Nonlinear Resonance Research Articles

Infrared imaging with nonlinear silicon resonator governed by high-Q quasi-BIC states

Nonlinear light-matter interactions have emerged as a promising platform for various applications, including imaging, nanolasing, background-free sensing, etc. Subwavelength dielectric resonators offer unique opportunities for manipulating light at the nanoscale and miniturising optical elements. Here, we explore the resonantly enhanced four-wave mixing (FWM) process from individual silicon resonators and propose an innovative FWM-enabled infrared imaging technique that leverages the capabilities of these subwavelength resonators. Specifically, we designed high-Q silicon resonators hosting dual quasi-bound states in the continuum at both the input pump and signal beams, enabling efficient conversion of infrared light to visible radiation. Moreover, by employing a point-scanning imaging technique, we achieve infrared imaging conversion while minimising the dependence on high-power input sources. This combination of resonant enhancement and point-scanning imaging opens up new possibilities for nonlinear imaging using individual resonators and shows potential in advancing infrared imaging techniques for high-resolution imaging, sensing, and optical communications.

Adaptive frequency-stabilization of MEMS oscillators using mode coupling

Microelectromechanical systems (MEMS) oscillators with high frequency stability hold significant potential for a myriad of applications across diverse fields. This letter delves into an adaptive frequency stabilization system designed to significantly improve the performance of MEMS oscillators. Our approach leverages the concept of mode coupling to dynamically adjust the oscillator’s frequency based on phase control, ensuring optimal stability under varying operating conditions. The MEMS oscillator comprises a nonlinear low-frequency resonator and a linear high-frequency resonator. Through mode coupling and phase control, the nonlinear resonator is harnessed to regulate the oscillation frequency of the linear resonator. Experimental results prove that by applying the proposed approach, the frequency stability of the MEMS oscillator is enhanced by nearly 700 times for long-term stability at 1000 s. Additionally, in the scenario with varying temperature, the system also effectively improves the frequency stability by over 1000 times at 802 s.

Frequency comb generation via synchronous pumped χ(3) resonator on thin-film lithium niobate

Resonator-based optical frequency comb generation is an enabling technology for a myriad of applications ranging from communications to precision spectroscopy. These frequency combs can be generated in nonlinear resonators driven using either continuous-wave (CW) light, which requires alignment of the pump frequency with the cavity resonance, or pulsed light, which also mandates that the pulse repetition rate and cavity free spectral range (FSR) are carefully matched. Advancements in nanophotonics have ignited interest in chip-scale optical frequency combs. However, realizing pulse-driven on-chip Kerr combs remains challenging, as microresonator cavities have limited tuning range in their FSR and resonance frequency. Here, we take steps to overcome this limitation and demonstrate broadband frequency comb generation using a χ(3) resonator synchronously pumped by a tunable femtosecond pulse generator with on-chip amplitude and phase modulators. Notably, employing pulsed pumping overcomes limitations in Kerr comb generation typically seen in crystalline resonators from stimulated Raman scattering.

Nonlinear vibrations, bifurcations and chaos of piezoelectric composite lattice sandwich plate with four simply supported edges

This paper is devoted to investigate the nonlinear dynamics, bifurcation and chaos of the piezoelectric composite lattice sandwich plate with 1:3 internal resonance. Galerkin method is used to discretize the nonlinear partial differential governing equations of motion into the ordinary differential equations. The multi-scale method is used to obtain the modulation equations of the piezoelectric composite lattice sandwich plate in the polar coordinates and Cartesian coordinates in the primary and parametric resonances, respectively. Using Newton-Raphson method, the bifurcation diagrams of the steady-state equilibrium solution are obtained for the modulation equation with the change of the system parameters. The stability of the steady-state equilibrium solution is analyzed for the modulation equation. The existence of the static bifurcations, such as the saddle-node bifurcation, pitchfork bifurcation and Hopf dynamic bifurcations are found. The complex nonlinear jump phenomena caused by the existence of the multiple nonlinear steady-state solution regions are analyzed in detail. Fourth-order Runge-Kutta method is used to continue tracing the nonlinear periodic solution of the modulation equation in Cartesian coordinates. The time-history diagram, phase portrait and Poincaré map are obtained for the piezoelectric composite lattice sandwich plate in the nonlinear resonance. The dynamic process of the nonlinear periodic solution is described for the modulation equation from the limit cycle oscillation to the chaotic attractor in detail.

