Nonlinear Gain Coefficient Research Articles

Vibration control of nonlinear viscoelastic systems with displacement delay feedback

In this study, the nonlinear vibration characteristics of a nonlinear Zener model under harmonic excitation, equipped with linear and nonlinear displacement delay feedback control, were investigated. The amplitude–frequency curve of the system’s main resonance was computed using the multi-scale method. Stability conditions for the system were then established based on the Lyapunov stability theory. The influence of several parameters on the system’s dynamic behavior was also analyzed, including time delay, displacement feedback gain coefficient, nonlinear term coefficient, damping coefficient, and external excitation. The findings revealed that the nonlinear displacement feedback gain coefficient was observed to exert a more substantial effect on the system’s amplitude than other factors. Further, the nonlinear displacement delay feedback gain coefficient and time-delay value diminish the amplitude of the vibration, leading all solutions to achieve a stable state. In instances with time-delay control, the impact of the main system parameters on system vibration was significantly diminished. The aim of this study is to provide a theoretical basis for the implementation of displacement delay controllers in nonlinear viscoelastic systems.

Compact Brillouin comb laser in Chalcogenide fiber assisted by four-wave mixing

We experimentally demonstrate a multiwavelength Brillouin comb generation employing a segment of As2S3 chalcogenide fiber as the Brillouin gain medium. The extremely high nonlinear and Brillouin gain coefficients allow the As2S3 fiber length to be as short as 4.2 m. A compact Brillouin comb laser composed of multiple Brillouin Stokes and anti-Stokes channels is generated from the As2S3 fiber either with or without ring cavity feedback through the interaction of stimulated Brillouin scattering and four-wave mixing effects. Different output couplings are used to extract the Brillouin comb laser when the cavity feedback is connected. A high laser power of 927 mW and multiple laser channels of 20 are achieved with an output coupling of 90 % and 10 %, respectively. A trade-off between the power threshold, laser channel number, output power and slope efficiency should be considered when optimizing the optical performance of the multiwavelength Brillouin laser.

Switchable fast-slow light in a cavity-magnon system by adding a squeezed drive field

We theoretically discuss the influence of a squeezed drive on the fast and slow light effect at different temperatures by focusing on two main factors: the nonlinear gain coefficient of optical parametric amplification and the phase of the pumping field. We show that the nonlinear gain coefficient and the phase of the pump field will affect the coupling strength between photon and magnon, which provides a way to achieve more obvious fast and slow light effects and good potential to realize the fast-slow light conversion. Moreover, by comparing two different temperatures, we find that the low temperature environment is more conducive to the production of fast light and slow light. With the addition of the squeezing drive field, the group delay of the system will get a larger value and the symmetry of the system will be destroyed, leading to asymmetric absorption. Our results provide more freedom for the realization and conversion of fast and slow light and is expected to find applications in optical communication and optical storage.

Carrier dynamic and carrier Temperature in Quantum Well

Carrier temperature in quantum well (QW)semiconductor optical amplifier (SOA) has been studied,depending density matrix theory (DMT) and carrier dynamicin quantum well. The effect of volume carrier density, dopingon effect, pulse shape, nonradiative relaxation, and nonlineargain coefficients on the carrier temperature and carrierheating has been investigated. The theoretical results showthat; the time recovery increases straightforward withnonradiative recombination, where the relaxation time ofnonradiative recombination reduces the rate of carrieroccupation in quantum states. Also, the carrier temperatureincreases with carrier density, free carrier absorption, carrierheating lifetime and reduces with pulse shape of pump pulses

Simultaneous measurement for amplitude and frequency of time-harmonic force based on optomechanically induced nonlinearity

An accurate readout of the mechanical motion using optomechanical coupling is highly desired for on-chip sensing applications but it remains challenging due to the uncertainty caused by time-dependent parameters and noisy fluctuations. Here, we propose an efficient scheme to realize simultaneous measurement for both amplitude and frequency of the time-harmonic force (THF) in a hybrid optomechanical system via a nonlinear sum sideband effect. In this optomechanical system assisted by a degenerate parametric amplifier (DPA), the nonlinear optomechanical interaction between the external THF, optical, and mechanical modes is used to construct the frequency component of optical sum sidebands. Using experimentally achievable parameters, we find that the conversion efficiency of the sum sidebands has a significant enhancement when the nonlinear gain coefficient of DPA increases. In the scheme of the dual-parameter measurement, we also report that the amplitude of THF could be independently detected by observing the intensity variation of the lower sum sideband, while the frequency of THF could be separately read by monitoring the frequency of the prominent peak in this nonlinear spectrum. Benefitting from the optical cooling of a mechanical element, the theoretical results show that the minimum resolutions for detecting the amplitude and the frequency of THF are approximately 8.8×10−12N and 16Hz, respectively.

