Nonlinear Loop Research Articles

Background-reduced spectral peak generation using a nonlinear loop mirror with a gas cell.

Spectral peaking in an optical fiber is a useful phenomenon for comb mode filtering and wavelength standards. However, for highly sensitive spectroscopic applications, it is important to suppress the pedestal components. Here we propose and demonstrate pedestal-suppressed spectral peak generation using a nonlinear fiber loop mirror with a molecular gas cell. The physical mechanism and fundamental properties were investigated numerically, and the output characteristics were examined experimentally. Almost background-free spectral peaks were generated successfully in the 1.65-µm wavelength range using a CH4 gas cell. The maximum signal-to-background ratio was more than 30 dB. Stable operation without any feedback control was achieved. It is expected that the proposed method is useful for highly sensitive spectroscopic applications.

978 Nm All-Polarization-Maintaining Mode-Locked Fiber Laser Based on Phase-Biased Nonlinear Amplifying Loop Mirror

Terahertz (THz) wave generation based on ultrafast laser are one of the most predominant and popular technologies. In particular, for THz generation by photoconductor antenna and optical rectification, higher optical to THz conversion efficiency usually requires ultrafast laser excitation into semiconductor or nonlinear crystal, therefore it is of great desire to develop ultrafast laser with high performance. CW Yb-doped lasers at 980 nm have been applied to generate THz wave range from 0.5 to 6 THz by DFG technique. To meet the demand of some THz wave generation (e.g. BNA crystal, gold nanoplasma), 980 nm ultrafast fiber laser are ideal pump sources and in desire to be developed. Here we demonstrate a 978 nm robust all-polarization-maintaining (PM) picosecond fiber laser mode- locked by phase-biased nonlinear amplifying loop mirror (PB- NALM). By introducing a nonreciprocal - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pi$</tex-math></inline-formula> /2 phase shifter into the fiber loop, a self-starting stable mode-locking is obtained with the center wavelength of 978.14 nm and a 3-dB bandwidth of 0.43 nm. The pulse duration is 8.1 ps corresponding to the time bandwidth product (TBP) of 1.09. The maximum average output power is 14.5 mW with a repetition rate of 45.438 MHz. After a master oscillator power amplification system, the 978 nm average output power reaches 2.12 W, which is then injected into a PPLN crystal for second harmonic generation and 52 mW 489 nm ultrashort lasers is obtained. This is, to the best of our knowledge, the first report of PB-NALM-based mode-locked fiber laser at 978 nm. The 978 nm ultrafast fiber laser and SHG to 489 nm have great potential in terahertz emission by shorter NIR and blue light.

Watt-level 1.6 μm dissipative soliton ultrafast laser and external generation of ∼70 fs noise-like pulses for supercontinuum generation

Here, we propose a high power dissipative soliton (DS) laser with a central wavelength of ∼1612 nm. The whole laser system includes the mode-locking oscillator and the corresponding master oscillator power amplifier (MOPA). The mode-locking oscillator is a nonlinear amplifier loop mirror (NALM) cavity, which has a net normal dispersion enabling the generation of nJ-level DS pulses. To further enhance the output power of the 1.6 μm DS pulses, the specially-designed MOPA system consisting of multiple-stage single-pass amplifier is constructed, which can amplify the output power to watt level and meanwhile keeps a high suppression ratio to C-band amplified spontaneous emission (ASE). This high power 1.6 μm DS laser will have further applications in biomedical research and material processing. In the amplifier, we observe the automatic evolution of the DS pulses into the noise-like (NL) pulses under high pumping strength. At the maximum pump power, the MOPA system delivers the NL pulses with an output power of over 2 W. The narrowest spike duration is ∼70 fs (fs). This 1.6 μm fs-scale NL laser is a good pump source for generating the mid-infrared supercontinuum without short wavelength region loss. To demonstrate the superiority of this NL laser, a broad supercontinuum from ∼0.87 μm to ∼3.75 μm waveband is achieved with a piece of highly germanium-doped (Ge-doped) fiber.

