Nonlinear Resonance Research Articles

Nonlinear Magnetic Sensing with Hybrid Nitrogen-Vacancy/Magnon Systems.

Magnetic sensing beyond the linear regime could broaden the frequency range of detectable magnetic fields, which is crucial to various microwave and quantum applications. Recently, nonlinear interactions in diamond nitrogen-vacancy (NV) centers are proposed to realize magnetic sensing across arbitrary frequencies. In this work, we enhanced these capabilities by exploiting the nonlinear spin dynamics in hybrid systems of NV centers and ferri- or ferromagnetic (FM) thin films. We studied the frequency mixing effect in the hybrid systems and demonstrated that the introduction of FM films not only amplifies the intensity of nonlinear resonance signals that are intrinsic to NV spins but also enables novel frequency mixing through parametric pumping and nonlinear magnon scattering effects. The discovery and understanding of the magnetic nonlinearities in hybrid NV/magnon systems position them as a prime candidate for magnetic sensing with a broad frequency range and high tunability, particularly meaningful for nanoscale, dynamical, and noninvasive materials characterization.

Asynchronous quantum repeater using multiple quantum memory.

A full-fledged quantum network relies on the formation of entangled links between remote location with the help of quantum repeaters. The famous Duan-Lukin-Cirac-Zoller quantum repeater protocol is based on long distance single-photon interference, which not only requires high phase stability but also cannot generate maximally entangled state. Here, we propose a quantum repeater protocol using the idea of post-matching, which retains the same efficiency as the single-photon interference protocol, reduces the phase-stability requirement and can generate maximally entangled state in principle. We also outline an implementation of our scheme based on the Kerr nonlinear resonator. Numerical simulations show that our protocol has its superiority by comparing with existing protocols under a generic noise model and show the feasibility of building a large-scale quantum communication network with our scheme. We believe our work represents a crucial step towards the construction of a fully-connected quantum network.

Nonlinear combined resonance of magneto-electro-elastic plates

The existing articles on the nonlinear resonances of magneto-electro-elastic (MEE) structures are mainly devoted to the parametric resonance and primary resonance, neglecting the coupling effect between parametric and forced excitations. To reveal this issue, the coupled longitudinal and transverse excitations are considered to investigate the combined resonance of MEE plates, in which the simply supported ends is considered. The expressions of magnetic-, electric- and displacement-fields are determined using the Maxwell's equation and first order shear deformation theory (FSDT). Applying the Galerkin method, the nonlinear ordinary differential equations are derived. The combined resonance problem of MEE plates with simply supported ends is solved by developing the method of varying amplitude (MVA). And the resonance trajectory is depicted by amplitude-frequency diagram in the follow-up analysis, in which the complicated dynamical phenomena with jump, hysteresis and multi-stable solution can be observed. To reveal the dynamic mechanism, comprehensive numerical analyses including electric potential, magnetic potential, excitations, temperature variation and other factors are conducted, the bifurcation and chaotic dynamic behaviors are also analyzed. The results elucidate that these parameters under discussion play significant roles.

Nonlinear simultaneous resonance behaviors of a shallow arch model under the moving load

By applying a moving load with the uniform velocity, this paper investigates nonlinear behaviors of a shallow arch model allowing for describing the effects of the initial configuration of the structure. Two different cases are taken into account, namely, simultaneous primary resonances of the first and third modes; simultaneous resonances of the first mode for two-term excitations. First, nonlinear ordinary differential equations (ODEs) of the shallow arch are derived by using Galerkin method. Through introducing different time scales, the ODEs are solved based on the widely utilized method of multiple time scales (MMTS). In this way, the modulation equations for the two cases are derived, on the basis of which the steady state frequency- and force-response curves are obtained. Meanwhile, phase portraits, power spectra and two-parameter bifurcation diagram are also given to assist in analysis on nonlinear behaviors. The results show that the large vibration of the shallow arch under the moving load may occur and primary resonance peaks of the different modes are located in distinct positions.