Multivariable Coordinated Nonlinear Gain Droop Control for PV-Battery Hybrid DC Microgrid Access System via a T-S Fuzzy Decision Approach

The PV-Battery hybrid DC microgrid is an important structural form for distributed renewable energy microgrid applications. This paper focuses on improving the access utilization rate of PV-Battery energy and enhancing the access stability of the DC bus voltage. Firstly, based on the voltage droop control method for multi-source access system, the relationship between the power margin of PV-Battery energy and the regulation of DC bus voltage deviation is analyzed. Then, a multivariable T-S fuzzy decision approach is used to design a nonlinear virtual resistance-based voltage droop gain coefficient function, which achieves a highly adaptive coordinated distribution of PV-Battery power as well as supports DC bus voltage stabilization. The T-S fuzzy input variables include the DC bus voltage deviation of the access point, the state of charge of the battery, and the PV sunlight intensity. Finally, the simulation system is built employing MATLAB/Simulink, and the feasibility and effectiveness of the proposed strategy are verified through multi-scheme simulations.

Simplified Empirical Equations to Coefficients of Linear and Nonlinear Gain of InGaAsP/InP Semiconductor Lasers and Application in Simulation of Noise

This paper presents modeling of the linear and nonlinear gain of long-wavelength In1−xGaxAsyP1−y/InP laser basing on a third-order perturbation approach using the density matrix analysis. We modify the perturbation approach in literature by taking account of electronic transitions between the conduction band and both the heavy and light-hole bands of the active layer. The obtained results on gain characteristics of this complicated approach are simplified by empirical equations that function in the bandgap energy of the active layer. Therefore, the gain characteristics of the laser can be simply calculated at the bandgap energy that corresponds to arbitrary compositions x and y of In1−xGaxAsyP1−y/InP1−ysupposing lattice matching with the base InP material. The results show that both the linear gain and nonlinear gain coefficients decrease with the increase of the bandgap energy. The obtained relationships of the gain characteristics are then used in the rate equation model to simulate the spectral properties of the relative intensity noise (RIN) of InGaAsP laser as a function of the bandgap energy over the relevant ranges of compositions x and y. Moreover, we introduce fitting equations to the RIN levels around the relaxation frequency of the laser as well as in the low-frequency range as functions of the bandgap energy. These RIN levels are shown to increase with the increase of the bandgap energy and are associated with a decrease in the relaxation frequency of the laser.

Squeezed Light Induced Symmetry Breaking Superradiant Phase Transition.

We theoretically investigate the quantum phase transition in the collective systems of qubits in a high quality cavity, where the cavity field is squeezed via the optical parametric amplification process. We show that the squeezed light induced symmetry breaking can result in quantum phase transition without the ultrastrong coupling requirement. Using the standard mean field theory, we derive the condition of the quantum phase transition. Surprisingly, we show that there exists a tricritical point where the first- and second-order phase transitions meet. With specific atom-cavity coupling strengths, both the first- and second-order phase transition can be controlled by the nonlinear gain coefficient, which is sensitive to the pump field. These features also lead to an optical switching from the normal phase to the superradiant phase by just increasing the pump field intensity. The signature of these phase transitions can be observed by detecting the phase space Wigner function distribution with different profiles controlled by the squeezed light intensity. Such superradiant phase transition can be implemented in various quantum systems, including atoms, quantum dots, and ions in optical cavities as well as the circuit quantum electrodynamics system.

Bipartite and tripartite entanglement caused by squeezed drive in magnetic-cavity quantum electrodynamics system

Utilizing optical nonlinearity for generating the entanglement is still a most widely used approach due to its quality and simplicity. Here in this paper, we propose a theoretical scheme to generate bipartite and tripartite entanglement in a cavity quantum electrodynamics (QED) system with one Yttrium iron garnet (YIG) sphere by using a squeezed drive. In such a system, the parametric down-conversion process is used to generate the nonlinearity and further increase the coupling between cavity and YIG. Thus, the enhanced coupling between the microwave cavity photons and the ferromagnetic resonance (FMR) mode/magnetostatic (MS) mode results in bipartite entanglements. By using the mean field theory, we show that the bipartite entanglements strongly depend on the detuning of the cavity and magnon mode. When the driving field is tuned to be resonant with the FMR mode, but the MS mode is far off-resonant, the entanglement between photons and the FMR mode reaches its maximum. However, when the driving field is tuned to be resonant with the MS mode, but the FMR mode is detuned very well, the entanglement between photons and the MS mode reaches its maximum. We show that the dissipation of the FMR/MS mode affects the entanglement greatly, and the bipartite entanglement decreases as the dissipation rate of the FMR/MS mode increases. Under the steady-state approximation, we also show that the tripartite entanglement can be generated, and the minimum residual contangle increases with the enhancement of the nonlinear gain coefficient. With the nonlinearity induced by the parametric down conversion process, the interaction between the driving field and the magnetic-cavity QED system leads to the tripartite entanglement involving the cavity photons, FMR mode and the MS mode. Likewise, we show that the tripartite entanglement also strongly depends on the dissipation rate of MS mode, and the minimum residual contangle increases as the dissipation rate of the MS mode decreases. We also show that the squeezed field induced tripartite entanglement is insensitive to the temperature and has good robustness. Our results suggest that the magnetic-cavity QED system could provide a promising platform for studying the macroscopic quantum phenomena, and the squeezing field opens a new method of generating the entanglement.