Tunable bandgaps of a metamaterial beam with nonlinear magnetic resonators

Tunable bandgaps of a metamaterial beam with nonlinear magnetic resonators

Nonlinear combination resonance analysis of parametric-forced excitation for an axially moving piezoelectric rectangular thin plate in thermal- electromechanical coupling field

In this paper, the combination resonance of parametric-forced excitation characteristics for an axially moving rectangular piezoelectric plate under a thermal-electromechanical field is studied. Based on Kirchhoff-Love plate theory and Von Karman theory, the transverse vibration governing equations are derived from Hamilton's principle. The equations are discretized to ordinary differential equations by the Galerkin method. Then, the multiple scales method is applied to solve the system combination resonance equation, two different resonance states and corresponding amplitude-frequency response equations are obtained by eliminating the secular term, respectively. Additionally, the stability of the steady-state responses is analyzed by Lyapunov stability. Based on the numerical analysis, the influence of axial velocity, external voltage, central temperature difference, structural damping, and other parameters on nonlinear combination resonance response are investigated. The effect of parameter variation on period-doubling bifurcation and the chaotic motion of the system are also discussed by the system global bifurcation diagram.

Sub‐MeV Electron Precipitation Driven by EMIC Waves Through Nonlinear Fractional Resonances

AbstractElectromagnetic ion cyclotron waves in the Earth's outer radiation belt drive rapid electron losses through wave‐particle interactions. The precipitating electron flux can be high in the hundreds of keV energy range, well below the typical minimum resonance energy. One of the proposed explanations relies on nonresonant scattering, which causes pitch‐angle diffusion away from the fundamental cyclotron resonance. Here we propose the fractional sub‐cyclotron resonance, a second‐order nonlinear effect that scatters particles at resonance order n = 1/2, as an alternate explanation. Using test‐particle simulations, we evaluate the precipitation ratios of sub‐MeV electrons for wave packets with various shapes, amplitudes, and wave normal angles. We show that the nonlinear sub‐cyclotron scattering produces larger ratios than the nonresonant scattering when the wave amplitude reaches sufficiently large values. The ELFIN CubeSats detected several events with precipitation ratio patterns matching our simulation, demonstrating the importance of sub‐cyclotron resonances during intense precipitation events.

Resonant Electron Signatures in the Formation of Chorus Wave Subpackets

AbstractA 2‐D GCPIC simulation in a dipole field system has been conducted to explore the excitation of oblique whistler mode chorus waves driven by energetic electrons with temperature anisotropy. The rising tone chorus waves are initially generated near the magnetic equator, consisting of a series of subpackets, and become oblique during their propagation. It is found that electron holes in the wave phase space, which are formed due to the nonlinear cyclotron resonance, oscillate in size with time during subpacket formation. The associated inhomogeneity factor varies accordingly, giving rise to various frequency chirping in different phases of subpackets. Distinct nongyrotropic electron distributions are detected in both wave gyrophase and stationary gyrophase. Landau resonance is found to coexist with cyclotron resonance. This study provides multidimensional electron distributions involved in subpacket formation, enabling us to comprehensively understand the nonlinear physics in chorus wave evolution.