Locating structural nonlinearities using linear frequency response functions and nonlinear orthogonal projections

This paper addresses the identification of the spatial location of nonlinearities based on classical modal testing. Interpreting nonlinear systems as linear systems with a nonlinear feedback loop shows that the nonlinear contribution to the response and the nonlinear restoring forces are related through the linear frequency response function (FRF) matrix. Specifically, if the nonlinearity is localized, the response’s nonlinear part is intimately linked with the linear FRF at the nonlinearity location. Thus, processing input–output data measured under pseudorandom excitation, the nonlinearity location can be inferred from the comparison of the nonlinear part of the response with the different measured FRFs. A second approach, which provides a direct estimation of the nonlinear restoring forces at the different degrees of freedom, also utilizes the same relations. Both procedures are demonstrated numerically and experimentally.

An adjustable machine learning gradient boosting-based controller for PV applications

Traditional Proportional, Integral, and Derivative (PID) controllers are employed in most industrial control applications because they are simple and easy to implement. However, they are fallible and exhibit poor performance in complicated, non-linear, time-delayed systems, and noisy feedback loops. In photovoltaic systems applications such as maximum power point (MPP) tracking, PI controller performance in low irradiance levels, varying load conditions, and partial shading scenarios is considerably inefficient in tracking the corresponding reference current, which generates MPP and causes considerable steady-state error. Machine learning can be used with selective input/output data from the PI controller to build a model that has the ability to adjust in case of steady-state error. Thus, an adjustable Machine Learning Gradient Boosting-based (MLGB) controller with a PV module and a DC-DC boost converter is proposed in this work. To create the raw dataset, a PI controller was simulated, and the input/output signals were recorded. Data preprocessing, utilizing feature engineering and Shapley Additive Explanations (SHAP) values, was used to explain the dynamic behavior of each feature, the inter-feature dependability, and their significance with reference to the model output. Hyperparameters were tuned with cross-validation while the model was being created using the CatBoost method. To assess the adjustment of each feature to minimize the error, particularly for lower irradiance values, varying load conditions, and partial shading, a regression model was built. Using the MATLAB Simulink Environment, a complete system controlled by both the PI and the MLGB controller was developed and tested. A random irradiance level fluctuation profile, along with varying load and partial shading scenarios, was used to compare three controllers, namely the PI, conventional MLGB, and adjusted MLGB controllers, to see how they respond to rapidly changing environmental conditions. It has been proven through a thorough simulation analysis that the novel adjustable MLGB controller exhibits good tracking performance to follow the DC-DC boost converter's inductor current. When compared to the traditional PI controller, the new controller exhibits better results in terms of steady-state behavior and transient responsiveness in general, with a much lower mean (3.059E-03), median (1.908E-03), and RMS value (2.168E-02) of the signal error under various conditions.

Delayed closed-loop neurostimulation for the treatment of pathological brain rhythms in mental disorders: a computational study.

Mental disorders are among the top most demanding challenges in world-wide health. A large number of mental disorders exhibit pathological rhythms, which serve as the disorders characteristic biomarkers. These rhythms are the targets for neurostimulation techniques. Open-loop neurostimulation employs stimulation protocols, which are rather independent of the patients health and brain state in the moment of treatment. Most alternative closed-loop stimulation protocols consider real-time brain activity observations but appear as adaptive open-loop protocols, where e.g., pre-defined stimulation sets in if observations fulfil pre-defined criteria. The present theoretical work proposes a fully-adaptive closed-loop neurostimulation setup, that tunes the brain activities power spectral density (PSD) according to a user-defined PSD. The utilized brain model is non-parametric and estimated from the observations via magnitude fitting in a pre-stimulus setup phase. Moreover, the algorithm takes into account possible conduction delays in the feedback connection between observation and stimulation electrode. All involved features are illustrated on pathological α- and γ-rhythms known from psychosis. To this end, we simulate numerically a linear neural population brain model and a non-linear cortico-thalamic feedback loop model recently derived to explain brain activity in psychosis.