Hopf Bifurcation Control for Rolling Mill Multiple-Mode-Coupling Vibration Under Nonlinear Friction

Rolling mill system may lose its stability due to the change of lubrication conditions. Based on the rolling mill vertical–torsional–horizontal coupled dynamic model with nonlinear friction considered, the system stability domain is analyzed by Hopf bifurcation algebraic criterion. Subsequently, the Hopf bifurcation types at different bifurcation points are judged. In order to restrain the instability oscillation induced by the system Hopf bifurcation, a linear and nonlinear feedback controller is constructed, in which the uncoiling speed of the uncoiler is selected as the control variable, and variations of tensions at entry and exit as well as system vibration responses are chosen as feedback variables. On this basis, the linear control of the controller is studied using the Hopf bifurcation algebraic criterion. And the nonlinear control of the controller is studied according to the center manifold theorem and the normal form theory. The results show that the system stability domain can be expanded by reducing the linear gain coefficient. Through choosing an appropriate nonlinear gain coefficient, the occurring of the system subcritical bifurcation can be suppressed. And system vibration amplitudes reduce as the increase of the nonlinear gain coefficient. Therefore, introducing the linear and nonlinear feedback controller into the system can improve system dynamic characteristics significantly. The production efficiency and the product quality can be guaranteed as well.

Frequency noise analysis of 1.55 µm indium arsenide/indium phosphide quantum dot lasers: impact of non‐linear gain and direct carrier transition

Frequency noise (FN) characteristic of 1.55 µm quantum dot (QD) lasers is investigated by introducing a theoretical model. A set of five rate equations are developed in presence of Langevin noise sources by writing a new equation for dynamics of the optical field phase. To investigate the effects of non-linear gain and direct carrier transition on FN spectrum of QD lasers, the auto and cross-correlation coefficients between carriers and photons have been calculated. Calculations demonstrate that the excited state and ground state (GS) carriers’ shot noises play dominant role on both the level and the resonance frequency of FN spectrum. Moreover, the level of FN declines by increasing the non-linear gain coefficient. On the other hand, direct carrier transition from wetting layer to the lasing state of GS leads to lower-frequency fluctuations. Finally, it is revealed that the linewidth of QD laser decreases by increasing the pumping current and its value is in the order of about 1 MHz.

Bi-soliton generation and its properties in stretched pulse fiber ring laser.

We studied the formation of bi-soliton pairs in Kerr-type stretched pulse fiber ring laser (SPFRL). By solving the modified Ginzburg-Landau (GL) equaition, which models the SPFRL, we show that anti-phase bi-soliton can be generated robustly if a low level Gaussian pulse is injected into the ring laser in the initial set-up stage. With the help of properly selected high order nonlinear gain coefficient, the observation of anti-phase bi-soliton pairs is expected to become feasible in experiments.

The effect of nonlinear gain on the characteristics of an optically injected VCSEL and cavity solitons

Using the Lagrange method to fit the curve of maximum gain as a function of carrier density for an active region consisting of an AlGaAs/GaAs layers sandwiched between DBR layers, it is found that the curve is better approximated assuming a quadratic dependence on the carrier density. By summarizing all of the calculations into a nonlinear gain coefficient parameter, \(\beta \), in the Maxwell–Bloch equations we numerically studied the effect of nonlinear gain on the characteristics of the VCSEL and also on the cavity solitons (CSs) forming in such a device. Particularly, it is shown that with nonlinear gain a wider locked region can be achieved along with enhanced sustained relaxation oscillation amplitude. The switching on/off time of CSs is modified and there appears a considerable enhancement in their efficiency and contrast.

Effect of the nonlinear saturation of the gain on the peak modulation frequency in lasers based on self-assembled quantum dots

Peak modulation frequency of lasers based on self-organized quantum dots is calculated taking into account the effect of nonlinear gain saturation. Because of a large nonlinear gain coefficient and a reduction in the differential gain with increasing optical losses, the peak modulation frequency is attained for an optimum loss level that is significantly lower than the saturated optical gain in the active region. For lasers based on multiply stacked arrays of quantum dots, the peak modulation frequency first increases with increasing number of quantum-dot layers before leveling off, with the limiting value being inversely proportional to the nonlinear gain coefficient.

