Nonlinear Frequency Research Articles

The effect of hydrogen enrichment on the conical premixed methane–air flame response and thermoacoustic modes coupling

This paper investigates the thermoacoustic dynamic responses of hydrogen-enriched laminar premixed conical methane–air flames under dual-mode coupling. Utilizing the level set method and the G-equation model, one meticulously derives the flame describing function (FDF) in relation to variations in hydrogen enrichment levels (ηH). This precisely derived FDF is then integrated into the low-order network model of the Rijke tube to analyze the thermoacoustic unstable modes of the system. Finally, dual-frequencies incoming flow velocity perturbations are reintroduced as inputs to obtain the flame response under thermoacoustic modes coupling. Results show that while keeping the unstretched steady flame aspect ratio constant, an increase in ηH not only raises the FDF’s cut-off frequency but also enhances the FDF gain within the nonlinear frequency region, leading to more unstable modes, especially high frequency modes within the Rijke tube system. Furthermore, the flame response is further altered under the excitation of dual unstable modes. When both modes are within the linear frequency region of the FDF, the flame response is co-controlled by the two modes, predominantly by the mode with a larger velocity perturbation amplitude, with weaker modes coupling leading to the additional frequency perturbation having a suppressive effect on the flame response at the original frequency. Conversely, when one or two modes are within the nonlinear frequency region of the FDF, the flame response is dominated by the lower-frequency mode, with higher nonlinear modes coupling allowing the additional frequency perturbation to both promote and suppress the response at the original frequency and also couple to produce a significant difference frequency response. Novelty and significance The novelty of this paper lies in the determination of the flame describing function (FDF) with varying hydrogen enrichment levels and the stability of thermoacoustic systems, and more significantly, conducting an in-depth and comprehensive investigation into the nonlinear dynamic responses of hydrogen-enriched flames to different types of dual-mode coupling perturbations. The dual-mode perturbations result in either attenuation or amplification of the flame response, depending on whether the corresponding frequencies lie within the linear or nonlinear frequency regions of the FDF, which innovatively incorporates the influence of the FDF phase and examines the responses at the difference frequencies generated by the coupling. This lays a foundation for further exploration into the mechanisms of modes coupling in hydrogen-enriched and other thermoacoustic systems.

Perfluorocarbons: a Material Platform for Tunable Nonlinear Frequency Conversion in Liquid Filled Suspended Core Fibers

Perfluorocarbons: a Material Platform for Tunable Nonlinear Frequency Conversion in Liquid Filled Suspended Core Fibers

Observation of modulation instability in a coherently driven active fiber ring resonator at 2 μm wavelength.

We report the first, to our knowledge, observation of the nonlinear phenomenon known as modulation instability (MI) in a coherently driven fiber resonator pumped at 1972 nm. To compensate for the very high losses in this spectral region, we have integrated a thulium-doped fiber amplifier inside the cavity. Lower losses allow a lower MI threshold, leading to the observation of this phenomenon at a moderate input power. The results align closely with the numerical simulations of the system. Our study shows that active compensation of loss can be implemented in the 2 µm wavelength range to construct fiber ring cavities with high finesse. It paves the way to the observation of more complex nonlinear effects optical frequency comb through cavity soliton generation.

A universal application of the general integral transform: New technique for the analysis of nonlinear oscillator systems

The wide applicability of a nonlinear oscillator is the main reason why it has gained so much attention from mathematicians and scientists, while it is difficult to be solved both numerically and theoretically. Variational iteration method is one of the numerical approaches which are used to investigate these nonlinear systems. In this paper, we present a nonlinear oscillator arising in a micro-electromechanical system as an example and derive its analytical solution by He’s frequency formula method and variational iteration method coupled with a new general integral transformation. The Lagrange multiplier is formulated and the new iterative format for the correction functional of the variational iteration method is given by the general integral transformation. The approximate nonlinear frequencies are achieved by this new technique and compared with the numerical ones obtained by the Runge–Kutta method. The new general integral transformation has the same essential qualities as those for Laplace and Fourier transform, and it becomes a promising tool to nonlinear problems when coupled with the variational iteration method.