A modified frequency–time domain method for nonlinear aeroelastic systems with initial conditions

The frequency–time domain method is a very powerful tool for analyzing nonlinear aeroelastic systems; however, it is limited to obtaining steady-state solutions. To investigate nonlinear dynamic behaviors with initial conditions, a modified frequency–time domain method is proposed. Initial conditions, represented as pseudo forces, are introduced into the nonlinear feedback loops and are subsequently transformed from the time domain into the frequency domain. Hence, the proposed method allows nonlinear responses with initial conditions. Owing to the characteristics and limitations of this method, certain skills are presented to simulate both accurately and efficiently. Numerical results are provided for, in addition to the Van Der Pol equation, a two-degree-of-freedom airfoil section, and a three-degree-of-freedom aeroelastic typical section with control surface freeplay. Consequently, the feasibility of introducing initial conditions is validated. The comparison with the Runge–Kutta algorithm demonstrates the accuracy and efficiency of the proposed method, as an alternative to time-marching approaches. Furthermore, several key parameters, such as the sampling frequency and ending time of convolution integral, are investigated to explore the efficiency. The sensitivity of parameters and calculation methods of convolution integral is observed, which contributes to the strategies for adequate accuracy.

The Butterfly Effect and its Implications for Resilience in Complex Socio-Ecological Systems

This study delves into the intriguing concept of the Butterfly Effect and its implications for resilience in complex socio-ecological systems. Drawing upon chaos theory, the Butterfly Effect posits that minute initial changes can yield substantial and unforeseen outcomes in dynamic systems. The research investigates how the Butterfly Effect influences the resilience of intricate systems, such as urban ecosystems, global supply chains, and social networks, when confronted with environmental, economic, or social disruptions. By scrutinizing case studies and employing mathematical modeling, this study seeks to unveil the nonlinear dynamics, tipping points, and feedback loops that amplify or mitigate the effects of minor perturbations in complex systems. Moreover, it explores how comprehending the Butterfly Effect can inform strategies for augmenting the resilience of socio-ecological systems, including adaptive management, scenario planning, and community engagement. The study also explores the ethical and governance considerations arising from the unpredictability and interconnectedness inherent in complex systems. It highlights the need for inclusive decision-making processes that account for diverse perspectives and values. Additionally, it emphasizes the importance of adaptive governance approaches that allow for flexible responses to changing circumstances and evolving knowledge. By delving into the Butterfly Effect and its implications, this research endeavors to contribute to the development of strategies and policies that foster resilience in the face of uncertainty and promote sustainable development in complex socio-ecological systems. It recognizes the need for integrated approaches that consider the interdependencies and feedbacks between social, economic, and environmental dimensions. Ultimately, this study underscores the significance of understanding the Butterfly Effect as a lens through which to view and manage complex systems. By acknowledging the potential for cascading effects from minor changes, decision-makers and practitioners can adopt proactive measures to enhance system resilience. This research calls for further exploration of the Butterfly Effect across different scales and contexts to better grasp its implications and potential applications. In conclusion, the Butterfly Effect serves as a powerful concept for understanding the dynamics of complex socio-ecological systems. This research contributes to the existing body of knowledge by shedding light on its implications for resilience and providing guidance for decision-making and policy development in an uncertain and interconnected world.

Structural evolution and coexistence of ferroelectricity and antiferromagnetism in Fe, Nb co-doped BaTiO3 ceramics

Multiferroics are materials that exhibit two or more primary ferroic properties within the same phase and have potential applications in sensors, spintronics and memory devices. Here, the dielectric, ferroelectric and magnetic properties of novel multiferroics derived from BaTi1−x(Fe0.5Nb0.5)xO3 (BTFN, 0.01 ≤ x ≤ 0.10) ceramics are investigated. Multiferroism in these ceramics is manifested by the coexistence of ferroelectric long-range ordering and antiferromagnetism. With increasing x-value, there is a structural evolution from a tetragonal perovskite to a mixture of tetragonal and cubic phases, accompanied by a decrease in the temperature of maximum permittivity. At room temperature, ferroelectric behaviour is evidenced by the presence of current peaks corresponding to domain switching in the current-electric field loops, while the observation of non-linear narrow magnetic hysteresis loops suggests dilute magnetism. The results indicate that in the x = 0.07 composition the antiferromagnetic order is established through an indirect super-exchange interaction between adjacent Fe ions.

