Bistable Hysteresis Research Articles

Manipulation of lasing modes in a deformed octagonal microcavity laser

We have demonstrated a deformed octagonal microcavity semiconductor laser with manipulated lasing modes for bistable operation and direct modulation. There are two sets of degenerated four-bounced modes, S01 and S02, in the octagonal microcavity, and the degeneracy between them is broken by introducing a square hole into the center of the cavity. In the deformed octagonal microcavity laser, mode S01 dominates the lasing process during the current rising process. However, mode S02 also lases when the current decreases and interacts nonlinearly with S01, which is caused by the non-uniform distribution of the refractive index induced by the square-ring-shaped current injection. We observe a counterclockwise bistable hysteresis loop with continuous injection current ranging from 31 to 13 mA at 288 K. We also study the small-signal modulation response of the laser at high and low states with different injection currents. By utilizing the photon-photon resonance effect between modes S01 and S02, we effectively increased the 3-dB bandwidth of the laser from 12 GHz to 16.2 GHz.

Dynamic all-optical memory switching based on atomic optical bistable behavior in a three level Λ-type atomic system

We theoretically investigate the atomic optical bistability (AOB) in a three-level Λ-type atomic system confined in a unidirectional optical ring cavity. The role of the intensity or detuning of the control field on AOB is explored, and results show that absorption, dispersion, and nonlinearity can be modified significantly by the control field due to quantum coherence and interference in multilevel atomic systems. Thus, tuning the intensity or detuning of the control field can manipulate the switch-up and switch-down thresholds, as well as the area of the bistable hysteresis loop. According to the controllability of AOB, we design various schemes to realize dynamical all-optical switching between the high and low outputs of two bistable curves for a fixed cavity input. In addition, dynamical all-optical memory switching can be implemented by adding a pulse sequence for the intensity or detuning of the control field. For appropriate parameters, such as the cooperative coefficient, the extinction ratio of the switching can be improved dramatically.

Modulation of Voltage-Gating and Hysteresis of Lysenin Channels by Cu2+ Ions.

The intricate voltage regulation presented by lysenin channels reconstituted in artificial lipid membranes leads to a strong hysteresis in conductance, bistability, and memory. Prior investigations on lysenin channels indicate that the hysteresis is modulated by multivalent cations which are also capable of eliciting single-step conformational changes and transitions to stable closed or sub-conducting states. However, the influence on voltage regulation of Cu2+ ions, capable of completely closing the lysenin channels in a two-step process, was not sufficiently addressed. In this respect, we employed electrophysiology approaches to investigate the response of lysenin channels to variable voltage stimuli in the presence of small concentrations of Cu2+ ions. Our experimental results showed that the hysteretic behavior, recorded in response to variable voltage ramps, is accentuated in the presence of Cu2+ ions. Using simultaneous AC/DC stimulation, we were able to determine that Cu2+ prevents the reopening of channels previously closed by depolarizing potentials and the channels remain in the closed state even in the absence of a transmembrane voltage. In addition, we showed that Cu2+ addition reinstates the voltage gating and hysteretic behavior of lysenin channels reconstituted in neutral lipid membranes in which lysenin channels lose their voltage-regulating properties. In the presence of Cu2+ ions, lysenin not only regained the voltage gating but also behaved like a long-term molecular memory controlled by electrical potentials.

Nonlinear optical bistability based on epsilon-near-zero mode in near-infrared band.

We propose a simple thin-layer structure based on epsilon-near-zero mode field enhancement to achieve optical bistability in the near-infrared band. The high transmittance provided by the thin-layer structure and the electric field energy limited in the ultra-thin epsilon-near-zero material means that the interaction between the input light and the epsilon-near-zero material can be greatly enhanced, creating favorable conditions for the realization of optical bistability in near-infrared band. The optical bistability hysteresis curve is closely related to the incident angle of light and the thickness of epsilon-near-zero material. This structure is relatively simple and easy to prepare, so we believe that this scheme will have a positive effect on the practicality of optical bistability devices in all-optical devices and networks.

First-Order Reversal Curves of Sets of Bistable Magnetostrictive Microwires.