A perturbative multi-mode model with finite parallel electric field for fast-ion-driven Alfvén eigenmodes

Abstract Alfvén eigenmodes are of great interest in any fusion device as they can be excited by fast ions in the plasma. If the modes grow to large amplitudes, they can cause transport and redistribution of the fast ions, thus limiting fusion performance. To save computational resources, the resonant kinetic interaction between the fast-particle species and the modes is often modelled by MHD-kinetic hybrid codes. Here, we present such a hybrid model which is applicable to three-dimensional magnetic fields, accounts for a finite parallel electric field and multiple MHD modes present at the same time. The model extends the one previously implemented in the CKA-EUTERPE code allowing for a better estimate of the damping due to the parallel electric field and nonlinear mode-mode interaction. The capabilities of our model are illustrated by applying the code to model nonlinear frequency chirping and fast-ion profile flattening.

All-fiber GHz few-cycle pulse generation at 2 µm.

We demonstrate an all-fiber GHz mode-locked laser system with few-cycle duration operating at 2 µm. Based on a dispersion-managed mode-locked oscillator, a multi-stage fiber amplifier, and a nonlinear pulse compressor, the laser system can deliver watt-level few-cycle pulses at a fundamental repetition rate of 1.041 GHz. This 2-µm pulsed laser offers outstanding performance metrics, including a pulse duration of 33 fs (corresponding to ∼5 optical cycles) and an average power of 4.17 W. Moreover, the all-fiber laser system exhibits excellent power stability, and the integrated relative intensity noise (RIN) is only 0.052% (10 Hz-1 MHz). It is anticipated that this new, to the best of our knowledge, laser source is promising for frontier applications, including coherent supercontinuum generation, nonlinear frequency conversion, and laser-material interaction.

Nonlinear optimal frequency control for dynamic vibration absorber and its application

A principal limitation of passive dynamic vibration absorber (DVA) lies in its intrinsic design constraint, as it is tuned to a specific resonant frequency, rendering it less effective at mitigating vibrations over a variable frequency range. To ensure that the DVA retains its vibration reduction capability under loads with time-varying frequencies, this paper proposes a method for designing the optimal suspension frequency based on the external load frequency. The approach involves altering the stiffness of the DVA through semi-active or active control to achieve the optimal suspension frequency and the best vibration reduction performance. In this study, the ratio R between the optimal suspension frequency and the load frequency is defined, and the nonlinear characteristic of R, based on the lowest vibration transmission rate, is studied using a two degree-of-freedom DVA model. Furthermore, an optimal suspension frequency variation control strategy based on load frequency identification is presented. Combined with the typical load with time-varying frequency encountered in metro vehicles, a multi-body dynamics theoretical model and a rigid–flexible coupling dynamics model are established to verify the effectiveness of the nonlinear optimal frequency control. Finally, the full-size railway vehicle roller rig is used to verify the correctness of the principle of optimal frequency curve. The research results show that when the mass ratio is 0.1, compared with rigid suspension, the nonlinear optimal frequency control can reduce the root mean square (RMS) value of the carbody’s entire time period acceleration during variable speed operation by 62.2%, and the maximum RMS value is reduced by 83.6%. In nonlinear control, unlike passive DVA, the vibration is never higher than that of rigid suspension within a specific velocity range. Compared with linear control strategy, nonlinearity can further reduce the elastic vibration. The test results from roller rig indicate that the semi-active DVA can effectively reduce the elastic vibrations of the carbody, while also validating the correctness of the nonlinear optimal suspension frequency principle. Therefore, the nonlinear frequency control in this study can provide reference for structural vibration control under loads with time-varying frequencies.

Investigating resonance frequency in advanced composite structures as the main part of bridge construction: a multi-physics simulation approach

This paper investigates the nonlinear vibration characteristics and resonance frequencies of a graphene oxide powders (GOP) reinforced beam structure, which is in contact with fluid, serving as a crucial component in bridge construction. Utilizing a multi-physics simulation approach, this study integrates both mathematical modeling and COMSOL simulations to analyze the behavior of the GOP-reinforced beam. The fluid in the analysis is modeled as incompressible, non-viscous, and irrotational, contributing to the interaction with the beam structure. The isogeometric approach, coupled with the harmonic balance method and the arc-length technique, is employed to solve the complex nonlinear partial differential equations (PDEs). This coupled method ensures the accurate capture of the nonlinear response and resonance frequencies of the beam, which are critical for the safe design and performance of bridge structures. The findings reveal the significant influence of GOP reinforcement on the vibration and stability characteristics of the beam, highlighting its potential to enhance structural performance under dynamic loading conditions. The study also emphasizes the importance of considering fluid-structure interactions in the design process, as the fluid’s presence substantially affects the vibration behavior. This research contributes to the understanding of the dynamic behavior of advanced composite structures in fluid environments, offering valuable insights for the design and analysis of bridge components. The results demonstrate the efficacy of the proposed simulation approach in addressing the complexities of nonlinear vibrations in fluid-structure interaction systems, paving the way for future developments in civil engineering applications.

