Detuning Factor Research Articles

Detuning analysis and power tracking of dual‐ended resonant circuit based on improved variable‐step perturbation observation for wireless power transfer system

AbstractA power tracking method based on improved variable‐step perturbation observation approach has been proposed in this paper. This method is aimed at addressing the detuning issues caused by capacitor parameter drift in MCR‐WPT systems based on S‐S compensation circuits. Compared with traditional tuning methods, the proposed method has fast response, high accuracy, low complexity, and less prone to over‐tracking. Firstly, a mathematical model of the system based on the detuning factor has been established. Secondly, the impact of different detuning conditions on the system at the initial resonant frequency has been studied. Thirdly, the response characteristics of the system to different frequencies under different detuning conditions have been studied. Fourthly, based on the above researches, an improved variable‐step perturbation observation method based on the single‐step power drop factor has been proposed. Finally, an experimental platform was constructed, and relevant experiments were conducted. Experimental results validate the effectiveness of power tracking under different detuning conditions, with the lowest transmission efficiency being 81.51%.

Chimera states in a large laterally coupled laser array with four different waveguide structures.

Chimera states are rich and fascinating phenomena existing in many networks, where the identical oscillators self-organize into spatially separated coexisting domains of coherent and incoherent oscillations. Here, we report these states in the large laterally coupled laser array with four different waveguiding structures, with which a variety of chimera patterns can be revealed. We present the bifurcation diagrams giving birth to them and find that the chimeras exist in the boundary of the steady state and multi-period oscillation solutions, which applies to all the prevalent waveguiding structures considered. We also find that the waveguiding structures play an important role in the chimera states, e.g., the array composed of the index antiguiding with gain-guiding has a wider chimera region compared to other waveguides considered. Additionally, the effects of the crucial parameters including the laser separation ratio, pump rate, frequency detuning, and linewidth enhancement factor on the observed phenomena are discussed. Our analysis shows that the frequency detuning between lasers and the linewidth enhancement factor affects the lifetime and pattern of chimeras. The results could guide the design of laser arrays or introduce more insight into a new understanding of the dynamical behaviors of networks.

High Sensitivity Temperature Sensor Based on Harmonic Vernier Effect

A high-sensitivity temperature sensor based on the harmonic Vernier effect is proposed and verified by experiments. The main component of the sensor is a Sagnac interferometer consisting of two sections of polarization maintaining fibers (PMFs) spliced with an intersection angle of 45° between their fast axes. The harmonic Vernier effect is achieved by setting the length of one of the PMFs an integral multiple (i-times) of the length of the other plus a detuning factor. Compared with the Sagnac interferometer based on the fundamental Vernier effect, the temperature sensitivity of the harmonic Vernier effect is higher, reaching i+1 times of that of the fundamental Vernier effect (i is the order of the harmonic).

Diverse optical solitons solutions of the fractional complex Ginzburg-Landau equation via two altered methods

<abstract> <p>This work evaluates the fractional complex Ginzburg-Landau equation in the sense of truncated M- fractional derivative and analyzes its soliton solutions and other new solutions in the appearance of a detuning factor in non-linear optics. The multiple, bright, and bright-dark soliton solutions of this equation are obtained using the modified $\left({{{G'} / {{G^2}}}} \right)$ and $\left({{1 / {G'}}} \right) - $expansion methods. The equation is evaluated with Kerr law, quadratic –cubic law and parabolic law non-linear fibers. To shed light on the behavior of solitons, the graphical illustrations in the form of 2D and 3D of the obtained solutions are represented for different values of various parameters. All of the solutions have been verified by substitution into their corresponding equations with the aid of a symbolic software package. The various forms of solutions to the aforementioned nonlinear equation that arises in fluid dynamics and nonlinear processes are presented. Moreover, we guarantee that all the solutions are new and an excellent contribution in the existing literature of solitary wave theory.</p> </abstract>

Characteristic Study on Parallel Reservoir Computation Based on VCSEL Dynamics With Optoelectronic Feedback

We proposed a new reservoir computation (RC) structure using polarization dynamics of vertical cavity surface emitting lasers (VCSELs) with optoelectronic feedback. Santa-Fe time-series prediction and nonlinear channel equalization were used to evaluate its parallel processing capability. We numerically discussed the effects of feedback strength, injection strength, frequency detuning, injection current and scaling factors on the RC performance of the system. The results show that, the operation range of negative feedback is larger than that of positive feedback; under appropriate feedback and lager injection strengths, good RC performance can be achieved for a wider injection current; with continuous variation of feedback strength from negative to positive values, the optimized location for frequency detuning moves from positive to negative values. We also evaluated the processing rate of proposed RC structure. The related study is helpful for the design and optimization of VCSEL-based RC under optoelectronic feedback.