Research on the nonlinear resonance response of the high-speed spindle system supported by preloaded ball bearings

Research on the nonlinear resonance response of the high-speed spindle system supported by preloaded ball bearings

Effects of gap entrance configuration on gap resonances between two free-heaving barges: Vortex shedding behaviors

This paper mainly concentrates on the influences of the vortex shedding pattern and the behaviors of the generated vortex bubbles on the hydrodynamic performances of two identical side-by-side barges when encountering the linear and nonlinear gap resonances. The vortex shedding pattern around the entrance of the gap is highly influenced by the gap entrance configuration, and thus, two kinds of gap entrance configurations, i.e., round edge and square edge, are taken into account. The vortex shedding patterns are identified during the linear and nonlinear gap resonances for all conditions. Meanwhile, the effects of incident-wave height and barges' heave responses are considered when interacting with different edge shapes. Numerical results demonstrated that both the gap resonances and barges' heave responses are influenced by the vortex generation pattern. Significantly, the magnitudes of the wave elevation at gap during the linear and nonlinear gap resonances are influenced by the coupling effect between the vortex bubbles' pre-behaviors, i.e., vortex shedding pattern, and their post-behaviors, i.e., vortex bubbles' behaviors post-shedding from shear layers, underscoring the importance of understanding vortex shedding patterns and the behaviors of vortex bubble in investigating the gap resonances.

Nonlinear optical properties of La3+-Doped tellurite-zinc glasses: Impact of chemical bonding and physical properties via Raman and XPS

Understanding the connection between the local environments of lanthanum ions in tellurite glasses and their nonlinear optical (NLO) properties is essential for various technological applications. Rare earth ions can serve as probes for the local environments of the host material if the structure-property correlations are well understood. In this study, we investigated glasses with compositions 70TeO2 - (30-x)ZnO - (x)La2O3 (mol%) (x = 0, 5, 7, 9) fabricated by the melt-quenching technique. The capabilities of combined Raman and X-ray photoemission (XPS) spectroscopy were used to identify these glasses and define spectral deconvolution for distinguishing them in the formation of bridging oxygens (BO) and non-bridging oxygens (NBO). NLO properties were evaluated using open-aperture (OA) and closed-aperture (CA) Z-scan measurements with femtosecond (fs) laser pulses (∼220 fs, 750 Hz) at wavelengths ranging from 600 to 1500 nm. Raman spectra revealed a shift to higher frequencies from 731 to 746 cm−1, with increasing of La3+ ions, indicating the conversion of TeO4 polyhedra to TeO3 structural units, affecting the Te-O- Zn2+ or Te=O bonds and resulting in a variation of the polarizability. Besides the conventional analysis of oxidation state and chemical shifts of the core-level peaks, XPS spectroscopy included a careful analysis of the type oxygen bridges and metal-oxygen bond length to distinguish otherwise similar spectral contributions of different TZL glasses. Glasses with a high fraction of Zn2⁺ ions bonded with oxygen form NBO and modify the local structure of the glass network, while La³⁺ ions coordinate with oxygen atoms or interact with the lone pairs of tellurium atoms. By analyzing the correlation in different concentrations of La3+ ions, the Te-O bonds and NBO/(BO + NBO) ratio were clearly demonstrated. These findings suggest charge compensation between the Zn2⁺ and La³⁺ ions, for maintaining structural stability within the glass network. This study also reveals an enhancement of NLO properties as a function of La3+ ions concentration in TZL glasses under fs laser excitation due to resonant nonlinearity. The third-order optical nonlinearities showed an increase in the two-photon absorption coefficient (β) from 0.26 × 10−2 cm GW−1 (TZL5) to 0.62 × 10−2 cm GW−1 (TZL9), along with an increase in the nonlinear refractive index (n2) from 0.32 × 10−18 m2 W−1 to 0.65 × 10−18 m2 W−1. This enhancement is attributed to the increased number of NBOs and the high polarizability of La3+ ions. For all-optical switching (AOS) applications, two figures of merit were applied using the n2, α0, and β coefficients. The results suggest that the TZL glasses studied are potential candidates for AOS devices. Thus, this work not only elucidates the factors underlying the NLO properties but also highlights the promising potential of these glasses for use in AOS devices.

Data-driven modeling of subharmonic forced response due to nonlinear resonance

Complex behavior in nonlinear dynamical systems often arises from resonances, which enable intricate energy transfer mechanisms among modes that otherwise would not interact. Theoretical, numerical and experimental methods are available to study such behavior when the resonance arises among modes of the linearized system. Much less understood are, however, resonances arising from nonlinear modal interactions, which cannot be detected from a classical linear analysis. Academic examples of such phenomena have been known, but no systematic method has been developed to detect and model nonlinear resonant interactions purely from numerical or experimental data. Here, we develop such a data-driven methodology that identifies nonlinear resonant response on low-dimensional spectral submanifolds (SSMs) of the dynamical system. Our approach is generally applicable to nonlinear resonances, but we specifically focus here on one particular behavior: subharmonic response in forced nonlinear systems without any resonance among the linearized frequencies of the unforced system. We first illustrate analytically how such a response is born out of a nonlinear resonance hidden in the conservative limit of the system. We then show how this effect can be identified and modeled purely from data. As our main example, we isolate and model previously unexplained response patterns in fluid sloshing experiments.