Solving Nonlinear Algebraic Loops Arising in Input-Saturated Feedbacks

We propose a dynamic augmentation scheme for the asymptotic solution of the nonlinear algebraic loops arising in well-known input saturated feedbacks typically designed by solving linear matrix inequalities (LMIs). We prove that the existing approach based on dynamic augmentation, which replaces the static loop by a dynamic one through the introduction of a sufficiently small time constant, works under some restrictive sufficient well-posedness conditions, requiring the existence of a diagonal Lyapunov matrix. However it can fail in general, even when the algebraic loop is well-posed. Then, we propose a novel approach whose effectiveness is guaranteed whenever well-posedness holds. We also show how this augmentation allows preserving the guaranteed region of attraction with Lyapunov-based designs, as long as a gain parameter is sufficiently large. We finally propose an adaptive version of the scheme where this parameter is adjusted online. Simulation results show the effectiveness of the proposed solutions.

Pulse convergence analysis and pulse information calculation of NOLM fiber mode-locked lasers based on machine learning method

Nowadays, mode-locked fiber laser has been extensively applied in various fields such as communication, biomedical, nuclear physics and material processing. By controlling the parameters of cavity elements, people can realize the output of ultrafast pulse with different states. Utilizing the traditional numerical method, the influence of different cavity parameters on the pulses can be computed accurately, which provides the simulation basis for the fabrication of mode-locked fiber lasers. However, with the development of the practical application demand, the performance requirements of the mode-locked pulse are also increasing. The traditional numerical methods have shown some defects in the calculation speed and analysis ability at this time. To improve the shortcomings of the existing numerical methods, in this work, we propose using the machine learning method to analyze the mode-locked pulse convergence of the nonlinear loop mirror (NOLM) fiber mode-locked laser and calculated its pulse information. Firstly, the mapping between cavity parameters and convergence region is established by the support vector machine (SVM) model, and utilizing it, the influence of different cavity parameters on mode-locking is investigated. Then, we train two artificial neural networks (ANN) for calculating the pulse shape and spectral shape in the mode-locked state and find out the cavity parameters under which.the spectral shape approximates to a parabola based on genetic algorithm and the ability of ANN in rapid computing. Finally, we construct the laser cavity according to the numerical result and obtain the mode-locked pulse with a parabolic shape spectrum. The authors believe that the model presented in this work will show widely application prospects in the numerical calculation of fiber lasers.

Improve Model Testing by Integrating Bounded Model Checking and Coverage Guided Fuzzing

Eectromechanical systems built by Simulink or Ptolemy have been widely used in industry fields, such as autonomous systems and robotics. It is an urgent need to ensure the safety and security of those systems. Test case generation technologies are widely used to ensure the safety and security. State-of-the-art testing tools employ model-checking techniques or search-based methods to generate test cases. Traditional search-based techniques based on Simulink simulation are plagued by problems such as low speed and high overhead. Traditional model-checking techniques such as symbolic execution have limited performance when dealing with nonlinear elements and complex loops. Recently, coverage guided fuzzing technologies are known to be effective for test case generation, due to their high efficiency and impressive effects over complex branches of loops. In this paper, we apply fuzzing methods to improve model testing and demonstrate the effectiveness. The fuzzing methods aim to cover more program branches by mutating valuable seeds. Inspired by this feature, we propose a novel integration technology SPsCGF, which leverages bounded model checking for symbolic execution to generate test cases as initial seeds and then conduct fuzzing based upon these worthy seeds. Over the evaluated benchmarks which consist of industrial cases, SPsCGF could achieve 8% to 38% higher model coverage and 3x-10x time efficiency compared with the state-of-the-art works.

Supercontinuum generation in NALM fiber laser with pulse type switchable

We report a supercontinuum (SC) generation based on pulse type switchable nonlinear amplification loop mirror (NALM) mode-locked fiber laser. In the experiment, we obtained a dissipative soliton (DS) mode-locked pulse with a spectral width of 20.04 nm and a pulse duration of 1.68 ps, which is used as a SC generation. The spectrum width of SC generated by DS is up to 940 nm (1460–2400 nm), and the unflatness of SC in 1580.2–2177.6 nm is less than 0.9 dB. By adjusting the polarization controller (PC) and pump power, the switching between DS and bound state soliton (BSS) is realized. The spectral width of SC generated by BSS is up to 962 nm (1438–2400 nm), and the 10 dB bandwidth is 689.2 nm. In addition, we carried out temperature sensing experiments and proved that our SC system has good smoothness and fineness. Our results demonstrate the SC generation with two switchable pulse type, which provides the possibility for different application requirements.