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

This work investigates the complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics, which represents soliton propagation in the presence of a detuning factor. The φ^6-model expansion approach is used to find optical solitons such as dark, bright, singular, and periodic as well as the combined soliton solutions to the model. The results presented in this study are intended to improve the CGLE's nonlinear dynamical characteristics, it might also assist in comprehending some of the physical implications of various nonlinear physics models. The hyperbolic sine, for example, appears in the calculation of the Roche limit and gravitational potential of a cylinder, while the hyperbolic cotangent appears in the Langevin function for magnetic polarization. The current research is frequently used to report a variety of fascinating physical phenomena, such as the Kerr law of non-linearity, which results from the fact that an external electric field causes non-harmonic motion of electrons bound in molecules, which causes nonlinear responses in a light wave in an optical fiber. The obtained solutions' 2-dimensional, 3-dimensional, and contour plots are shown.

On the Synchronization Behavior of Coupled Friction-Induced Oscillators Subjected to Base Excitation

Abstract The primary objective of this paper is to analyze the synchronization phenomena in a coupled friction-induced oscillator consisting of two cantilever beams with tip-masses subjected to base excitations. The coupling is achieved by connecting a linear spring between the tip-masses, which are in frictional contact with a rigid rotating disk. The Pearson time correlation coefficient is used to measure the strength and mode of synchronization between the oscillations of the coupled system. Periodicity of the motions is determined by evaluating the Poincaré map wherein the zero velocity crossing from positive to negative is considered as the Poincaré section. The fundamental frequency of the coupled motion and its harmonics are obtained from the Fast Fourier Transform (FFT) of the time responses. A bifurcation study is conducted to identify the periodicity of motion of both the uncoupled and coupled systems. The coupled system is found to be synchronized for the single-periodic, multiperiodic, and quasi-periodic motions, but not for chaotic motions. Multiple basins of attractions of initial conditions corresponding to different synchronization characteristics are observed. The coupled system shows a large dependence of the mass ratio detuning factor (MRDF) on the synchronization characteristics; in-phase synchronization is obtained for smaller MRDF, which eventually becomes out-of-phase for larger MRDF. A special study conducted confirms that the coupling can be used to control the amplitude as well as the stick-phase of motion in friction oscillators.

Quality factor of plasmonic monopartite and bipartite surface lattice resonances

Surface lattice resonance (SLR) is the collective excitation of nanoparticle resonances arising from the hybridization between localized surface plasmons (LSPs) and propagating Rayleigh anomalies (RAs). When comparing with the corresponding LSPs, SLRs exhibit a much higher quality factor. In fact, as the quality factor depends on the constituting resonances and their hybridization, how one can parametrize it in an analytic form is an important issue. We have studied the SLRs arising from two-dimensional Au monopartite nanoparticle arrays by angle- and polarization-resolved reflectivity spectroscopy, temporal coupled mode theory (CMT), and finite-difference time-domain simulation. The scattering matrix of the SLRs is formulated, revealing the importance of the spectral detuning and the interaction strengths between the LSP and the RAs in governing the quality factor. We then extend the CMT approach to study bipartite arrays where a nanoparticle dimer is employed and find the coupling between two LSPs plays a major role in further boosting the quality factor. Specifically, the coupling takes part in controlling the detuning factor as well as determining whether the coupled bright or dark mode is hybridized with the RAs. The dark mode hybridization can strongly enhance the quality factor, which is otherwise not possible in the monopartite counterparts.

A new method for experimental tuning of PI controllers based on the step response

In this paper we present a new method for tuning Proportional Integral (PI) controllers from experimental data obtained through an open loop step test over the process to be controlled. The tuning procedure requires first the measurement of the process gain, and the times taken to reach the 5%, 35.3% and 85.3% of the final output and then applying a set of tuning equations. The tuning equations approximate the controller that minimizes the Integral of Absolute Error (IAE) of the disturbance response for a model with three real poles and time delay and are very accurate for a wide range of non oscillatory stable systems. The user can select the desired robustness (through the required maximum of the Sensitivity function (Ms)), as a difference with usual methods that allow only to choose among two or three predefined robustness. The PI controller that minimizes the disturbance IAE is defined by default, but the user can also select a detuning factor to define slower controllers with the same robustness, allowing to find the desired compromise between performance and actuator activity due to sensor measurement noise. An application for Android, that can be downloaded for free, and a web based application, have been developed to implement the tuning procedure.

