Bistable Curve Research Articles

Ultra low-power multistability in [formula omitted]-symmetric periodic structures with saturable coupling, gain and loss

The present work investigates the switching dynamics of conventional fiber Bragg gratings (FBGs) with saturable coupling and parity-time (PT)-symmetric fiber Bragg gratings (PTFBGs) with saturable coupling (SC) and saturable gain-loss (SGL) in the presence of Kerr nonlinearity (KNL) [model - I] and saturable nonlinearity (SNL) [model - II]. Both system models can generate distinct optical multistability (OM) and bistability (OB) curves, including S-shaped, ramp-like, and mixed OM curves in both unbroken and broken PT-symmetric regimes. The impact of each control parameter on controlling switching intensities, hysteresis width, and the number of stable states is thoroughly examined for both of these system models. The direction of right light incidence enables a significant reduction in the switching intensities to below 100 W/cm2, the lowest critical power ever reported in the literature of PTFBGs, thanks to the concept of both saturable coupling, gain and loss.

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.

Numerical investigation of optical bistability in a nonlinear plasmonic structure containing a phase change material

In this paper, a controllable nonlinear plasmonic structure is proposed based on a phase change material (PCM) layer to achieve tunable bistability characteristics. To this end, the Ge2Sb2Te5 (GST) layer (as a PCM) is sandwiched between a thin film of Ag and a Kerr material substrate. Then, this multilayered structure is used as a substrate for the ZnSiAs2 grating whose grooves are filled with the Kerr nonlinear material. Next, the grating is covered with a layer of CaF2. In this structure, we first calculate the reflection spectrum for different crystallization fractions using the finite element method (FEM) in the linear regime. The reflectance spectrum shows a dip in the near-infrared region, which is redshifted with increasing the crystallization fraction of the GST layer. This effect results from the movement of surface plasmon resonance to longer wavelengths with increasing the crystallization fraction. Then, we find that the dip in the reflectance spectrum is redshifted with enhancing the input intensity of the incident wave for different crystallization fractions in the nonlinear regime. This behavior confirms the existence of optical bistability through the proposed structure. So, we calculate the bistability curves at a fixed operating wavelength of 1550 nm for different crystallization fractions. Our results demonstrate that as the phase transition from the amorphous to the crystalline state occurs at a fixed operating wavelength, the bistability thresholds reduce while the hysteresis width also decreases and the bistability effect eventually disappears. Therefore, for each crystallization fraction of the GST layer we find a special wavelength at which a reasonable bistability curve with a reasonable hysteresis width is obtained. This operating wavelength is shifted by 33 nm as the crystallization fraction varies from 0.2 to 0.8. Finally, the effects of increasing the thickness of the GST layer on the bistability characteristics are examined. Our results show that stronger tunability of the operating wavelength by 50 nm with variation of crystallization degree from 0.2 to 0.8 is achieved when a thicker GST layer is used instead of a thinner one.

Low-Threshold Optical Bistability Based on Photonic Crystal Fabry–Perot Cavity with Three-Dimensional Dirac Semimetal

In this paper, we investigate theoretically the tunable low threshold optical bistability (OB) in the terahertz range based on photonic crystals’ Fabry–Perot (FP) cavity with a three-dimensional Dirac semimetal (3D DSM). On the one hand, a 3D DSM with a high nonlinear refractive index coefficient creates conditions for the generation of OB. Additionally, the finite film thickness of 3D DSMs leads to significantly a enhanced interaction volume compared to graphene, which allows easier preparation and has stable properties. On the other hand, the resonance of the FP cavity plays a positive role in promoting the tunable low-threshold OB. It was found that the OB threshold and hysteresis curve can be continuously adjusted by manipulating the Fermi energy and relaxation times of a 3D DSM. Additionally, the bistable curve of the composite structure is also closely related to the angle of incident light. Through parameter optimization, OB with a threshold approaching 105 V/m can be obtained. The photonic crystal’s FP cavity with a 3D DSM structure provides a feasible way to achieve low-threshold OB and a building block for future integrated all-optical devices.

Fractional critical slowing down in some biological models

The critical slowing down (CSD) phenomenon of the switching time in response to perturbation β (0 < β < 1) of the control parameters at the critical points of the steady state bistable curves, associated with two biological models (the spruce budworm outbreak model and the Thomas reaction model for enzyme membrane) is investigated within fractional derivative forms of order α (0 < α < 1) that allows for memory mechanism. We use two definitions of fractional derivative, namely, Caputo’s and Caputo-Fabrizio’s fractional derivatives. Both definitions of fractional derivative yield the same qualitative results. The interplay of the two parameters α (as memory index) and β shows that the time delay τD can be reduced or increased, compared with the ordinary derivative case (α = 1). Further, τD fits: (i) as function of β the scaling inverse square root formula 1/β at fixed fractional derivative index (α < 1) and, (ii) as a function of α (0 < α < 1) an exponentially increasing form at fixed perturbation parameter β.

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.