Wideband multiwavelength Brillouin fiber laser with switchable channel spacing.

A multiwavelength Brillouin fiber laser (MBFL) with a switchable channel spacing is demonstrated using a 1.55-µm single-mode AlGaInAs/InP hybrid square-rectangular laser as a seeding source. The scheme employs a highly nonlinear fiber loop with a feedback path to generate a 10-GHz-spacing MBFL. Then, assisted by a tunable optical bandpass filter, MBFLs with spacing from 20GHz to 100GHz at a step of 10GHz are generated in another highly nonlinear fiber loop based on the cavity-enhanced four-wave mixing. More than 60 lasing lines with an optical signal-to-noise ratio over 10dB are obtained successfully in all the switchable spacings. The total output power and the channel spacing of the MBFLs are proved to be stable.

Effects of thermal fluctuation when an optical cavity possesses neutral atoms and a two-mode laser system

Quantum-based experiments and their applications in lasers and magnetic fields have long been paramount, yet how to achieve exact stability for a long time is a merely answered question. This article develops a coupled laser map with cavity loss via a one-dimensional laser map, where complex phenomena in the newly developed mathematical model, dynamical properties with coupling delay, and thermal fluctuation of the lasing system are discussed numerically and analytically. It is deduced that the intensity of the laser beam can be controlled and stabilized for a long time, and large values of the effective gain coefficient can be reached when thermal noise exists in the optical cavity and when a nonlinear feedback loop is provided with coupling delay. Utilizing noise and coupling delay as a nonlinear feedback loop to the coupled laser map, we observed non-autonomous behaviour at different growth rate values. In contrast, symmetrical and phase-entrained synchronized mirror imaged orthogonal strange attractors and fractals were seen at the same growth rate values. At specific values of the controlling parameters, the peculiar attractors experience cyclic collisions with their basin boundaries, which break symmetry and synchronization and cause irregular behaviour.

All-optical reservoir computing system based on polarization dynamics

Reservoir computing (RC) is a simplified recurrent neural network and can be implemented by using a nonlinear system with delay feedback, thus it is called delay-based RC. Various nonlinear nodes and feedback loop structures have been proposed. Most of existing researches are based on the dynamical responses in intensity of the nonlinear systems. There are also a photoelectric RC system based on wavelength dynamics and an all-optical RC based on the phase dynamics of a semiconductor laser with optical feedback, as well as so-called polarization dynamics of a vertical cavity surface emitting laser (VCSEL). However, these VCSEL-RCs actually are based on the intensity dynamics of two mutually orthogonal polarization modes, or polarization-resolved intensity dynamics. The RC based on rich dynamical responses in polarization has not yet been found. A semiconductor optical amplifier (SOA) fiber ring laser can produce rich dynamical states in polarization, and is used in optical chaotic secure communication and distributed optical fiber sensing. To further expand the application of polarization dynamics of the SOA fiber ring laser and open up a new direction for the research of optical RC neural network, an all-optical RC system based on polarization dynamics of the ring laser is proposed. The ring laser is used as the reservoir, and the SOA as the nonlinear node. After the input signal is masked according to a synchronization scheme, it is injected into the reservoir by intensity modulation for a continuous wave generated by a superluminescent light emitting diode (SLED). The dynamical response in polarization of the ring laser is detected by a polarizer and a photodetector. The influences of the SOA operation current, output power of the SLED and attenuation of a variable optical attenuator (VOA) in the fiber loop on the polarization dynamic characteristic (mainly referring to the output degree of polarization) of the laser are analyzed experimentally. The fading memory and nonlinear response of the RC system based on the polarization dynamic response and intensity dynamic response are compared experimentally. The influences of output power of the SLED and attenuation of the VOA on fading memory, consistency and separation of the RC system based on the two kinds of dynamic responses are investigated experimentally. Thus the range of the VOA attenuation is determined. The network performance of the polarization dynamics RC system is evaluated by processing a Santa Fe time series prediction task and a multi-waveform recognition task. The normalized mean square error can be as low as 0.0058 for the time series prediction task, and the identification rate can be as high as 100% for the recognition task under the appropriate system parameters and only 30 virtual nodes. The experimental results show that the polarization dynamics RC system has good prediction performance and classification capability, which are comparable to the existing RC system based on intensity dynamics of the ring laser. The system can be expected to process two tasks in parallel when the polarization dynamics and intensity dynamics are used at the same time.