All-optical simultaneous OR and AND optical logic gates based on nonlinear photonic crystal ring resonator

Abstract An all-optical simultaneous OR and AND logic gates using the nonlinear Kerr effect and ring resonator based on a two-dimensional photonic crystal are proposed in this paper. The proposed structure has a resonant wavelength of 1551.3 nm and a power consumption (1 kW/μm2). The proposed structure is suitable for all-optical photonic integrations because of its simplicity and small size (23 μm x 30.4 μm). Moreover, the structure executes two logic operations without requiring an additional spare/control signal through a single structure, making fabrication easy. The total footprint of the photonic crystal ring resonator structure measures approximately 699 μm². A very high contrast ratio of 26.10 dB and 25.34 dB is obtained for the OR and AND logic gates, with response times equal to 2 ps and 0.67 ps, respectively. In addition, the calculated bit rates for OR and AND logic gates are approximately 0.5 and 1.5 Tbps, respectively. Using the Rsoft CAD commercial software, the FullWAVE and BandSOLVE module of the software is used for numerical and theoretical investigation of the structure.

Study on nonlinear coupled dynamic response of the integrated polar ocean nuclear energy platform

An integrated polar ocean nuclear energy platform is capable of providing adequate electrical and thermal energy essential for polar oceanic development activities. Precisely forecasting the platform's motion response within the marine environment is pivotal for the assurance of its safety. A scenario where the natural frequencies of heave, roll, and pitch of such an integrated polar ocean nuclear energy platform align closely to a 2:1:1 ratio, and when the wave frequency nearly matches the aggregate of the platform's natural heave and pitch frequencies, could induce a phenomenon known as sum-type nonlinear internal resonance. This phenomenon can significantly amplify the swing (roll or pitch) motion of the platform, posing a grave risk to both personnel and equipment onboard. Investigating these nonlinear internal resonance phenomena within the nuclear energy platform is critical for informing both the design and practical deployment of these platforms. Following the validation of the numerical simulation against experimental results, a detailed analysis of sum-type nonlinear internal resonance phenomena in the integrated polar ocean nuclear energy platform under regular wave conditions was performed using a combination of numerical simulations and nonlinear dynamics theory. It was observed that upon exceeding a certain wave height threshold, the platform enters a state of sum-type nonlinear internal resonance, engendering highly complex motion patterns. Notably, irrespective of initial conditions, this resonance triggers the roll motion of the platform, facilitating the external dissipation of energy in a half-sub-harmonic vibration manner. Increasing damping can effectively suppress the occurrence of nonlinear internal resonance phenomena in the platform. In designing the integrated polar ocean nuclear energy platform, it's crucial to avoid having the natural frequency ratios of heave, pitch, and roll align as 2:1:1. If unavoidable, adding side plates to increase damping can mitigate the effects of sum-type nonlinear internal resonance.

Nonlinear resonance of fractional order viscoelastic PET films under temperature loading

The effects of oven temperature during printing on nonlinear vibration for fractional-order PET films are considered in this paper. The effect of temperature, fractional order modelling and some other parameters are analysed with respect to the response of the resonance. Fractional order kelvin-Voigt ontological relationship is used to describe the characteristics of viscoelastic materials. The differential equations for nonlinear vibrations are inferred according to the second law of Newton and the theory of von Karman. Discretization for nonlinear equations on locomotion using the Bubnov–Galerkin method. Forced co-oscillatory amplitude-frequency response equations for thin-films systems under temperature loading were calculated using the multiple scales method. Results of numeral results show that temperature, and fractional-order visco-elastic modelling influence the membrane's response to resonance. These results provide a basis for studying fractional-order visco-elastic films vibrations and identifying regions of stable operation in moving systems to prevent divergent instabilities for flexible electronic device manufacturing.

Electromagnetic Landau Resonance: Nonlinear Dynamics and Harmonic Generation

AbstractIn situ particle observations provide useful information for determining the significance of nonlinearity in wave‐particle interactions. Here, we examine an electromagnetic Landau resonance event observed by the Magnetospheric Multiscale mission near the dayside magnetopause along this line of thought. During this event, protons with energy 748 eV and pitch angle are observed to resonate with electromagnetic‐ion‐cyclotron waves. Detailed data analysis reveals the existence of a second harmonic signal in proton modulation. Using an observation‐based test particle simulation, this signal is explained as a low‐resolution manifestation of phase space rolled‐up structures, which themselves are not observable due to limited instrument resolution. The presence of these rolled‐up structures suggests that the waves induce significant displacement of the protons in phase space, consequently confirming the nonlinear nature of the observed interaction. Based on the observations, we further discuss the possibility of the nonlinear electromagnetic Landau resonance generating second harmonic waves.

