent crystallization process at 400 °C for 30 min under the tuning of Al 2 O 3 . The formed La 0.8 Sr 0.2 FeO 3 were well distributed in matrix without aggregation. Structure and chemical valence study revealed the aluminum abnormality effect and the Sr 2+ induced multi-valence states of Fe ions and oxygen vacancies in La 0.8 Sr 0.2 FeO 3 lattice. Such modification clearly influenced the optical absorption, refractive index, polarizability, energy band gap shrinkage and nonlinearity. Physical parameters such as oxygen packing density, free volume etc. were calculated to confirm the influence of Al 2 O 3 tailored La 0.8 Sr 0.2 FeO 3 crystallization to glass. The glass with 10%Al 2 O 3 amount exhibited a large thermal stability (132 °C), low thermal expansion coefficient (10.2 ×10 -6 /K) and high BO 4 /AlO 4 units, providing suitable environment for La 0.8 Sr 0.2 FeO 3 crystallization. About 20 nm nanocrystals were formed and well distributed in glass which contributed to large nonlinearity absorption coefficient (5.19 ×10 −10 m/W) and FOM (13.6 ×10 3 esu cm) which much superior than from relative literatures. The obtained glass with extremely good optical linear and nonlinearity performances can be promising candidate for photonics device applications. • Synthesis and characterization of La 0.8 Sr 0.2 FeO 3 nanocrystals in PbO-Bi 2 O 3 -B 2 O 3 glass under Al 2 O 3 tailoring. • 10 nm-nanocrystals of orthogonal La 0.8 Sr 0.2 FeO 3 were synthesized at 400 °C for 30 min at 10% Al 2 O 3 . • Sr 2+ induced oxygen vacancy and multi-valence states of Fe ions in lattice increased polarizability. • La 0.8 Sr 0.2 FeO 3 crystallization red shifted optical absorption edge and decreased E g of glass. • Glass with large α 3 (5.19 ×10 −10 m/W) and FOM (13.6 ×10 3 esu) is promising for nonlinear devices.

Nonlinear optical properties of Bi0.5Na0.5TiO3 thin films grown by PLD

The present work investigates the role of oxygen partial pressure (PO2) during the thin film growth in obtaining phase and controlling the crystallinity and optical responses in the thin films. Rietveld refinement of X-ray diffraction confirmed a rhombohedral structure of BNT as a major phase with secondary phase of Bi2Ti2O7 and Bi4Ti3O12. The diminutions of the secondary phase are observed with an increase in PO2, which signifies the crystal structure closely related to the partial oxygen pressure. The refractive index of films was found to be improved and optical bandgap energy was reduced with PO2 due to the increase in crystallinity as well as decrease in oxygen vacancies. Nonlinear optical properties show a strong PO2 dependency, self-focusing behaviour with a positive, large optical nonlinearity (n2 = 4.62 × 10−6 cm2/W) and strong absorbance (β = 0.755 cm/W) for the film deposited at 10 Pa, which makes a potential candidate for the nonlinear photonic device applications.

Near-infrared sensitive two-wave mixing adaptive interferometer based on a liquid crystal light valve with a semiconductor substrate.

Two-wave mixing adaptive interferometer based on a liquid crystal light valve with a semiconductor GaAs substrate is realized and studied at 1064 nm wavelength. The local response of the dynamic hologram recorded in the liquid crystal layer of the light valve allows for detection of small phase modulations of the object beam. The characteristics of the interferometer are estimated experimentally. The temporal adaptability lies in the subsecond range. The large optical nonlinearity of the cell is favorable for measurements of small displacements with high sensitivity.

Third-order optical nonlinearity of CsPb(Br/I)3 metal halide perovskites nano-crystals embedded chalcogenide glass.

The nonlinear optical properties of emerging metal halide perovskites (MHP) materials are sufficiently intriguing that this topic has become the hotspots in the realm of material science. Hence, we investigate the third-order nonlinear optical properties of CsPbBrx/I3-x (x = 1, 2, 3) MHP nano-crystals (NCs) embedded chalcogenide glass (ChG) within a GeS2-Sb2S3 pseudo-binary system, by monitoring the composition, excitation wavelength and intensity dependencies via femtosecond Z-scan technique. We have found that the intrinsic large optical nonlinearity of ChG can be further enhanced because of the incorporation of MHP NCs, and that the optical nonlinearity of MHP-ChG containing pristine Br NCs is more pronounced compared to its counterparts with mixed Br/I NCs, due to a combination of multiple factors.