Design of a PEM fuel cell powered autonomous quadcopter

The purpose of this paper is to design a PID controller for a detailed nonlinear model of a custom-made quadcopter and utilise the power requirements in designing a proton exchange membrane (PEM) fuel cell system. The first principles methodology to commence with unmanned aerial vehicle architecture is delineated. The empirical actuator response of the brushless DC (BLDC) is obtained which further adds accuracy to the mathematical model of the system. The paper also presents simulations for nonlinear open loop and closed loop feedback with PID controller. The controller gains are obtained from the simulations for hover flight mode. The experimental implementation of battery powered quadcopter is validated with simulation results of PID control design. Finally, for the designed quadcopter, a mathematical model of a PEM fuel cell system to replace battery-specific power requirements is obtained. The key limitation of this paper is the absence of experimental data for fuel cell model due their high cost and low-availability.

Environment-stable sub-100 fs Er: fiber laser with a 3 dB bandwidth of 78 nm.

A robust all polarization-maintaining (PM) passively mode-locked Er-doped fiber laser is demonstrated based on the biased nonlinear amplifier loop mirror (NALM). With a π/2 nonreciprocal free-space phase shifter, stable single pulse mode locking can be obtained at the central wavelength of 1565.7 nm with a 3 dB spectral bandwidth of 24.6 nm in the soliton regime. The repetition rate of the pulse train is 98.13 MHz. The direct output pulse duration is 109 fs, which is nearly transform-limited. After the intracavity dispersion management, the robust self-started mode-locking in the stretched-pulse regime is realized at 1564 nm, and the 3 dB spectral bandwidth reaches up to 78 nm. The repetition rate of the pulse train is 199.6 MHz. In particular, the direct output pulse width is only 77 fs with a low integrated relative intensity noise (RIN) of only 0.0044% (integrated from 1 Hz to 1 MHz). To the best of our knowledge, this is the shortest pulse width directly from the all-PM NALM laser oscillator.

A Nonlinear Loop Filter based PLL With Harmonic Filtering Capability for Single-Phase Grid Integrated System With Improved Dynamic Performance

The major concern for the single-phase grid-connected inverter system is the phase and frequency error of the phase-locked loop (PLL) under various grid disturbances. This paper employs an effective cascaded band pass filter (CBPF) to eliminate the effects of the DC offset and harmonics present in the grid voltage. However, the presence of a prefilter slowed the dynamic performance of all-pass filter (APF) based PLL, implied to generate the orthogonal signal in the single-phase system. To improve the dynamic performance along with the harmonics filtering capability, a nonlinear loop filter (LF) based PLL with CBPF is proposed. The nonlinear LF contains a nonlinear function applied in proportional-integral control to improve the dynamic response of the PLL. Under various grid disturbances, the proposed controller has a faster dynamic response with less overshoot. Furthermore, the proposed PLL is capable of eliminating the effects of DC offset and subharmonics. The proposed PLL is compared with different state-of-the-art PLLs to assess the performance under various grid disturbances. The efficacy is validated experimentally as well as through simulation results.

Electric vehicle charging station modelling using FOH approximation and material selection based on temperature

In this article analytical model of New Energy Charging Station for vehicle is derived. It creates a nonlinear closed loop, when power electronic devices are connected to Grid due to the interaction with the grid’s impedance. It is particularly concerning because the prevalence of such devices, such as massive EV charging stations, distributed generation, distributed storage and APFs, is predicted to grow.. Furthermore, fast variable closed-loop dynamics are also illustrated when it comes to APFs. The primary contribution of this study is that it use DQ-theory to transform a closed loop (non-linear) into a closed loop of LTI. A straightforward, DT-controlled APF connected to a basic power source is used to test this technology in the beginning, producing a group of LTI differencial equations with easily determinable transient and stability response. Furthermore, the method may be done to a wide range of APFs linked to any power system with ease. It is finally validated using MATLAB/Simulink. The main objective is to develop a simplified model that ignores potential instability caused by nonlinear feedback loop and this can be used to examine the stability of the system using the developed model.