Chalcogenide Ge20Sb5Se75 photonic crystal fiber with seven air-hole rings for ultraflat mid-infrared supercontinuum generation

Supercontinuum (SC) generation in solid-core circular photonic crystal fibers (PCFs) made of Ge20Sb5Se75 is numerically analyzed. A large core is projected to increase light coupling efficiency into selected PCFs as well as raise coupling to standard silica fibers. High nonlinear coefficient and near-zero flat dispersion allow ultraflat SC spanning 1.5–4.6 μm in an all-normal dispersion regime. This requires 3 kW of peak power with 180 fs of pulse duration. The fiber with one zero-dispersion wavelength (ZDW) generates SC bandwidth in the range of 1.54–7.39 μm at 3.5 μm using peak power of 10 kW. For the same input power, the SC spectral covers from 1.39 to 7.36 μm in 10 cm of fiber with two ZDWs. These are wider SC bandwidths than those of previous chalcogenide fibers reached with lower peak powers. Therefore, the proposed Ge20Sb5Se75 PCFs are excellent candidates for the broadband ultraflat mid-infrared SC spectra used in high-speed nonlinear imaging and frequency measurement.

Supercontinua from integrated gallium nitride waveguides

Supercontinua are broadband spectra that are essential to optical spectroscopy, sensing, imaging, and metrology. They are generated from ultrashort laser pulses through nonlinear frequency conversion in fibers, bulk media, and chip-integrated waveguides. For any generating platform, balancing the competing criteria of strong nonlinearity, transparency, and absence of multiphoton absorption is a key challenge. Here, we explore supercontinuum generation in integrated gallium nitride (GaN) waveguides, which combine a high Kerr nonlinearity, mid-infrared transparency, and a large bandgap that prevents two- and three-photon absorption in the technologically important telecom C-band, where compact erbium-based pump lasers exist. Using this type of laser, we demonstrate tunable dispersive waves and gap-free spectra extending to almost 4 µm in wavelength, which is relevant to functional group chemical sensing. Additionally, leveraging the material’s second-order nonlinearity, we implement on-chip f-to-2f interferometry to detect the pump laser’s carrier-envelope offset frequency, which enables precision metrology. These results demonstrate the versatility of GaN-on-sapphire as a platform for broadband nonlinear photonics.

Second Harmonic Generation in Apodized Chirped Periodically Poled Lithium Niobate Loaded Waveguides Based on Bound States in Continuum

With the rapid development of optical communication and quantum information, the demand for efficient and broadband nonlinear frequency conversion has increased. At present, most single-frequency conversion processes in lithium niobate on insulator (LNOI) waveguides suffer from lateral leakage without proper design, leading to an additional increase in propagation loss. Achieving broadband frequency conversion also encounters this problem in that there are no relevant works that have solved this yet. In this paper, we theoretically propose an efficient and flat broadband second harmonic generation (SHG) in silicon nitride loaded apodized chirped periodically poled LNOI waveguides. By using a bound states in the continuum (BICs) mechanism to reduce the propagation loss and utilizing the characteristic that the BICs are insensitive to wavelength, an ultra-low-loss wave band of 80 nm is realized. Then, by employing an apodized chirped design, a flat broadband SHG is achieved. The normalized conversion efficiency (NCE) is approximately 222%W−1cm−2, and the bandwidth is about 100 nm. Moreover, the presented waveguides are simple and can be fabricated without direct etching of lithium niobate, exhibiting excellent fabrication tolerance. Our work may open a new avenue for exploring low-loss and flat broadband nonlinear frequency conversion on various on-chip integrated photonic platforms.

A nonlinear vibration isolator with an essentially nonlinear converter

This paper introduces nonlinearity into bilinear springs and proposes an efficient asymmetrical nonlinear frequency converter (NC) that has a non-reciprocal transmission, which cascades a nonlinear spring and a rope. To solve the vibration equations of both NC and the conventional NES, the Runge-Kutta method is utilized. A comparison is conducted between the amplitude attenuation rates of the NC and the conventional NES. The rate of energy dissipation is indicated by analyzing the remaining energy. According to numerical analysis results, NC has a better performance in suppressing vibration than the conventional NES within a certain range. The energy dissipation rate is higher under a wide initial condition. In addition, NC can cause energy to shift from low-frequency regions to high-frequency regions with wide frequency bands. NC has a broader frequency range and a wider range of applications. This research offers a new approach and strategy for exploring effective devices for damping vibrations.