Amorphous microwires have attracted substantial attention in the past decade because of their useful technological applications. Their bistable magnetic response is determined by positive or negative magnetostriction, respectively. First-order reversal curves (FORC) are a powerful tool for analyzing the magnetization reversal processes of many-body ferromagnetic systems that are essential for a deeper understanding of those applications. After theoretical considerations about magnetostatic interactions among microwires, this work introduces a systematic experimental study and analysis of the FORC diagrams for magnetostrictive microwires exhibiting an individually bistable hysteresis loop, from a single microwire to sets of an increasing number of coupled microwires, the latter considered as an intermediate case to the standard many-body problem. We performed the study for sets of quasi-identical and different hysteretic microwires where we obtained the coercivity Hc and interaction Hu fields. In the cases with relevant magnetostatic interactions, FORC analysis supplies deeper information than standard hysteresis loops since the intrinsic fluctuations of the switching field generate a complex response. For sets of microwires with very different coercivity, the coercivity distributions of the individual microwires characterize the FORC diagram.

Magnetic-field-engineered coherent perfect absorption and transmission

An experimental work [W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011)] showed that a resonator that contains a loss medium instead of a gain medium enables coherent perfect absorption (CPA) by interference. Here, we propose an alternative approach to realize such a CPA and coherent perfect transmission (CPT) as well as the switching between CPA and CPT in a cavity quantum electrodynamics (CQED) system by applying an external magnetic field. The proposed CPA and CPT scheme is based on the magnetically induced transparency (MIT) configuration, instead of the conventional electromagnetically induced transparency configuration, which offers a sensitive method to tune CPA and CPT and also is conducive to the flexible control of the CPA and CPT scheme. Under the linear and nonlinear excitation regimes, we derive the approximate analytical solutions of the cavity-output power and the CPA criteria of the CQED system, and find that the CPA can occur at different frequencies in both regimes. In the nonlinear excitation regime, the relationship between the cavity-output power and the cavity-input power can show a bistable characteristic by the control of the static magnetic field, and the CPA point is near the turning point of the cavity-input power on the bistable return hysteresis curve. Furthermore, the line shape and the threshold value for optical bistability can be flexibly controlled by varying the magnetic field under experimentally accessible conditions, thus the magnetic field can well tune the CPA. Also, we compare the analytical and numerical results of the cavity-output power in the nonlinear excitation regime, and they are in good agreement. Our results show that the CQED system based on the MIT configuration can be used as a perfect absorber or nearly perfect transmitter, which may have practical applications in optical logic and optical communication devices.

Nonlinear dynamics analysis of a dual-rotor-bearing-casing system based on a modified HB-AFT method

This paper presents a modified harmonic balance-alternating frequency/time domain (HB-AFT) method to analyze the nonlinear dynamics of a dual-rotor-bearing-casing system. The motion equations of a dual-rotor-bearing-casing system subjected to the unbalanced excitations of the two rotors are formulated with 284 degrees of freedom, in which, the complex nonlinear factors of the inter-shaft bearing such as exponential nonlinear restoring force, radial clearance and varying stiffness excitation are taken into consideration. The HB-AFT method is modified by applying the AFT procedure to obtain the harmonic expending coefficients of the harmonic balance residuals rather than that of the nonlinear terms, hence, the Jacobian matrix is calculated programmatically and efficiently, as a result the performance of the HB-AFT method is improved greatly. The primary resonance of the system is analyzed by employing the three-dimensional diagrams of amplitude-frequency responses of each node of the system, including the inner casing and the outer casing. In addition, the amplitude-frequency response curves with separated frequencies and orbits of the two rotors are also discussed. Furthermore, the pseudo-arclength continuation procedure is introduced into the modified HB method, then all periodic solution branches of the system including the unstable solutions are obtained. The results show that there are two resonant peaks in the amplitude-frequency response curves of the system and the vibration of each part of the system, i.e., LPC, LPT, HPC, HPT, inner casing and outer casing, is synchronous. Besides, the nonlinear dynamic behaviors such as vibration jumping, bi-stable and resonance hysteresis are revealed. Accordingly, the dynamic load of the inter-shaft bearing is calculated. The results show that the evolution of the inter-shaft bearing’s dynamic load is associated with the vibration responses of the two rotors. The nonlinear characteristics of the force-frequency responses of the inter-shaft bearing are consistent with that of the two rotors and casings. In addition, with the increase of the inter-shaft bearing clearance, the nonlinear characteristics of the force-frequency responses of the inter-shaft bearing are more significant. In comparison with the Newmark method, the modified HB-AFT method proposed in this paper has a great advantage in computing efficiency, and it can also grasp all solution branches of the system including the unstable solutions. Consequently, it has great potential to deal with high-dimensional systems with complex nonlinearities and multifrequency excitations in practical engineering.