Inhomogeneous nonlinearity meets parity–time-symmetric Bragg structures: route to ultralow power steering and peculiar stable states

In the context of parity–time ( P T )-symmetric fiber Bragg gratings, tailoring the nonlinear profile along the propagation coordinate serves as a new direction for realizing low-power all-optical switches. The scheme is fruitful only when the nonlinearity profile will be either linearly decreasing or increasing form. If the rate of variation of the nonlinearity profile is high, the critical intensities fall below the input power of value 0.01 in the unbroken regime provided that the light launching direction is right. Nowadays, every new theoretical inception into the parity–time fiber Bragg grating (PTFBG) has started making sense of switching in the broken P T -symmetric regime, which was once believed to be the instability regime. When the inhomogeneous nonlinearity acts together with the broken P T symmetry and right light incidence, it leads to two peculiar settings. First, the switch-up intensities are ultralow. Second, the switch-down action takes place at zero critical intensities. Such optical bistability curves are unprecedented in the context of conventional gratings and found only in plasmonic devices and anti-directional couplers. Even though the nonlinearity is inhomogeneous, the ramp-like first stable states persist in the broken P T -symmetric regime, giving an additional indication that the broken PTFBG is closely associated with the plasmonic structures. In the existing PTFBG systems, the switching intensities are relatively higher in the broken regime. However, the proposed system records the lowest switching intensities in the broken regime. The reported intensities ( < 0.005 ) are also the lowest-ever switching intensities recorded in the perspective of PTFBGs to date.

Optical bistability modulation based on the photonic crystal Fabry-Perot cavity with graphene.

We investigate the low-threshold optical bistability of transmitted beams at the terahertz range based on the photonic crystal Fabry-Perot cavity with graphene. Graphene with strong nonlinear conductivity is placed in the middle of the Fabry-Perot cavity and the resonance of the cavity plays a positive role in promoting the low-threshold optical bistability. The optical bistability curve is closely related to the incident angle of light, the parameters of graphene, and the structural parameters of the Fabry-Perot cavity. Through parameter optimization, optical bistability with threshold of 105 V/m can be obtained, which has reached or is close to the range of the weak field.

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.

Broadband coherent perfect absorption by cavity coupled to three-level atoms in linear and nonlinear regimes

A broadband coherent perfect absorption (CPA) scheme consisting of an optical resonator coupled with three-level atoms excited by single cavity mode is proposed and analyzed. We show the output light field from the system is completely suppressed under specific conditions when the system is excited in linear and nonlinear regimes by two identical light fields from two ends of optical cavity. An analytical broadband CPA criterion for central and sideband excitations of cavity quantum electrodynamics system is derived in linear regime. Moreover, we show the resonant excitation criterion for CPA is greatly extended in nonlinear regime. A new type of bistability behavior is found. The output field intensity and the bistability curve can be well tuned by dynamically adjusting system parameters. Our results demonstrate that the CPA is quite universal, and it should be useful in a variety of applications in optical logic and optical communication devices.

Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.

Time-delayed feedback with global and local contributions on spatiotemporal dynamics of waves in fiber cavity

Lugiato–Lefever model is applied through a combined global and local time-delay feedback to study the dynamic of waves in fiber cavity. Delayed feedback describes how the state of the system at a present time is influenced by its value in the past. Naturally, we carry out an analysis of the linear stability and reveal the role of the strength and the phase of the optical feedback in the presence of its two contributions on the shape of the bistable curve as well as on the regions of instability. We show that the delay feedback strongly impacts the spatiotemporal dynamical behavior resulting from modulational instability by shifting the regions with different spatial eigenvalue spectra, reducing the threshold associated with modulational instability and decreasing the critical frequency at the onset of this instability. We show that for fairly moderate input intensities, it is possible to generate drifting cavity solitons with asymmetric radiation emitted by the soliton tails. The feedback also induces the formation of periodic and superperiodic waves, and extreme events.

Collective atomic correlations in absorptive optical bistability without adiabatic elimination: Exemplifying nonclassicality from a linearized treatment of fluctuations

We determine the incoherent spectrum, squeezing properties and second-order correlation function of the collective atomic degrees of freedom in absorptive optical bistability. This is accomplished via a linearized Fokker-Planck equation in the positive P representation, guided by the analysis of [H. J. Carmichael, Phys. Rev. A 33, 3262 (1986)] which does not resort to adiabatic elimination. We focus on the regimes of weak and strong intracavity excitation, addressing the good-cavity and bad-cavity limits as well as the limit of collective strong coupling. Adiabatic elimination of the intracavity field sustained by an auxiliary resonator coupled to the ensemble is used to probe the atomic correlations via the formation of a collective emission channel. We compare to the corresponding expressions for the forwards-scattered light with reference to experimental results, discussing key differences between the lower and upper branch of the steady-state semiclassical bistability curve. Our analysis is carried out around the stable states situated far away from the turning points, where analytical expressions can be obtained self-consistently, demonstrating a clear departure from classical behavior.