Towards digitally programmed nonlinear electroacoustic resonators for low amplitude sound pressure levels: Modeling and experiments

Passive acoustic foams have limitations in efficiently reducing low-frequency noise below 800 Hz due to the associated wavelengths for reasonable material thickness. To address this challenge, passive or semi-active resonators are commonly employed solutions. Linear resonators are very efficient within a narrow frequency bandwidth. However, nonlinear oscillators can broaden this bandwidth, but activation of their nonlinear responses typically requires high excitation amplitudes, beyond human hearing tolerance amplitudes. Furthermore, the specific type of nonlinearity in such devices is often predetermined by the inherent properties of the resonator. In this study, we employ a novel digital control algorithm, allowing to activate the nonlinear response of the electroacoustic resonator at low excitation amplitudes. This algorithm, which relies on real-time integration, facilitates the creation of nonlinear resonators featuring polynomial or diverse non-polynomial nonlinearities within the range of low amplitudes. The nonlinear control is carried out on a loudspeaker equipped with a microphone. Our research highlights the potential to create nonlinear resonators with different, versatile and programmable behaviors. Unprecedented non-polynomial nonlinear behaviors are experimentally exhibited, we consider cubic, piece-wise linear, and logarithmic nonlinearities. These behaviors are implemented and compared to a semi-analytic model to control an acoustic mode of a tube under conditions of low excitation amplitudes and frequencies.

Vector form intrinsic finite element analysis for nonlinear parametric resonances of planar beam structures

The parametric resonance of a beam structure may lead to a disastrous consequence. To assess the safety of a structure, structural engineers need a straightforward and practical method to calculate the large-amplitude nonlinear parametric resonance responses of the beam structure. This paper proposes a newly developed vector form intrinsic finite element (VFIFE) calculation scheme to analyse the nonlinear parametric resonance of planar beam structures. By taking into account the geometric stiffness effect of the internal axial force for the frame element, a new relationship between internal nodal forces and deformation components is first established based on the VFIFE principle and the parametric resonance mechanism of frame structures. A numerical example of a portal frame is presented to demonstrate the efficacy of this new calculation scheme. A parametric resonance test of the cantilever beam is conducted to verify the applicability of the VFIFE method. The numerical results show that the proposed scheme can well simulate the nonlinear phenomena of parametric resonances. The numerical predictions are consistent with the experimental observations. A filtering-based finite-time Lyapunov exponent approach is presented to determine the stability boundary of the structure. The numerical stability boundary of parametric resonance agrees well with the experimental boundary. Possible causes of deviations between the numerical and experimental results are discussed. The proposed VFIFE scheme is a simple and effective means of analysing the stability and nonlinear responses of the parametric resonance of planar beam structures.

Multi-harmonic phononic frequency comb generation in capacitive CMOS-MEMS resonators

Phononic frequency combs (PFCs) have emerged as a pivotal technology in precision measurements and advanced signal processing, harnessing the power of discrete, evenly spaced frequency lines. Their expansion into the realm of microelectromechanical systems (MEMS) presents potential opportunities for enhanced control in various applications, from telecommunications to quantum computing. This work presents an experimental study on the generation of PFCs at the fundamental frequency and its higher harmonics in a complementary metal oxide semiconductor based electrostatic MEMS resonator measured under an open-loop configuration. The phenomenon is attributed to nonlinear mode coupling and 1:2 internal resonance between two eigenmodes and their harmonics when the resonator operates in nonlinear resonance. The experimental approach employs a combination of optical and electrical characterization techniques. This study, primarily experimental in nature, provides crucial insights into the behavior of PFCs in MEMS resonators, suggesting possible multi-harmonic internal resonance as the underlying mechanism. These findings contribute significantly to the field of MEMS research, offering potential applications in high-precision frequency control for telecommunications, sensor technology, and quantum computing.

Non-Linear Resonances and Chaotic Dynamics of a Rotating Gyroscope Under a Fractional Order Derivative Damping

Non-Linear Resonances and Chaotic Dynamics of a Rotating Gyroscope Under a Fractional Order Derivative Damping

Nonlinear forced vibration of functionally graded hybrid three-phase nanocomposite toroidal shell segments reinforced by carbon nanotubes (CNTs) and graphene nanoplatelets (GPLs)