Fabrication and characterization of a water-free mid-infrared fluorotellurite glass

Using a physical and chemical dehydration technique and a high-pressure, ultradry O2 atmosphere in a semiclosed steel-chamber furnace, we fabricated a group of fluorotellurite glasses with a composition of (90-x)TeO2-xZnF2-10Na2O (mol.%, x=0-30). For x=30, no OH absorption was observed in the range of 0.38-6.1 μm. This is the first report of a water-free mid-IR fluorotellurite glass, to our knowledge, offering the common advantages of a robust oxide glass and an IR-transparent fluoride one. Besides optimized linear transmittance and absorption, the nonlinear refractive indices and Raman gain coefficients are reduced. These results are discussed in the context of mid-IR high-power laser generation and transmission.

Quantum dot lasers with controllable spectral and modal characteristics

Simple analytical expressions for the shape and width of the multi-frequency lasing spectra of quantum dot lasers are derived by using a parabolic approximation of the gain spectrum. A giant nonlinear gain coefficient of 2.5 × 10−15 cm3 was estimated from the experimental dependence of the lasing spectrum width on the output power. A monolithic diffraction optical filter was used to suppress lasing of higher-order transverse modes in a quantum dot laser with a relatively broad ridge waveguide. Stable lasing on a fundamental transverse mode is observed with the maximum continuous wave (CW) single-spatial-mode power of 700 mW.

Four-wave mixing and wavelength conversion in quantum dots

We perform a theoretical analysis based on density-matrix equations to determine the nonlinear susceptibilities and gain coefficients for a quantum-dot semiconductor optical amplifier. Our results show that for a single bound-state quantum-dot, carrier relaxation at large current densities is limited by the carrier capture time from the continuum to the bound state. We then compare our results with experiment and show that there is a significant contribution from carrier heating in the four-wave mixing efficiency. Our results and data fit indicate that efficient four-wave mixing on high-speed signals of greater than 160 Gb/s is possible.

Analysis of small-signal intensity modulation of semiconductor lasers taking account of gain suppression

This paper demonstrates theoretical characterization of intensity modulation of semiconductor lasers (SL’s). The study is based on a small-signal model to solve the laser rate equations taking into account suppression of optical gain. Analytical forms of the small-signal modulation response and modulation bandwidth are derived. Influences of the bias current, modulation index and modulation frequency as well as gain suppression on modulation characteristics are examined. Computer simulation of the model is applied to 1.55-µm InGaAsP lasers. The results show that when the SL is biased far-above threshold, the increase of gain suppression increases both the modulation response and its peak frequency. The modulation bandwidth also increases but the laser damping rate decreases. Quantitative description of the relationships of both modulation bandwidth vs. relaxation frequency and maximum modulation bandwidth vs. nonlinear gain coefficient are presented.

Controlling Chaos in a Semiconductor Laser via Weak Optical PositiveFeedback and Modulating Amplitude

Numerical analysis of weak optical positive feedback (OPF)controlling chaos is studied in a semiconductor laser. The physical model ofcontrolling chaos produced via modulating the current of semiconductor laseris presented under the condition of OPF. We find the physical mechanism thatthe nonlinear gain coefficient and linewidth enhancement factor of the laserare affected by OPF so that the dynamical behaviour of the system can beefficiently controlled. Chaos is controlled into a single-periodic state, adual-periodic state, a tri-periodic state, a quadr-periodic state, apenta-periodic state, and the laser emitting powers are increased by OPF insimulations. Lastly, another chaos-control method with modulating theamplitude of the feedback light is presented and numerically simulated tocontrol chaotic laser into multi-periodic states.

Modeling and control of hydraulic excavator’s arm

In order to find a feasible way to control excavator’s arm and realize autonomous excavation, the dynamic model for the boom of excavator’s arm which was regarded as a planar manipulator with three degrees of freedom was constructed with Lagrange equation. The excavator was retrofitted with electrohydraulic proportional valves, associated sensors (three inclinometers) and a computer control system (the motion controller of EPEC). The full nonlinear mathematic model of electrohydraulic proportional system was achieved. A discontinuous projection based on an adaptive robust controller to approximate the nonlinear gain coefficient of the valve was presented to deal with the nonlinearity of the whole system, the error was dealt with by robust feedback and an adaptive robust controller was designed. The experiment results of the boom motion control show that, using the controller, good performance for tracking can be achieved, and the peak tracking error of boom angles is less than 4°.