Exact Resonance Research Articles

Enhancing high-order harmonic mode-locking in Er/Yb-Doped fiber lasers with sub-MHz fundamental frequency via optoacoustic resonance

We present an experimental study of a long Er/Yb-doped fiber ring laser with a low fundamental frequency of 0.678 MHz. By solely adjusting the quarter-wave plate in the polarization controller, we uncovered a series of reproducible laser generation regimes. Among these, multiple soliton bunches were harmonically mode-locked to low-order cavity harmonics (from the 3rd to the 8th). Notably, we also identified a regime featuring a stable soliton train harmonically mode-locked to the 472nd cavity harmonic at 320 MHz. This regime demonstrated exceptional harmonic mode-locking stability, with a supermode suppression level of 49 dB corresponding to the timing jitter on the order of a few picoseconds. We attribute this remarkable stability to an exact optoacoustic resonance between the laser repetition rate and the fiber eigen acoustic mode frequencies, specifically identified as R06 and TR2,15. These findings represent a significant advancement in high-performance fiber laser operation, particularly in enhancing the stability of lasers with sub-MHz fundamental frequencies capable to generate regular pulses with much higher repetition rates.

Decoherence-induced formation of sub-poissonian entangled and steerable states of collective fields

The decoherence process has a tendency to yield the evolution of a pure state into a mixed one and to cause the quantum-to-classical transition by the coupling of a system of interest to the reservoir with infinitely many degrees of freedom. This is the major obstacle to the implementation of quantum computation and hence the realization of quantum computers. We propose a scheme to create unconditionally sub-Poissonian entangled and steerable states of the collective cavity field modes by use of the dissipation process. Based on the suitable choice of combination modes, the scheme uses the inherent, efficient and controllable two-mode squeezed vacuum reservoir coupled to the combination modes of concern rather than the original cavity modes in the two-level quantum beat laser. The decoherence is shown to pull the collective modes into the sub-Poissonian entangled and steerable states in the stationary regime, while the job of the dissipation of the individual cavity fields is to give rise to the degradation of the bipartite entanglement of the two individual modes and to inhibit the occurrence of the quantum steering from one cavity mode to the other. In particular for the case that the external driving field is close to the exact resonance with the atom, the collective fields are eventually prepared asymptotically in the stationary Einstein–Podolsky–Rosen state, while the two individual cavity modes are pulled into the vacuum states and reach steady state. The disappearance of the decoherence disables the nonclassical states of the collective modes, while the ignorance of the dissipation process of the cavity field modes guarantees the generation of the entanglement between the pair of individual modes. The decoherence-induced formation of a nonclassical source is ascribed to the four-wave mixing process together with the intrinsic amplitude and phase locking.

Mean-motion resonances with interfering density waves

ABSTRACT In this work, we study the dynamics of two less massive objects moving around a central massive object, which are all embedded within a thin accretion disc. In addition to the gravitational interaction between these objects, the disc–object interaction is also crucial for describing the long-term dynamics of the multibody system, especially in the regime of mean-motion resonances. We point out that near the resonance the density waves generated by the two moving objects generally coherently interfere with each other, giving rise to extra angular momentum fluxes. The resulting backreaction on the objects is derived within the thin-disc scenario, which explicitly depends on the resonant angle and sensitively depends on the smoothing scheme used in the two-dimensional theory. We have performed hydrodynamical simulations with planets embedded within a thin accretion disc and have found qualitatively agreement on the signatures of interfering density waves by measuring the torques on the embedded objects, for the cases of $2:1$ and $3:2$ resonance. By including in interference torque and the migration torques in the evolution of a pair of planets, we show that the chance of resonance trapping depends on the sign of the interference torque. For negative interference torques the pairs are more likely located at off-resonance regimes. The negative interference torques may also explain the $1~{{\ \rm per\ cent}}-2~{{\ \rm per\ cent}}$ offset (for the period ratios) from the exact resonance values as observed in Kepler multiplanet systems.

Steady-state triad resonance between a surface gravity wave and two hydroacoustic waves based on the homotopy analysis method

Under water compressibility, resonant triads can occur within the family of acoustic-gravity waves. This work investigates steady-state triad resonance between a surface gravity wave and two hydroacoustic waves. The water-wave equations are solved as a nonlinear boundary value problem using the homotopy analysis method (HAM). Within the HAM framework, a potential singularity resulting from exact triad resonance is avoided by appropriately choosing the auxiliary linear operator. The resonant hydroacoustic wave component, along with the two primary waves (one hydroacoustic wave and one gravity wave), is considered to determine an initial guess for the velocity potential. Additionally, by selecting an optimal “convergence-control parameter,” the steady-state resonance between a surface gravity wave and two hydroacoustic waves is successfully obtained. It is found that steady-state resonant acoustic-gravity waves are ubiquitous under certain circumstances. The two primary wave components and the resonant hydroacoustic wave component take up most of the energy in the steady-state resonant acoustic-gravity wave system. The amplitude of the resonant hydroacoustic wave component is mainly determined by the primary hydroacoustic wave component, and the amplitudes of both hydroacoustic waves are approximately equal in all cases considered. In addition, when the overall amplitude of the wave system increases, both dimensionless angular frequencies decrease, indicating that the nonlinearity of the entire wave system becomes stronger with an increase in the wave system amplitude. The amplitude of the primary hydroacoustic wave has a relatively large effect on the system's nonlinearity. This work will enrich and deepen our understanding of acoustic-gravity waves.