Solitons and Jacobi Elliptic Function Solutions to the Complex Ginzburg–Landau Equation

The complex Ginzburg–Landau (CGL) equation which describes the soliton propagation in the presence of the detuning factor is firstly considered; then its solitons as well as Jacobi elliptic function solutions are obtained systematically using a modified Jacobi elliptic expansion method. In special cases, several dark and bright soliton solutions to the CGL equation are retrieved when the modulus of ellipticity approaches unity. The results presented in the current work can help to complete previous studies on the complex Ginzburg–Landau equation.

Investigation of Phase-Locked Loop Statistics via Numerical Implementation of the Fokker–Planck Equation

The goal of this paper is to explore the effect of various parameters on the information geometric structure of the phase-locked loop (PLL) statistics, both transient and stationary. Comprehensive treatment on the behavior of PLL statistics will be given. The behavior of the phase-error statistics of the first-order PLL, in the presence of additive white Gaussian noise (WGN) is investigated through solving the differential equations known as the Fokker–Planck (FP) equation using the implicit Crank–Nicolson finite-difference method. The PLL is one of the most commonly used circuits in electrical engineering. A full knowledge of probability density functions (PDFs) of the phase-error statistics becomes essential in understanding the PLLs. Several illustrative examples are presented to provide profound insights on understanding the PLL statistics both qualitatively and quantitatively. Results covered include the transient and stationary statistics for the nonmodulo-2π probability density function, modulo-2π probability density function, and cycle slipping density function, of the phase error. Various numerical settings of PLL parameters are involved, including the detuning factor and signal-to-noise ratio (SNR). The results presented in this paper elucidate the link between various parameters and the information geometry of the phase-error statistics and form a basis for future investigation on PLL designs.

Gain Scheduled Multivariable control of a Continuous Stirred Tank Reactor

Most chemical reactors, representing Multi-Input Multi-Output (MIMO) systems, are highly nonlinear and require complex control than single-input single-output (SISO) systems. In the present work, the system is linearized around different operating points. As linear design strategies are intended to work in linear regions, they are employed to evaluate local controller parameters. Decentralized controllers using constant detuning factor and decoupling controllers using static decouplers are designed. A gain scheduler is developed to deal with changes in operating conditions. The performances are evaluated by simulating the nonlinear equations of the system. Decentralized controllers cannot mitigate the interactions due to its structure possessing single loop. It is exhibited that the decoupling controllers offer better control for tracking of desired set point and rejection of load disturbances than those of decentralized controllers. The superiority of the suggested controller has been portrayed by performing simulation study on a Continuous Stirred Tank Reactor (CSTR).

A methodology to achieve the maximum transfer efficiency for magnetic coupling wireless power transfer systems

Transfer efficiency is one of the most significant indexes of magnetic coupling wireless power transfer (MC-WPT) systems, which is severely affected by frequency splitting. In this paper, a novel method is proposed for MC-WPT systems to achieve the maximum transfer efficiency by introducing and controlling the circuit detuning factors while maintaining the operating frequency at constant. Firstly, the circuit model of tri-coil MC-WPT systems is established along with the derivation of some key concepts, including the transfer efficiency and circuit detuning factors. Then the analytical expressions of the optimal circuit detuning factors, maximum transfer efficiency and a comprehensive discriminant which could quickly and accurately determine the critical value for every system parameters are derived. Further, the physical interpretation of the maximum transfer efficiency is firstly elucidated from the perspective of energy flow: (1) when the system is in non-splitting region, the energy flow path of the maximum transfer efficiency is transmitter–relay–receiver; (2) when system is in splitting region, the energy flow path of the maximum transfer efficiency is directly from the transmitter to the receiver. Finally, simulation models and practical prototypes are designed to verify the theoretical results. The simulation and experimental results show that the proposed system can maintain an almost constant maximum transfer efficiency over a wide range of transfer distance. The derived discriminant is very useful for guiding the system design in the future, and the energy flow analysis method will be beneficial for maximizing the efficiency for multi-coil MC-WPT systems.

Effects of detuning, gain-guiding, and index antiguiding on the dynamics of two laterally coupled semiconductor lasers

Four examples of laterally coupled semiconductor lasers with different waveguiding structures have been studied using coupled mode theory and allowing for frequency detuning between the lasers. The structures include purely real index guiding, pure gain-guiding, and combinations of index guiding and antiguiding with gain-guiding. The dynamics of these four systems have been explored using AUTO software (standard numerical continuation package), linear stability analysis, and direct integration of the rate equations. Convincing agreement between results obtained by these three methods has been demonstrated, including effects due to variation of laser pumping rate, detuning, and linewidth enhancement factor. A periodicity of behavior with laser separation has been revealed that was previously overlooked. This periodicity has increasing influence on the bifurcations of the system as the structures develop from those with purely real guidance to a combination of index antiguiding and gain-guiding. The laser design and operating parameters used are realistic for a wide range of edge-emitting and surface-emitting lasers of practical importance, so that the dynamics studied here are relevant to real systems of coupled lasers.