New N-pyrimidinyl stilbazolium crystals for second-order nonlinear optics

We report a new π-conjugated cationic chromophore based on phenolic N-pyrimidinyl stilbazolium and its corresponding non-centrosymmetric crystals. The new cationic chromophore, HPR (4-(4-hydroxy-3-methoxystyryl)-1-(pyrimidin-2-yl)pyridin-1-ium), consists of a strong electron donor, the 4-hydroxy-3-methoxyphenyl group based on two electron-donating groups, and a strong electron acceptor, the N-pyrimidinyl pyridinium group based on two electron-withdrawing groups. The HPR chromophore possesses large molecular optical nonlinearity with first hyperpolarizability of up to 264 × 10−30 esu, which is significantly larger than that of the benchmark stilbazolium chromophores. In solution, the HPR chromophore showed co-existence of phenol- and phenolate-like forms with two absorption bands (∼460 and ∼610 nm, respectively). In the crystalline state, all HPR-based derivatives with three different counter anions, N2S (naphthalene-2-sulfonate), VBS (4-vinylbenzenesulfonate), and NBS (3-nitrobenzenesulfonate), exhibit a macroscopic second-order nonlinear optical response. HPR-N2S crystals exhibit non-centrosymmetric monoclinic Pn space group symmetry and large off-diagonal effective macroscopic optical nonlinearity (94 × 10−30 esu), which is approximately four times higher than that of the benchmark stilbazolium crystals. Therefore, the newly developed HPR-based crystals are highly promising materials for second-order nonlinear optical applications.

Phonon-Suppressing Intermolecular Adhesives: Catechol-Based Broadband Organic THz Generators.

Solid‐state molecular phonons play a crucial role in the performance of diverse photonic and optoelectronic devices. In this work, new organic terahertz (THz) generators based on a catechol group that acts as a phonon suppressing intermolecular adhesive are developed. The catechol group is widely used in mussel‐inspired mechanical adhesive chemistry. Newly designed organic electro‐optic crystals consist of catechol‐based nonlinear optical 4‐(3,4‐dihydroxystyryl)‐1‐methylpyridinium (DHP) cations and 4‐(trifluoromethyl)benzenesulfonate anions (TFS), which both have multiple interionic interaction capability. Interestingly, compared to benchmark organic crystals for THz generators, DHP‐TFS crystals concomitantly achieve top level values of the lowest void volume and the highest crystal density, resulting in an exceptionally small amplitude of solid‐state molecular phonons. Simultaneously achieving small molecular phonon amplitude, large optical nonlinearity and good phase matching at infrared optical pump wavelengths, DHP‐TFS crystals are capable of generating broadband THz waves of up to 16 THz with high optical‐to‐THz conversion efficiency; one order of magnitude higher than commercial inorganic THz generators.

Measuring free surface elevation of shoaling waves with pressure transducers

An assessment of formulas to recover wave surface elevation from pressure measurements was carried out in the present study. The investigation focused on the formulas’ performance in the shoaling region, i.e. where the wave nonlinearity gradually increases as the wave travels towards shallower waters. Formulas based on linear wave theory alongside nonlinear reconstructions were considered. Experiments in a large-scale wave flume provided with a concrete beach profile were performed, in which regular waves were generated and surface elevation was measured with acoustic, resistive and pressure gauges. The considered formulas require the application of a cutoff frequency to the wave signal in order to avoid high frequencies amplification that progressively arise as wave shoaling occur. A simple but effective method to obtain a reference cutoff frequency is proposed in the present work; the method is based on a polynomial fitting of the unfiltered wave energy spectrum. A sensitivity analysis of each formula to the variation of this cutoff frequency was carried out. Results showed that all the investigated formulas recover wave elevation fairly well for low-nonlinearity waves, whereas overestimating wave crest height as nonlinearity increases. Wave reconstruction of the linear formulation performance was comparable to nonlinear formulations in terms of wave crest height reconstruction, although tending to amplify frequencies in the wave trough. Moreover, the performance of the formulas to correctly recover the asymmetry and flatness of the surface elevation distribution was assessed by analysing third- and fourth-order moment statistics. In this sense, nonlinear reconstruction formulas performed better in recovering the asymmetric distribution of the wave elevation, with the formula based on linear wave theory underestimating skewness and kurtosis for large nonlinearity waves.