This study proposes a unique three-phase functionally graded (FG) hybrid nanocomposite material reinforcing the toroidal shell segments to investigate the nonlinear forced vibration using Reddy's higher-order shear deformation theory, von Karman geometrical nonlinearity and Stein-McElman's assumption along with the Hamilton principle. The examined toroidal shell's material consists of polymeric resin, carbon nanotubes (CNTs), and graphene platelets (GPLs) as nanocomposites. The material properties have been derived based on a modified Halpin-Tsai micromechanical model. Four distribution patterns have been studied: uniform (UD), FG-X, FG-O, and FG-V. The continuous distribution of GPLs and CNTs leads to inhomogeneous position-dependent properties throughout the shell thickness. The obtained differential equations of motion have been reduced to ordinary equations using Galerkin's technique. A multi-scales method (MSM) is used to estimate a closed-form solution representing the frequency-amplitude relation, and the state space representation is used along with numerical fourth-order Runge Kutta method (RK4) to obtain the nonlinear dynamic response of the toroidal shell. The accuracy of the current results obtained has been verified by comparing them with the relevant literature and numerical results using (RK4). In addition, the influence of both GPLs and CNTs weight fractions, nanofillers’ distribution types, longitudinal and circumferential wave numbers, elastic foundation parameters, static axial compression load, transverse excitation load, damping ratio, geometrical characteristics of the toroidal shell on the dimensionless natural frequency, nonlinear primary resonance (frequency-amplitude curve), and nonlinear dynamic response are carefully studied. The results found that combining (GPLs & CNTs) into the shell's matrix improves performance, especially in concave shells compared to convex ones. The FG-X pattern reduces peak resonance amplitude and improves natural frequency. A reduction of 12.3 % is observed for convex shells, and 21.5 % for concave shells compared to FG-O.

Latched detection of zeptojoule spin echoes with a kinetic inductance parametric oscillator.

When strongly pumped at twice their resonant frequency, nonlinear resonators develop a high-amplitude intracavity field, a phenomenon known as parametric self-oscillations. The boundary over which this instability occurs can be extremely sharp and thereby presents an opportunity for realizing a detector. Here, we operate such a device based on a superconducting microwave resonator whose nonlinearity is engineered from kinetic inductance. The device indicates the absorption of low-power microwave wavepackets by transitioning to a self-oscillating state. Using calibrated pulses, we measure the detection efficiency to zeptojoule energy wavepackets. We then apply it to measurements of electron spin resonance, using an ensemble of 209Bi donors in silicon that are inductively coupled to the resonator. We achieve a latched readout of the spin signal with an amplitude that is five hundred times greater than the underlying spin echoes.

Quasi-integrability and nonlinear resonances in cold atoms under modulation.

Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces (PESs): one of them is binding, while the other one is scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents a scenario reminiscent of Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system that is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit systems.

Effects of nonlinearities on the gap resonances between two free-heaving barges

The hydrodynamic characteristics of the gap resonances between two identical side-by-side barges are investigated in a constrained interpolation profile method-based numerical wave tank. Each barge can heave freely under the excitation of the incident waves. This paper mainly concentrates on the influences of the nonlinearities during the gap resonances on their hydrodynamic performance, via the parameter study of the incident-wave height. Numerical results demonstrated that the nonlinear gap resonances' magnitudes may reach close to or exceed that of the linear gap resonance and naturally contain strong nonlinearities when considering the heave responses of the side-by-side barges. Meanwhile, the effects of the heave responses on the key hydrodynamic parameters cannot be ignored as well. Therefore, the wave run-ups of the barges are of significant importance for the investigation. On the one hand, the wave run-ups directly reflect the coupling effects between the gap resonances and the twin barges' heave responses. On the other hand, the nonlinearities of the wave run-ups perform stronger than the wave elevation at the gap. Moreover, the linear wave run-ups are proposed via the linear formulas to qualitatively and quantitively investigate the effects of the nonlinearities on the inner process of the wave run-ups by comparison. Based on the harmonic analysis, the features of the distributions of the first four order harmonics of the wave elevation at the gap, the wave run-ups, and the wave loads are illustrated.