Diagnosis of Voltage Losses of the Proton Exchange Membrane Water Electrolyzer with Nonlinear Frequency Response Method

Proton exchange membrane water electrolyzer (PEMWE) takes a central place in the hydrogen economy as a crucial technology for green hydrogen production. However, this technology still faces challenges, such as the cost of the materials, performance losses at high current densities, and durability. To overcome these obstacles, better comprehension of the phenomena occurring in the PEMWE is necessary. Typical electrochemical methods, such as polarization curves and high-frequency response measurements, lack detailed information about the individual contributions to the overall voltage losses and cannot point out the causes of the performance shortcomings. Therefore, the development of advanced diagnosis techniques for PEMWE is of importance both for the state of health analysis during the operation, as well as for the testing of new materials.In this work, a nonlinear frequency response (NFR) method was applied for the diagnosis of a lab-scale PEMWE. The NFR method represents an extension of the electrochemical impedance spectroscopy to the nonlinear domain by investigating the second-order frequency response function (FRF) in addition to the first-order FRF (equivalent to the impedance) [1]. Typical features corresponding to processes occurring in the PEMWE were observed in both the first- and the second-order FRFs. The experimental observations were interpreted based on a simple nonlinear model. The features observed at frequencies higher than 0.1 Hz were attributed to the electrochemical half-reactions, while a high current density feature observed at lower frequencies, could be attributed to the mass transport. During the analysis, the first-order FRF (impedance) was found not to be sensitive enough for the discrimination of the different sets of parameters and the second-order FRF had to be included for better parameter identification. The obtained parametrized model is dynamic and nonlinear and, thus, it can be utilized for model predictive control of the PEMWE and optimization of the overall green hydrogen production system.[1] Vidaković-Koch, T., Miličić, T., Živković, L.A., Chan, H.S., Krewer, U., Petkovska, M., Cur. Opin. Electrochem., 2021, 30, 100851

Analysis of Vibration Electromechanical Response Behavior of Poly(Vinylidene Fluoride) Piezoelectric Films

Studying the electromechanical response behavior of piezoelectric thin films under different loading conditions is of great value for the development and optimization of piezoelectric sensors and flexible portable electronic devices. This paper establishes the theory of large deflection vibration of rectangular four-edge simply supported piezoelectric thin films using the energy method, and analyzes the electromechanical response characteristics of vibration force (including resonant frequency and nonlinear vibration). Meanwhile, the electromechanical response behavior of Poly(vinylidene fluoride) (PVDF) films under different loading conditions (static and harmonic vibration) is analyzed. The study investigates the nonlinear vibration characteristics and resonance frequency variations under different film sizes and thickness conditions in the case of various loading conditions. The developed model can predict the resonance frequency associated with the plate dimensions. This study is of great significance for the research and application of laminated piezoelectric film sensors.

Ultrafast structured light through nonlinear frequency generation in an optical enhancement cavity.

The generation of shaped laser beams, or structured light, is of interest in a wide range of fields, from microscopy to fundamental physics. There are several ways to make shaped beams, most commonly using spatial light modulators comprised of pixels of liquid crystals. These methods have limitations on the wavelength, pulse duration, and average power that can be used. Here we present a method to generate shaped light that can be used at any wavelength from the UV to IR, on ultrafast pulses, and a large range of optical powers. By exploiting the frequency difference between higher-order modes, a result of the Gouy phase, and cavity mode matching, we can selectively couple into a variety of pure and composite higher-order modes. Optical cavities are used as a spatial filter and then combined with sum-frequency generation in a nonlinear crystal as the output coupler to the cavity to create ultrafast, frequency comb structured light.

Quantum linewidth limitation of a laser stabilized with a nonlinear microcavity.

We show that the linewidth of a laser locked to an optical cavity characterized with nonzero optical cubic nonlinearity is restricted by the value of the nonlinear frequency shift of the cavity mode per single photon localized in the mode. This effect is masked by the fundamental thermodynamic noise in monolithic microcavities. The quantum limit of the linewidth can be measured using two independent lasers separately locked to spatially overlapping modes of the nonlinear resonator.