Optical bi-stability in cubic silicon carbide microring resonators.

We measure the photothermal nonlinear response in suspended cubic silicon carbide (3C-SiC) and 3C-SiC-on-insulator (SiCOI) microring resonators. Bi-stability and thermo-optic hysteresis is observed in both types of resonators, with the suspended resonators showing a stronger response. A photothermal nonlinear index of 4.02×10-15 m2/W is determined for the suspended resonators, while the SiCOI resonators demonstrate one order of magnitude lower photothermal nonlinear index of 4.32×10-16 m2/W. Cavity absorption and temperature analysis suggest that the differences in thermal bi-stability are due to variations in waveguide absorption, likely from crystal defect density differences throughout the epitaxially grown layers. Furthermore, coupled mode theory model shows that the strength of the optical bi-stability, in suspended and SiCOI resonators can be engineered for high power or nonlinear applications.

Design, Computational Modelling and Experimental Characterization of Bistable Hybrid Soft Actuators for a Controllable-Compliance Joint of an Exoskeleton Rehabilitation Robot

This paper presents the mechatronic design of a biorobotic joint with controllable compliance, for innovative applications of “assist-as-needed” robotic rehabilitation mediated by a wearable and soft exoskeleton. The soft actuation of robotic exoskeletons can provide some relevant advantages in terms of controllable compliance, adaptivity and intrinsic safety of the control performance of the robot during the interaction with the patient. Pneumatic Artificial Muscles (PAMs), which belong to the class of soft actuators, can be arranged in antagonistic configuration in order to exploit the variability of their mechanical compliance for the optimal adaptation of the robot performance during therapy. The coupling of an antagonistic configuration of PAMs with a regulation mechanism can achieve, under a customized control strategy, the optimal tuning of the mechanical compliance of the exoskeleton joint over full ranges of actuation pressure and joint rotation. This work presents a novel mechanism, for the optimal regulation of the compliance of the biorobotic joint, which is characterized by a soft and hybrid actuation exploiting the storage/release of the elastic energy by bistable Von Mises elastic trusses. The contribution from elastic Von Mises structure can improve both the mechanical response of the soft pneumatic bellows actuating the regulation mechanism and the intrinsic safety of the whole mechanism. A comprehensive set of design steps is presented here, including the optimization of the geometry of the pneumatic bellows, the fabrication process through 3D printing of the mechanism and some experimental tests devoted to the characterization of the hybrid soft actuation. The experimental tests replicated the main operating conditions of the regulation mechanism; the advantages arising from the bistable hybrid soft actuation were evaluated in terms of static and dynamic performance, e.g., pressure and force transition thresholds of the bistable mechanism, linearity and hysteresis of the actuator response.

Optical hysteresis shape transformation using linear polarization components

We provide a mathematical model to elucidate how a linear polarizer can be used to transform the shape of an optical-power hysteresis curve into the canonical counterclockwise (CCW) shape, clockwise (CW) shape, and upward-switching and downward-switching butterfly shapes. This transformation is possible for optical signals whose states of polarization also exhibit hysteresis. Critical to our model is a generalized Malus' law that accounts for elliptical input polarization as well as insertion loss, finite extinction ratio, and pass-axis orientation angle of the linear polarizer. The generalized Malus' law reveals that the transmittivity of the polarizer itself exhibits a bistable hysteresis curve, and this transmittivity acts on the input-power hysteresis curve to produce the variety of output-power shapes. Additionally, we model the optimization of the hysteresis contrast of the CCW and CW shapes, achieving 20 dB or more by using a polarization controller placed upstream of the polarizer. Modeling and experimental validation are carried out using a polarization-varying bistable signal generated by an anisotropic Fabry–Perot semiconductor optical amplifier, and the results are applicable to other nonlinear resonators and means of polarization-varying signal generation. This model can be used for the study, design, and optimization of a variety of sequential and combinational all-optical signal processing applications.

Landau-like theory for buckling phenomena and its application to the elastica hypoarealis

Bifurcation phenomena are ubiquitous in elasticity, but their study is often limited to linear perturbation or numerical analysis since second or higher variations are often beyond an analytic treatment. Here, we review two key mathematical ideas, namely, the splitting lemma and the determinacy of a function, and show how they can be fruitfully used to derive a reduced function, named Landau expansion in the paper, that allows us to give a simple but rigorous description of the bifurcation scenario, including the stability of the equilibrium solutions. We apply these ideas to a paradigmatic example with potential applications to various softly constrained physical systems and biological tissues: a stretchable elastic ring under pressure. We prove the existence of a tricritical point and find bistability effects and hysteresis when the stretching modulus is sufficiently small. These results seem to be in qualitative agreement with some recent experiments on heart cells.