Electron Resonant Interaction With Coherent ULF Waves: Hamiltonian Approach

AbstractElectron resonant interaction with ultra‐low‐frequency (ULF) waves is considered to be a driver of electron radial transport in Earth’s inner magnetosphere. Traditional concept of such interaction assumes the electron slow diffusive scattering by a broad‐band ULF spectrum, but recent spacecraft observations reported a possibility for electrons to resonate nonlinearly with intense coherent ULF waves. This study proposes a theoretical model describing the main elements of such nonlinear resonant interactions. We implement a Hamiltonian approach to describe equatorial electron motion in a dipole magnetic field and electric ULF wavefield and demonstrate the ULF‐electron interactions has two basic nonlinear resonant regimes: phase bunching and phase trapping. Finally, we discuss possible applications of the proposed theoretical approach and the importance of ULF‐electron nonlinear resonances.

Selective active resonance tuning for multi-mode nonlinear photonic cavities

Resonant enhancement of nonlinear photonic processes is critical for the scalability of applications such as long-distance entanglement generation. To implement nonlinear resonant enhancement, multiple resonator modes must be individually tuned onto a precise set of process wavelengths, which requires multiple linearly-independent tuning methods. Using coupled auxiliary resonators to indirectly tune modes in a multi-resonant nonlinear cavity is particularly attractive because it allows the extension of a single physical tuning mechanism, such as thermal tuning, to provide the required independent controls. Here we model and simulate the performance and tradeoffs of a coupled-resonator tuning scheme which uses auxiliary resonators to tune specific modes of a multi-resonant nonlinear process. Our analysis determines the tuning bandwidth for steady-state mode field intensity can significantly exceed the inter-cavity coupling rate g if the total quality factor of the auxiliary resonator is higher than the multi-mode main resonator. Consequently, over-coupling a nonlinear resonator mode to improve the maximum efficiency of a frequency conversion process will simultaneously expand the auxiliary resonator tuning bandwidth for that mode, indicating a natural compatibility with this tuning scheme. We apply the model to an existing small-diameter triply-resonant ring resonator design and find that a tuning bandwidth of 136 GHz ≈ 1.1 nm can be attained for a mode in the telecom band while limiting excess scattering losses to a quality factor of 106. Such range would span the distribution of inhomogeneously broadened quantum emitter ensembles as well as resonator fabrication variations, indicating the potential for the auxiliary resonators to enable not only low-loss telecom conversion but also the generation of indistinguishable photons in a quantum network.

Joint Resonance Analysis in Multiple Modes of Soft Ferromagnetic Rectangular Thin Plate

In this article, the nonlinear principal and internal resonance properties of a soft ferromagnetic rectangular thin plate are investigated in a magnetic field environment. The nonlinear partial differential equation of motion of a soft ferromagnetic rectangular thin plate is derived under the effect of homogeneous simple harmonic excitation. The system of nonlinear differential equations with multiple degrees of freedom is established by the assumed one-sided fixed trilateral simply support condition using the Galerkin’s method. The system of nonlinear differential equations is solved by the multiscale method to obtain the response of two modes under the simple harmonic force at the principal and internal resonance. The numerical results of the system response show that when the frequency of the simple harmonic force is close to one of the modes (first-order or second-order mode) causing it to resonate, the other mode will also resonate internally. The magnetic field can have an inhibiting effect on the resonant response of the system and also affect the kinematic state of the system. The internal resonance provides a mechanism for transferring energy from a high mode to a lower mode.

Nonlinear behavior of wave resonances in moonpool with a recess under wave actions

Nonlinear wave resonance in moonpool with a recess under wave actions is studied by using CFD simulations based on OpenFOAM® package. Compared to the rectangular moonpool, the influence of free surface nonlinearity plays an important role in the wave resonance in the recess moonpool. Harmonic analysis indicates that the higher-order harmonic induced sloshing-mode resonance even approaches the same magnitude as the first-order harmonic induced piston-mode motion. The superposition between them also leads to extreme free surface oscillation in the recess moonpool. A peak appears in the total horizontal wave forces by the higher-order harmonic induced sloshing resonance due to the anti-symmetric mode. In a word, the free surface nonlinearity is an indispensable factor in the response of fluid resonance in moonpool with recess configurations.