Femtosecond pulse shaping using wavelength-selective directional couplers: proposal and simulation.

The femtosecond pulse-shaping capabilities of wavelength-selective directional couplers are investigated. Numerical results show that, depending on the coupling length and coupling coefficient, one can achieve very different temporal shapes at the output of the directional couplers. For instance, temporal re-shaping of Gaussian-like pulses into Hermite-Gaussian pulses, parabolic pulses, square temporal waveforms and sequences of equalized multiple pulses with time widths down to the femtosecond range can be achieved using readily feasible fiber/waveguide designs. The detrimental influence of the second-order variation of the detuning factor in these pulse shapers is also numerically investigated.

Theory of Reduction of Residual Amplitude Modulation in Mid-Infrared Wavelength Modulation Spectroscopy by Injection Locking of Quantum Cascade Lasers

A simplified rate equation model is used to investigate suppression of residual amplitude modulation in injection-locked quantum cascade lasers with the master laser modulated by its drive current. Quasi-static and dynamic expressions for intensity modulation suppression and frequency modulation reproduction by the slave laser are presented. The suppression peaks at a specific value of the injection ratio for a given detuning and linewidth enhancement factor. The frequency modulation reproduction is less than 100% and decreases rapidly at frequencies higher than 300 MHz. The intensity modulation suppression remains constant during this frequency range. The effects of injection ratio, detuning, coupling efficiency and linewidth enhancement factor are discussed.

A Study of Residual Amplitude Modulation Suppression in Injection Locked Quantum Cascade Lasers Based on a Simplified Rate Equation Model

Using results that come out of a simplified rate equation model, the suppression of residual amplitude modulation in injection locked quantum cascade lasers with the master laser modulated by its drive current is investigated. Quasi-static and dynamic expressions for intensity modulation are used. The suppression peaks at a specific value of the injection ratio for a given detuning and linewidth enhancement factor. The intensity modulation suppression remains constant over a range of frequencies. The effects of injection ratio, detuning, coupling efficiency and linewidth enhancement factor are considered.

Mode-locked ultrashort pulse generation from on-chip normal dispersion microresonators.

We describe generation of stable mode-locked pulse trains from on-chip normal dispersion microresonators. The excitation of hyperparametric oscillation is facilitated by the local dispersion disruptions induced by mode interactions. The system is then driven from hyperparametric oscillation to the mode-locked state with over 200nm spectral width by controlled pump power and detuning. With the continuous-wave-driven nonlinearity, the pulses sit on a pedestal, akin to a cavity soliton. We identify the importance of pump detuning and wavelength-dependent quality factors in stabilizing and shaping the pulse structure, to achieve a single pulse inside the cavity. We examine the mode-locking dynamics by numerically solving the master equation and provide analytic solutions under appropriate approximations.

Modeling vocal fold asymmetries with coupled Van der Pol oscillators

Models of the glottal sound source are being developed to extend a recent synthesizer of disordered voices [Fraj et al., J. Acoust. Soc. Am. 132, 2603–2615 (2012)]. The synthesizer was based on a nonlinear wave-shaping algorithm, which generates a glottal excitation to a concatenated-tube representation of the trachea and vocal tract. The purpose of the present work is to incorporate a physics-based model of the vibrating vocal folds in order to increase the anatomical fidelity of the synthesizer. Further, the model will permit to characterize left-right fold asymmetries and explore the effect of those asymmetries on the resultant vocal timbre. In this report, the vocal folds are represented as a system of two coupled Van der Pol oscillators with noise terms and a detuning factor between their natural frequencies. Regions of phase locked and unlocked oscillations are determined and illustrated with bifurcation diagrams. Also, the effect of frequency detuning on the resultant frequency jitter is analyzed. The results are discussed in terms of their implications for modeling abnormal vocal fold behavior. [Work supported by CNPq (Brazil) and FNRS (Belgium).]

Trace distance and scaling behavior of a coupled cavity lattice at finite temperature

We use an alternative approach to study the quantum phase transition in a coupled cavity lattice at finite temperature. As an illustrative example, we investigate the behaviors of the trace distance and quantum phase transition in a Jaynes-Cummings lattice at finite temperature. It is found that the trace distance can be used to describe the critical point of the quantum phase transition at finite low temperatures and the critical points are sensitive to the atom-field interaction strength and the detuning factor. For non-equilibrium states, we demonstrate that the time evolution of the trace distance's maximum value is also a good indicator of the critical points. Moreover, we show that the scaling behavior of derivative of the trace distance at the critical points and the scaling rule are dependent on the external parameters of the Hamiltonian.