Hysteresis and linear stability analysis on multiple steady-state solutions to the Poisson-Nernst-Planck equations with steric interactions.

In this work, we numerically study linear stability of multiple steady-state solutions to a type of steric Poisson-Nernst-Planck equations with Dirichlet boundary conditions, which are applicable to ion channels. With numerically found multiple steady-state solutions, we obtain S-shaped current-voltage and current-concentration curves, showing hysteretic response of ion conductance to voltages and boundary concentrations with memory effects. Boundary value problems are proposed to locate bifurcation points and predict the local bifurcation diagram near bifurcation points on the S-shaped curves. Numerical approaches for linear stability analysis are developed to understand the stability of the steady-state solutions that are only numerically available. Finite difference schemes are proposed to solve a derived eigenvalue problem involving differential operators. The linear stability analysis reveals that the S-shaped curves have two linearly stable branches of different conductance levels and one linearly unstable intermediate branch, exhibiting classical bistable hysteresis. As predicted in the linear stability analysis transition dynamics, from a steady-state solution on the unstable branch to one on the stable branches, are led by perturbations associated to the mode of the dominant eigenvalue. Further numerical tests demonstrate that the finite difference schemes proposed in the linear stability analysis are second-order accurate. Numerical approaches developed in this work can be applied to study linear stability of a class of time-dependent problems around their steady-state solutions that are computed numerically.

Optical bistability in gap-plasmon metasurfaces in consideration of classical nonlocal effects.

Optical bistability of linear reflectance and third-harmonic generation is investigated in a metasurface consisting of metallic grating coupled with metallic film spaced with nonlinear dielectric material. Linear optical reflectance and electric field enhancement are achieved for gaps <20 nm in the presence of classical nonlocality in metallic nanostructures. Enlarged thresholds from the higher to lower reflectance states are observed from 140 kW/cm2 for the local model to 300 kW/cm2 for the nonlocal model for 0.5-nm gaps. Though the linear reflectance almost overlaps for local and nonlocal models for 20-nm gaps, the optical bistability hysteresis loops retain large differences because local field differences are amplified owing to the relation of nonlinear refraction with square of local field and historical evolution of the optical bistability.

Coherent perfect absorption in a weakly coupled atom-cavity system

We study coherent perfect absorption (CPA) theoretically based on a weakly coupled atom-cavity system with an optically pumped second-order nonlinear crystal (SOC) embedded in the cavity. Our system does not require a strong coupling, which is often needed for CPA in previous studies but is challenging to implement experimentally in some systems. The role of the SOC is to introduce a tunable effective decay rate of the cavity, which can lead to CPA in the weak coupling regime. The proposed system exhibits bistable behaviors, with bistable patterns switchable between conventional and unconventional shapes. By varying the properties of the SOC, the operation point of CPA can be tuned to be inside or outside the bistable regime. It can also be located at the upper or the lower stable branch or even the unstable branch of the bistable hysteresis loop. It is however robust against the parameters of the SOC for any fixed effective decay rate. Our system can potentially be applied to realize optical devices such as optical switches in the weakly coupled regime.

Optimum diameter for laser beam and effect of temperature rise on the optical bistability hysteresis loops

In this research, analytical study for simulating a Fabry-Perot bistable etalon (F-P cavity) filled with a dispersive optimized nonlinear optical material (Kerr type) such as semiconductors Indium Antimonide (InSb). An optimization procedure using reflective (~85%) InSb etalon (~50µm) thick is described. For this etalon with a (50 µm) spot diameter beam, the minimum switching power is (~0.078 mW) and switching time is (~150 ns), leading to a switching energy of (~11.77 pJ) for this device. Also, the main role played by the temperature to change the etalon characteristic from nonlinear to linear dynamics.

Ferromagnetic glass-coated microwires for cell manipulation

The application of magnetic nanoparticles allows labeling the cell for its manipulation via the external magnetic field. In this work, it is proposed to use glass-coated magnetic microwires as a magnetic pin system to create a strong and well-localized magnetic field at the end of such microwires. Magnetic microwires manufactured by the Taylor − Ulitovsky method exhibit tunable magnetic properties correlated with their unique micromagnetic structure. The control of magnetic properties can be achieved by, for example, the chemical composition of the wire: Fe-based microwire shows bistable hysteresis and thus strong stray fields at the ends, while Co-based one demonstrates S-shaped hysteresis with almost zero remanent magnetization because of a closed domain structure. In this research, we discovered by theoretical calculation and experiments the usability of both kinds of microwires for different approaches of cell manipulations.