Asymmetrical temporal dynamics of edge modes in Su-Schrieffer-Heeger lattice with Kerr nonlinearity

Optical bistability and oscillating phases exist in a Sagnac interferometer and a single ring resonator made of a χ(3) nonlinear medium where the refractive indices are modulated by the light intensity due to the Kerr nonlinearity. An array of coupled nonlinear ring resonators behave similarly but with more complexity due to the presence of the additional couplings. Here we theoretically demonstrate the bifurcation of edge modes, which leads to optical bistability in the Su-Schrieffer-Heeger lattice with the Kerr nonlinearity. We also demonstrate periodic and chaotic switching behaviors in an oscillating phase resulting from the coupling between the edge mode and bulk modes with different chiralities, i.e., clockwise and counterclockwise circulations. Published by the American Physical Society 2024

Adaptive stochastic resonance enhanced weak linear frequency modulated signal perception in low signal-to-noise ratio environments

Abstract The linear frequency modulated (LFM) signal has gained extensive utilization in radar, sonar and covert communication system due to its large time-bandwidth product, high-precision distance measurement and low detection probability. The perception of weak LMF signals holds significant importance yet encounters substantial challenges within the increasing complexity of the electromagnetic environments. Consequently, this paper proposes an adaptive stochastic resonance (ASR) enhanced approach for perceiving weak LFM signals in low signal-to-noise ratio (SNR) conditions. This approach initially commences a pioneering study on the quantitative synergistic resonance mechanism among LFM signals, random noise, and nonlinear stochastic resonance (SR) systems. Subsequently, the ASR system’s implementation becomes straightforward through the adaptive adjustment of SR system parameters according to the LFM signal and noise characteristics. This implementation leverages the inherent property of noise energy transfer to signal energy, facilitating the enhancement of ordered weak signals via random noise. Following the enhancement of the output signal by the ASR system, the Wigner–Ville distribution (WVD) transform’s time-frequency concentration property is employed to extract the time-frequency characteristics. Building on the WVD transform, the Radon transform with linear integral projection is applied to further harness the time-frequency domain energy concentration, thereby achieving the effective perception of weak LFM signals. Finally, the effectiveness of the proposed method in improving the perception performance of weak LFM signal in very low SNR conditions is verified through numerical simulations. It is anticipated that this method will have potential application value in fields such as radar, sonar, and communication under complex electromagnetic environments.

Wideband vibration attenuation of a metamaterial beam via integrated hardening and softening nonlinear resonators

Wideband vibration attenuation of a metamaterial beam via integrated hardening and softening nonlinear resonators

Novel energy exchange behaviors and mechanisms in nonlinear acoustic metamaterials with multiple nonlinear resonators

Wave-wave interactions in a nonlinear metamaterial or structure with two propagating waves can induce energy exchange within the nonlinear systems. The effects of nonlinear resonators on these interactions and energy exchanges in a nonlinear acoustic metamaterial have not been extensively studied in the literature. In this paper, a nonlinear monatomic acoustic metamaterial with multiple nonlinear resonators (NMAM-MNR) is constructed to investigate the new behaviors and mechanisms introduced by these nonlinear resonators. Stability analyses reveal that stability can be tuned by adjusting the number of nonlinear resonators and by selecting different intensities or masses of the resonators and the chain. Additionally, direct numerical simulations are performed to study the novel energy exchange behaviors and mechanisms in NMAM-MNR systems. The results demonstrate that the degree and frequency of energy exchange can be tuned by altering the mass ratios, stiffness ratios, intensities, and natural frequencies of the nonlinear resonators and the chain. The influence of mass and stiffness ratios on the time taken for the B-wave magnitude to first reach its maximum value in NMAM-MNR systems is also studied, showing that the rate of energy exchange induced by wave-wave interactions can be tuned by changing the stiffness and mass ratios of multiple nonlinear resonators. These properties have potential applications in the fields of energy harvesters, waveguides, and resonant energy transfer mechanisms.