Hybrid Integration of Deterministic Quantum Dot‐Based Single‐Photon Sources with CMOS‐Compatible Silicon Carbide Photonics

AbstractThin film 4H‐silicon carbide (4H‐SiC) is emerging as a contender for realizing large‐scale optical quantum circuits due to its high CMOS technology compatibility and large optical nonlinearities. Though, challenges remain in producing wafer‐scale 4H‐SiC thin film on insulator (4H‐SiCOI) for dense integration of photonic circuits, and in efficient coupling of deterministic quantum emitters that are essential for scalable quantum photonics. Here, hybrid integration of self‐assembled InGaAs quantum dot (QD)‐based single‐photon sources (SPSs) with wafer‐scale 4H‐SiC photonic chips prepared by ion slicing technique is demonstrated. By designing a bilayer vertical coupler, generation and highly efficient routing of single‐photon emission in the hybrid quantum photonic chip are realized. Furthermore, a chip‐integrated beamsplitter operation for triggered single photons through fabricating a 1 × 2 multimode interferometer (MMI) with a symmetric power splitting ratio of 50:50 is realized. The successful demonstration of heterogeneously integrating QD‐based SPSs on 4H‐SiC photonic chip prepared by ion slicing technique constitutes an important step toward CMOS‐compatible, fast reconfigurable quantum photonic circuits with deterministic SPSs.

Efficient Low Threshold Frequency Conversion in AlGaAs-On-Insulator Waveguides

A design study is presented for an efficient, compact and robust device to convert the frequency of single-photons from the near-infrared to the telecom C-band. The material platform aluminum gallium arsenide (AlGaAs)-on-insulator, with its relatively large second-order nonlinearity, is used to create highly confined optical modes. This platform can feasibly incorporate single-photon emitters such as indium arsenide (InAs) on gallium arsenide (GaAs), paving the way towards direct integration of single-photon sources and nonlinear waveguides on the same chip. In this design study, single-pass difference-frequency generation (DFG) producing C-band single-photons is enabled via form birefringent phase-matching between a 930 nm single-photon pump and continuous wave (CW) idler at 2,325 nm. In particular the idler and single-photons are combined with an on-chip directional coupler, and then tapered to a single waveguide where the three modes are phase-matched. The design is studied at a special case, showing high fabrication tolerances, and an internal conversion efficiency up to 41%.

Conserved spacing multi-wavelength mode-locked erbium-doped fiber laser based on barium titanate saturable absorber

A compact multi-wavelength harmonic passive mode-locked (MWHML) erbium-doped fiber laser (EDFL) has been demonstrated by integrating a Barium Titanate (BaTiO3) in the ring cavity configuration. The BaTiO3 with 9.5% modulation depth serves as a saturable absorber (SA) and is optically deposited by the Top-Down method to form an end face fiber integrated saturable absorber. Both the saturable absorption property and the large third-order nonlinearity of BaTiO3 assisted in generating a second-order harmonic pulse beside the fundamental frequency. Moreover, in real-time, eight wavelengths around 1560 nm with 0.7 nm wavelength spacing were produced with a maximum output power of 2.7 mW pulse duration of 5.2 ps. These results further suggest that BaTiO3 could be a good candidate for the saturable absorber and high nonlinear photonic device for related applications.