Simultaneous nonlinear polarization rotation and dispersive optical bistability: theoretical and experimental analysis

We study the simultaneous occurrence of dispersive optical bistability and nonlinear polarization rotation in a nonlinear photonic resonator. The demonstrated bistable hysteresis curves of the Stokes parameters broaden the notion of optical bistability in nonlinear resonators beyond that of the traditional optical-power hysteresis curve. We present a theoretical model to fully understand the polarization hysteresis curves observed in the laboratory and to establish the relevant scaling parameters for bistable action. By optimizing the optical-signal power injected into each polarization mode of the resonator and optimizing the small-signal birefringence of the resonator by selection of the signal wavelength, a polarization rotation of 30% orthogonality was achieved between stable polarization states in the lab. The theoretical and experimental methods reported here are carried out for the case of a Fabry–Perot semiconductor optical amplifier, and are extendable to the investigation of simultaneous occurrence of these phenomena in other nonlinear media (such as Kerr media) and other photonic resonators.

Dynamical switching and memory via incoherent pump assisted optical bistability

We analyze the dynamical behavior of all-optical switching and memory based on tunable optical bistability in a three-level Λ-type atomic system driven by a probe field circulating in an optical ring cavity, a coherent coupling field and an incoherent pump field outside cavity. Owing to the incoherent pump process, the absorption and Kerr nonlinearity near the atomic resonance change dramatically as a result of varied population distribution and atomic coherence, and then the switch-up and switch-down thresholds, as well as the width (or area) of bistable curve, can be manipulated effectively. By tuning the intensity of either coherent coupling field or incoherent pump field, we can make the system output flip between the lower and upper branches of different bistable hysteresis loops while the cavity input keeps to a constant value. Accordingly, all-optical switching and memory can be implemented via dynamical control of the bistable behavior under the assistance of incoherent pump. The proposed scheme can find potential applications in all-optical communication and computation.

Optical Bistability under Nonresonant Excitation in Spinor Polariton Condensates.

We realize bistability in the spinor of polariton condensates under nonresonant optical excitation and in the absence of biasing external fields. Numerical modeling of the system using the Ginzburg-Landau equation with an internal Josephson coupling between the two spin components of the condensate qualitatively describes the experimental observations. We demonstrate that polariton spin bistability strongly depends on the condensate's overlap with the exciton reservoir by tuning the excitation geometry and sample temperature. We obtain noncollapsing bistability hysteresis loops for a record range of sweep times, [10 μs, 1s], offering a promising route to spin switches and spin memory elements.

Review of inductively coupled plasmas: Nano-applications and bistable hysteresis physics

Many different gas discharges and plasmas exhibit bistable states under a given set of conditions, and the history-dependent hysteresis that is manifested by intensive quantities of the system upon variation of an external parameter has been observed in inductively coupled plasmas (ICPs). When the external parameters (such as discharge powers) increase, the plasma density increases suddenly from a low- to high-density mode, whereas decreasing the power maintains the plasma in a relatively high-density mode, resulting in significant hysteresis. To date, a comprehensive description of plasma hysteresis and a physical understanding of the main mechanism underlying their bistability remain elusive, despite many experimental observations of plasma bistability conducted under radio-frequency ICP excitation. This fundamental understanding of mode transitions and hysteresis is essential and highly important in various applied fields owing to the widespread use of ICPs, such as semiconductor/display/solar-cell processing (etching, deposition, and ashing), wireless light lamp, nanostructure fabrication, nuclear-fusion operation, spacecraft propulsion, gas reformation, and the removal of hazardous gases and materials. If, in such applications, plasma undergoes a mode transition and hysteresis occurs in response to external perturbations, the process result will be strongly affected. Due to these reasons, this paper comprehensively reviews both the current knowledge in the context of the various applied fields and the global understanding of the bistability and hysteresis physics in the ICPs. At first, the basic understanding of the ICP is given. After that, applications of ICPs to various applied fields of nano/environmental/energy-science are introduced. Finally, the mode transition and hysteresis in ICPs are studied in detail. This study will show the fundamental understanding of hysteresis physics in plasmas and give open possibilities for applications to various applied fields to find novel control knob and optimizing processing conditions.