Exploring cyclic networks of multisite modification reveals origins of information processing characteristics

Multisite phosphorylation (and generally multisite modification) is a basic way of encoding substrate function and circuits/networks of post-translational modifications (PTM) are ubiquitous in cell signalling. The information processing characteristics of PTM systems are a focal point of broad interest. The ordering of modifications is a key aspect of multisite modification, and a broad synthesis of the impact of ordering of modifications is still missing. We focus on a basic class of multisite modification circuits: the cyclic mechanism, which corresponds to the same ordering of phosphorylation and dephosphorylation, and examine multiple variants involving common/separate kinases and common/separate phosphatases. This is of interest both because it is encountered in concrete cellular contexts, and because it serves as a bridge between ordered (sequential) mechanisms (representing one type of ordering) and random mechanisms (which have no ordering). We show that bistability and biphasic dose response curves of the maximally modified phosphoform are ruled out for basic structural reasons independent of parameters, while oscillations can result with even just one shared enzyme. We then examine the effect of relaxing some basic assumptions about the ordering of modification. We show computationally and analytically how bistability, biphasic responses and oscillations can be generated by minimal augmentations to the cyclic mechanism even when these augmentations involved reactions operating in the unsaturated limit. All in all, using this approach we demonstrate (1) how the cyclic mechanism (with single augmentations) represents a modification circuit using minimal ingredients (in terms of shared enzymes and sequestration of enzymes) to generate bistability and oscillations, when compared to other mechanisms, (2) new design principles for rationally designing PTM systems for a variety of behaviour, (3) a basis and a necessary step for understanding the origins and robustness of behaviour observed in basic multisite modification systems.

A goblet-like non-linear electromagnetic generator for planar multi-directional vibration energy harvesting

A novel electromagnetic energy harvester for in-plane multi-directional vibrations is developed by letting a magnetic ball move on a two-dimensional surface which is generated from the rotation of a one-dimensional bi-stable potential curve. A goblet-like structure is designed to keep the ball on the nonlinear potential surface. Due to the special symmetric configuration, in-plane excitations from any direction can equivalently force the motion of the magnetic ball and thus produce electricity in the coils on the outer surface of the structure. Meanwhile, the good features of nonlinearities on bandwidth extension are preserved. Continual circular motions were observed for a wide frequency range. The operation bandwidth could reach a high value of 8 Hz and simultaneously the maximum power of 7.649mW was captured in experiments under a harmonic excitation of 1 g, corresponding to a normalized power density of 72.5 µW cm−3 g−2. In particular, the proposed harvester showed good performance for low frequency vibrations and is especially suitable for human body energy harvesting. With the harvester attached to the ankle, 1.4mW was obtained when walking at 5 km h−1. Notably, the method can be applied to other one-dimensional potential portraits for constructing the corresponding two-dimensional potential surface.

Dynamic Bistable Switches Enhance Robustness and Accuracy of Cell Cycle Transitions

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies indicate that the shape of the bistable response curve changes dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time.

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.

Polariton surface solitons under a resonant pump.

We address the formation of stable dissipative surface solitons in the exciton-polariton condensate in a one-dimensional array of microcavity pillars under the action of a localized resonant pump acting in the edge resonator. We show that the localization degree and peak amplitudes of surface solitons can be effectively controlled by the pump frequency and that the allowed energy gap of the periodic structure determines the energy range, where surface solitons can form. One observes bistability at sufficiently large pump amplitudes and a nonlinearity-induced shift of the position of the resonance peak from the allowed energy band of the periodic array into its forbidden energy gap. The growth of the spatial period of the array reduces coupling between pillars and currents from a surface pillar into bulk pillars which leads to the increase of the surface soliton amplitude. Strong expansion into the depth of the array occurs for pump frequencies corresponding to the middle of the allowed energy band. Surface solitons can be excited from the broadband Gaussian noise. Above certain threshold noise levels, solitons from a stable upper branch of the bistability curve are excited while, below threshold, solitons from the lower branch form.

All-optical switching and flip-flop based on dynamically controlled bistability in a V-type atomic system

We have proposed a scheme for all-optical switching and flip-flop based on controllable optical bistability in a simple three-level V-type atomic system assisted by an incoherent pump field. Due to the auxiliary incoherent pump, the atomic population is redistributed in the three levels, and then the absorption-dispersion property and the Kerr nonlinearity of the medium are different from those of the conventional V-type electromagnetically induced transparency system. The results show that both the thresholds and the area (or shape) of the hysteresis loop can be controlled efficiently via the adjustment of either the incoherent pump field or the coupling field. As a result, with a constant cavity input, the output of the optical cavity can be switched between the low- and high-power states of different bistable curves by tuning the optical fields. Based on this effect, we realize all-optical steady-state switching and set-reset flip-flop operation by adding a pulse sequence (positive pulse or set-reset pulse) onto either the incoherent pump field or the coupling field. Such a simple and effective technique of optical switching and flip-flop can find application in all-optical signal processing systems.

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.