Stock Price Prediction Using XCEEMDAN-Bidirectional LSTM -Spline

Bidirectional Long Short Term Memory (Bidirectional LSTM) is a machine learning technique with the ability to capture data context by traversing backward data to forward data and vice versa. However, the characteristics of stock data with large fluctuations, high dimensions and non-linearity become a challenge in obtaining high stock price prediction accuracy values. The purpose of this study is to provide a solution to the problem of stock data characteristics with large fluctuations, high dimensions and non-linearity by combining the Complete Ensemble Empirical Mode Decomposition With Adaptive Noise method for exogenous features (XCEEMDAN), Bidirectional Long Short Term Memory (LSTM), and Splines. The predicted data will go through normalization and preprocessing using XCEEMDAN then the XCEEMDAN decomposition results are divided into high and low frequency signals. The bidirectional LSTM handles high frequency signals and the Spline model handles low frequency signals. The test is carried out by comparing the proposed XCEEMDAN-Bidirectional LSTM-Spline model with the XCEEMDAN-LSTM-Spline model using the same parameters and changing the noise seed randomly 50 times. The test results show that the proposed model has the smallest RMSE average value of0.787213833 while model which is compared only has the smallest RMSE average value of 0.807393567.

Observation of Nonlinearity of Generalized King Plot in the Search for New Boson

We measure isotope shifts for neutral Yb isotopes on an ultranarrow optical clock transition S10−P03 with an accuracy of a few hertz. Combined with one of the recently reported isotope-shift measurements of Yb+ on two optical transitions, the result allows us to construct the King plots—a set of scaled isotope shifts data on two different optical transitions plotted in two-dimensional plane. When only the leading-order terms of isotope shifts are taken into account, a King plot should exhibit a linear relation as a result of elimination of the leading nuclear-size dependence. Extremely large nonlinearity unexplainable by a quadratic field shift is revealed, which was proposed previously as a source of the observed nonlinearity of the King plot. We further construct the generalized King plot with three optical transitions so that we can eliminate the contribution arising from a higher-order effect within the standard model. Our analysis of the generalized King plot shows a deviation from linearity at the 3σ level, indicating that there exist at least two higher-order contributions in the measured isotope shifts. Under reasonable assumptions, we obtain the upper bound of the product of the couplings for a new boson, mediating a force between electrons and neutrons—|yeyn|/(ℏc)<1×10−10 for the mass less than 1 keV—with the 95% confidence level, providing an important step toward probing new physics via isotope-shift spectroscopy.2 MoreReceived 18 October 2021Accepted 16 March 2022DOI:https://doi.org/10.1103/PhysRevX.12.021033Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectronic structure of atoms & moleculesElectronic transitionsHypothetical particle physics modelsNuclear charge distributionPhysical SystemsAtomsHypothetical particlesTechniquesPrecision measurementsSpectroscopyAtomic, Molecular & OpticalParticles & Fields

An Unusual Damped Stability Property and its Remedy for an Integration Method

An unusual stability property is found for a structure-dependent integration method since it exhibits a different nonlinearity interval of unconditional stability for zero and nonzero damping. Although it is unconditionally stable for the systems of stiffness softening and invariant as well as most systems of stiffness hardening, an unstable solution that is unexpected is obtained as it is applied to solve damped stiffness hardening systems. It is found herein that a nonlinearity interval of unconditional stability for a structure-dependent method may be drastically shrunk for nonzero damping when compared to zero damping. In fact, it will become conditionally stable for any damped stiffness hardening systems. This might significantly restrict its applications. An effective scheme is proposed to surmount this difficulty by introducing a stability factor into the structure-dependent coefficients of the integration method. This factor can effectively amplify the nonlinearity intervals of unconditional stability for structure-dependent methods. A large stability factor will result in a large nonlinearity interval of unconditional stability. However, it also introduces more period distortion. Consequently, a stability factor must be appropriately selected for accurate integration. After choosing a proper stability factor, a structure-dependent method can be widely and easily applied to solve general structural dynamic problems.

Enhancement of the second harmonic generation from monolayer WS2 coupled with a silica microsphere

Monolayer transition metal dichalcogenides (TMDs) are widely used for integrated optical and photoelectric devices. Owing to their broken inversion symmetry, monolayer TMDs have a large second-order optical nonlinearity. However, the optical second-order nonlinear conversion efficiency of monolayer TMDs is still limited by the interaction length. In this work, we theoretically study the second harmonic generation (SHG) from monolayer tungsten sulfide (WS2) enhanced by a silica microsphere cavity. By tuning the position, size, and crystal orientation of the material, second-order nonlinear coupling can occur between the fundamental pump mode and different second harmonic cavity modes, and we obtain an optimal SHG conversion efficiency with orders of magnitude enhancement. Our work demonstrates that the microsphere cavity can significantly enhance SHG from monolayer 2D materials under flexible conditions.