Unconventional phonon blockade effect in array of three coupled weakly nonlinear nanomechanical resonators

Phonon antibunching, a phenomenon arising from the quantum statistics of mechanical vibrations, has attracted significant attention due to its potential applications in quantum information processing, sensing, and energy harvesting. Here, we present a comprehensive investigation of phonon antibunching in a system consisting of three weakly nonlinear coupled nanomechanical resonators. We analytically derive and study the antibunching behavior of phonons in the proposed system and bring insight into the underlying mechanisms. The optimal phonon blockade results from destructive quantum interference due to distinct two-phonon excitation pathways. Due to this quantum interference, these unconventional phonon blockade systems can achieve antibunched statistics even in weakly nonlinear regimes, in contrast to conventional phonon blockade systems that require strong nonlinearity. We show that with the inclusion of an additional resonator, there are multiple additional two-phonon excitation pathways compared to two resonator cases, which results in stronger phonon antibunching and supports single phonon for longer duration. These findings are interesting for practical phononics using coupled-resonator systems.

Towards enhanced metamaterials via shape memory alloy-embedded nonlinear resonators

Standard acoustic metamaterials create an attenuation around specific frequency bands. Finite structures, with distinct boundary conditions and a limited number of unit cells, present less attenuation and narrower bands than those predicted by idealized infinite systems. A critical engineering goal is enhancing performance to motivate practical applications. To that aim, this work incorporates shape memory alloys into a quasi-zero stiffness resonator design, allowing the tuning of each cell's internal resonance. Such a feature enables the system reconfiguration to achieve different purposes, from following a disturbance frequency fluctuation to realizing graded nonlinear metamaterials. While the former can work under an adaptive framework, the latter can result in time-invariant locally resonant metamaterials with wideband vibration attenuation. The proposed design combines a frame that axially compresses an SMA beam in the vicinity of its buckling. The critical buckling force changes by thermally activating the SMA, affecting the residual stiffness, hence the unit cell resonant frequency. The unit cell concept is developed analytically and via finite elements, then built and validated experimentally. The promising results indicate the viability of the proposed concept. Preliminary numerical simulations and experiments show the advantages of the proposed smart resonator over a linear time-invariant counterpart.

Theoretical and experimental analysis of a nonlinear vibro-acoustic energy sink

This study is concerned with the experimental and theoretical analysis of a vibroacoustic nonlinear system devoted to absorption application. Based on the nonlinear energy sink principle, the dynamics of the system is reduced to two coupled degrees of freedom, one of which exhibits nonlinear behavior due to a large displacement mechanism. The set-up allows for precisely characterizing the nonlinear function of the mechanical system, first uncoupled and then coupled with an acoustic and linear resonator. Continuation procedures are performed experimentally and numerically, respectively using a phase-locked loop (PLL) and the asymptotic numerical method implemented in the MANLAB software package. The comparison between theoretical predictions and experimental results obtained on the uncoupled system allows for a parameter identification of the nonlinear resonator. Measurements on the coupled system highlight the energy pumping phenomenon, which can be predicted from numerical predictions in which identified parameters are introduced. The procedure aims at proposing analytical models for achieving efficient level attenuation, and providing design guidelines for sound reduction at high levels in confined spaces.

Two-dimensional viscous study of coupled nonlinear fluid resonances in two narrow gaps

The wave-induced hydrodynamics of coupled nonlinear piston-mode fluid resonances within two narrow gaps between three barges are numerically investigated using a two-dimensional viscous wave flume. This study aims to explore the time-dependent nonlinear interactions between fluid oscillations in the two gaps. The coupled synchronous dynamic behaviors of fluid oscillations during the transient evolution stage are first examined in terms of amplitude and frequency modulation. It is shown that phase dynamics, including phase slipping, trapping, and locking, play significant roles in establishing the coupled synchronous dynamic evolutions of fluid oscillations in the two gaps. The quasi-steady state of the amplitude- and phase-frequency responses of fluid oscillations within the gaps, along with the reflection and transmission waves in front of and behind the three-barge system, are further analyzed. This analysis clarifies the significance of viscous damping energy dissipation and radiation damping energy transfer involved in gap resonance problems. This clarification also explains the performance of fully nonlinear potential flow solvers in predicting fluid resonances in the two narrow gaps. Finally, the nonlinear dynamic features of fluid oscillations are examined. The effects of incident wave nonlinearity, i.e., wave steepness, on resonant frequencies, response amplitudes, energy dissipation, and reflection and transmission coefficients are investigated. Harmonic analysis via Fourier transformation reveals the contributions of first-, second-, and third-order harmonics to the overall response amplitudes. The physical insights gained from this study provide a deeper understanding of the coupled nonlinear dynamics of piston-mode fluid resonances in multiple narrow gaps.