Enhanced vertical second harmonic generation from layered GaSe coupled to photonic crystal circular Bragg resonators

Abstract Two-dimensional (2D) layered materials without centrosymmetry, such as GaSe, have emerged as promising novel optical materials due to large second-order nonlinear susceptibilities. However, their nonlinear responses are severely limited by the short interaction between the 2D materials and light, which should be improved by coupling them with photonic structures with strong field confinement. Here, we theoretically design photonic crystal circular Bragg gratings (CBG) based on hole gratings with a quality factor as high as Q = 8 × 103, a mode volume as small as V = 1.18 (λ/n)3, and vertical emission of light field in silicon nitride thin film platform. Experimentally, we achieved a Q value up to nearly 4 × 103, resulting in a 1,200-fold enhancement of second harmonic generation from GaSe flakes with a thickness of 50 nm coupling to the CBG structures under continuous-wave excitation. Our work endows silicon-based photonic platforms with significant second-order nonlinear effect, which is potentially applied in on-chip quantum light sources and nonlinear frequency conversion.

Multiple-signal-joint-processing-based guard interval shortening method for a CS-NFDM system.

Aiming to further improve the spectral efficiency (SE) of a continuous spectrum modulated nonlinear frequency division multiplexing (CS-NFDM) system, we propose a novel ,to the best of our knowledge, multiple-signal-joint-processing (MSJP)-based guard interval (GI) shortening method. In this method, multiple NFDM time-domain signals are jointly processed as a whole to carry out nonlinear Fourier transform and inverse nonlinear Fourier transform (NFT-INFT) operations. These operations can fuse the multiple NFDM time-domain signals together, which is equivalent to the corresponding inverse process of a fiber transmission. Experimental results show that the normalized SE of the proposed method can reach 0.99 when approaching the limit value of 1 and obtain a 2.33 dB Q2-factor improvement compared with the pre-dispersion compensation (PDC) method under the same GI of 0.03 ns in an 80 km SSMF transmission of a 46 GHz signal bandwidth. Furthermore, in comparison with the PDC method, the proposed method can achieve 32.86% normalized SE improvement in the 1120 km SSMF transmission of 32 GHz signal bandwidth under the SD-FEC of 2.4E-2.

Silicon Carbide Microring Resonators for Integrated Nonlinear and Quantum Photonics Based on Optical Nonlinearities

Silicon carbide (SiC) electronics has seen a rapid development in industry over the last two decades due to its capabilities in handling high powers and high temperatures while offering a high saturated carrier mobility for power electronics applications. With the increased capacity in producing large-size, single-crystalline SiC wafers, it has recently been attracting attention from academia and industry to exploit SiC for integrated photonics owing to its large bandgap energy, wide transparent window, and moderate second-order optical nonlinearity, which is absent in other centrosymmetric silicon-based material platforms. SiC with various polytypes exhibiting second- and third-order optical nonlinearities are promising for implementing nonlinear and quantum light sources in photonic integrated circuits. By optimizing the fabrication processes of the silicon carbide-on-insulator platforms, researchers have exploited the resulting high-quality-factor microring resonators for various nonlinear frequency conversions and spontaneous parametric down-conversion in photonic integrated circuits. In this paper, we review the fundamentals and applications of SiC-based microring resonators, including the material and optical properties, the device design for nonlinear and quantum light sources, the device fabrication processes, and nascent applications in integrated nonlinear and quantum photonics.

Nonlinear dynamics of a dual-rotor system with active elastic support/dry friction dampers based on complex nonlinear modes

In this study, the nonlinear dynamics of a dual-rotor system with active elastic support/dry friction dampers (ESDFDs) are investigated based on complex nonlinear modes (CNMs). The finite element method (FEM) combined with a full-3D friction model is introduced to construct the governing equation for the system. Additionally, the Craig–Bampton technique is applied to downscale the finite element model of the system. Based on the reduced order model (ROM), the nonlinear modal damping ratio of the target mode is employed to measure the dry friction damping performance of active ESDFD. The effects of the active ESDFD position, normal force, and tangential contact stiffness on the nonlinear modal damping ratio and modal frequency are analysed. Moreover, the softening characteristics of the active ESDFD are revealed, and the critical speed intervals of the active ESDFD/dual-rotor system are determined. Furthermore, by using the harmonic balance–alternating frequency/time domain (HB–AFT) method, the steady-state response of the system under unbalanced excitation is calculated. The accuracy and effectiveness of nonlinear modal analysis are validated based on the relationships between nonlinear modes and steady-state unbalanced responses. Conversely, the vibration mitigation effects of active ESDFD are determined by the unbalanced response amplitude. Additionally, the controllable region and optimal normal force for effective vibration control in the target mode are defined. Depending on the controllable region, a control strategy for turning on/off the optimal normal force is developed. The findings demonstrate that the developed control strategy enables the active ESDFD to significantly reduce the response amplitude of the dual-rotor system across various excitation levels, showing substantial potential for engineering applications.