Exploiting a strong coupling regime of organic pentamer surface plasmon resonance based on the Otto configuration for creatinine detection.

The sandwiched material-analyte layer in the surface plasmon resonance (SPR)-Otto configuration emulates an optical cavity and, coupled with large optical nonlinearity material, the rate of light escaping from the system is reduced, allowing the formation of a strong coupling regime. Here, we report an organic pentamer SPR sensor using the Otto configuration to induce a strong coupling regime for creatinine detection. Prior to that, the SPR sensor chip was modified with an organic pentamer, 1,4-bis[2-(5-thiophene-2-yl)-1-benzothiopene]-2,5-dioctyloxybenzene (BOBzBT2). To improve the experimental calibration curve, a normalisation approach based on the strong coupling-induced second dip was also developed. By using this procedure, the performance of the sensor improved to 0.11 mg/dL and 0.36 mg/dL for the detection and quantification limits, respectively.

Tunable microcavities coupled to rare-earth quantum emitters

Electro-optical control of on-chip photonic devices is an essential tool for efficient integrated photonics. Lithium niobate on insulator (LNOI) is an emerging platform for on-chip photonics due to its large electro-optic coefficient and high nonlinearity. Integrating quantum emitters into LNOI would extend their versatility in classic photonics to quantum computing and communication. Here, we incorporate rare-earth ion (REI) quantum emitters into electro-optical tunable lithium niobite (LN) thin films and demonstrate control of LN microcavities coupled to REIs over a frequency range of 160 GHz with 5 µs switching speed. Dynamic control of the cavities enables modulation of the Purcell enhancement of REIs with short time constants. Using Purcell enhancement, we show evidence of detecting single Y b 3 + ions in LN cavities. Coupling quantum emitters in fast tunable photonic devices is an efficient method to shape the waveform of the emitter. It also offers a platform to encode quantum information in the integration of a spectral–temporal–spatial domain to achieve high levels of channel multiplexing, as well as an approach to generate deterministic single-photon sources.

A backpropagation with gradient accumulation algorithm capable of tolerating memristor non-idealities for training memristive neural networks

Memristive neural network (MNN) has emerged as a new computing architecture with high speed and low power consumption, but its hardware implementation is hampered mainly by the device non-idealities of memristors. Here, we propose a backpropagation with gradient accumulation (BP-GA) algorithm which can effectively tolerate the memristor non-idealities. We first show that a memristor-based single-layer perceptron trained with BP-GA achieves high image recognition accuracies (>85% on the MNIST dataset) with a wide range of learning rates (0.01–50), large nonlinearities (>6), a small number of conductance states (even down to 3 states), a broad spectrum of ON/OFF ratios (across 3 orders of magnitude), and large noises (up to 40%). The origin for such good robustness against the learning rate and memristor non-idealities is then investigated and revealed to be associated with the operation mechanism of BP-GA. In this algorithm, the weights can keep increasing in magnitude due to the gradient accumulation and therefore become movable even at a small learning rate (or a large ON/OFF ratio equivalently). Moreover, the weights corresponding to the foreground and background of the input image are appropriately moved to the positive and negative boundaries of the weight range, respectively, thus allowing the learning of the image features using only a small number of conductance states. These boundary weights are trapped there without significant oscillation under the effects of accumulated gradients, resulting in immunity to large nonlinearity and noise. Therefore, BP-GA enables the MNN to be insensitive to the learning rate and robust against the memristor non-idealities. The performance of BP-GA is further evaluated on the memristor-based multilayer perceptron (on the MNIST dataset) and convolutional neural network (on the Cifar-10 dataset). For both MNNs, BP-GA exhibits relatively high accuracies and good tolerance against memristor non-idealities, demonstrating its applicability to complex networks and problems. This study provides a viable approach at the algorithm level for addressing some important hardware implementation issues of MNNs using realistic memristors.