On the steady-state interfacial waves with two-dimensional type-A double exact resonance

Steady-state interfacial waves under two-dimensional (2D) type-A exact triad resonance and other related resonances are researched in a two-layer liquid model with a free surface in contact with air. Five groups (groups 1–5) of convergent series solutions are achieved via the homotopy analysis method. It is found that the phenomenon of double exact resonance could exist in periodic interfacial waves if physical parameters correspond to the intersection of two exact resonance curves. The double exact resonance considered here contains a 2D type-A triad resonance and an other resonance. Under the 2D type-A exact triad resonance, the other resonant triad could obviously enlarge or reduce the wave amplitudes and energy proportions of primary and resonant components. Nevertheless, other resonant quartet, quintet, sextet, and septet all produce no influence on interfacial waves when the 2D type-A exact triad resonance occurs. The above-mentioned results indicate that in the neighborhood of the double exact triad resonance, small perturbations of wave vector of a primary component can cause huge changes on wave profiles of free surface and interface, wave amplitude spectrum, and energy distribution of internal waves in real ocean. In addition, the closer the interfacial waves are to the double exact triad resonance, the more possible energy combinations exist in the wave system, and the greater the number of steady-state interfacial wave solutions. All of this should deepen our understanding of nonlinear resonance interactions in short-crested internal waves.

Electron nonlinear dynamics in a compact accelerator based on the circular rotating TM110 mode

The present study investigates the electron autoresonant acceleration using the rotating transverse magnetic mode TM110 microwave field within an inhomogeneous magnetostatic field. Differential equations governing the evolution of the phase shift between the electron’s angular position and the angle at which transferred power is maximized, the total electron energy, and the longitudinal electron velocity are derived. Magnetic field profiles required to sustain electron acceleration are determined. The results demonstrate that an electron injected along the cavity axis with an energy of 30keV can be accelerated up to approximately 200keV, using an electric field amplitude of 20kV/cm, a frequency of 8GHz, and a linear magnetic field profile. Additionally, we consider the case of electron acceleration under exact resonance conditions, and the corresponding magnetic field profile predicted by the model is obtained.The findings presented in this paper are valuable for the design of RF accelerators utilizing the circular rotating TM110 mode, particularly in applications such as x-ray sources for medical purposes, airport security, and various other fields.

Theoretical Study of Multicascade Raman Microlasers Based on TeO2–WO3–Bi2O3 Glass

The development and investigation of miniature narrow-line coherent light sources based on microresonators with low-power-consumption whispering gallery modes (WGMs) is an actual trend in modern photonics. Raman WGM microlasers can operate at wavelengths inaccessible to traditional laser media and provide a huge pump frequency tuning range. Here, we propose and theoretically study multicascade Raman microlasers based on soft tellurite TeO2–WO3–Bi2O3 glass WGM microresonators (microspheres) which can operate in the near-IR and mid-IR with the pump in the telecommunication range. Thanks to a large Raman gain (120 times exceeding the maximum Raman gain of silica glass) and a huge Raman frequency shift of 27.5 THz for this glass, the Raman waves at 1.83 µm, 2.21 µm, 2.77 µm, and 3.7 µm in the first, second, third, and fourth cascades, respectively, are theoretically demonstrated with a pump at 1.57 µm. We analyze in detail the influence of different factors on the characteristics of the generated Raman waves, such as microsphere diameters, Q-factors, pump powers, and detuning of the pump frequency from exact resonance. We also solve a thermo-optical problem to show that the temperature of a soft glass microresonator heated due to partial thermalization of pump power remains below the glass transition temperature. To the best of our knowledge, mid-IR tellurite glass Raman WGM microlasers have not been studied before.

Investigation of the equivalent circuit and performance of an ultrasonic transducer under a force load

In ultrasonic processing technology applications, the force load can cause a drift in the resonance frequency of the ultrasonic transducer and significantly reduce its mechanical quality factor. The traditional equivalent circuit of an ultrasonic transducer can only be used to calculate performance parameters without a force load but not with a force load. Based on Mason’s equivalent circuit, a new equivalent circuit for ultrasonic transducers under a force load is derived while considering the effects of the force load on the material parameters and various types of losses in piezoelectric ceramics. Furthermore, performance parameters are analyzed, such as the resonance frequency, effective electromechanical coupling coefficient, and mechanical quality factor. The ultrasonic transducer sample is produced and the experimental platform is constructed for applying force loads on the ultrasonic transducer. The theoretical model is verified by static loading on the ultrasonic transducer. The proposed equivalent circuit provides theoretical guidance for tracking the exact resonance frequency and performance parameters of force-loading ultrasonic transducers.

Steady-state interfacial gravity waves with one-dimensional class-IV triad resonance

Steady-state interfacial waves under a one-dimensional (1-D) class-IV exact triad resonance are investigated in a two-layer fluid with a free surface upper boundary. Four groups (G1–G4) of convergent series solutions are obtained by the homotopy analysis method. Though the harmonic resonance conditions are contained in the class-IV resonance criteria, the influences of 1:2 harmonic resonances on the energy spectrum could be neglected. Unlike former steady-state resonant interfacial wave spectrum where all the components joining the resonance are significant, the energy of one primary component can be ignored for two groups (G2 and G4) of wave solutions obtained in this paper. It is found that a little energy induced from the external environment might greatly change the energy spectrum for G1. However, the energy introduced from the outside cannot vary the wave energy distribution for G2. The reason for the extremely high crests on the instantaneous profiles of free surfaces of G2 and G4 is that the peaks of the class-IV exactly resonant and some trivial components momentarily overlap at some special horizontal positions. The class-IV exact triad resonance curve could be divided into four pieces containing the existence ranges of G3 and G4 and two regions with no solution found. One of the regions without convergent solutions results from an infinite number of singularities or small divisors caused by infinite exact or near resonances. Our results indicate that steady-state interfacial waves with class-IV triad resonance interactions among one surface and two internal wave modes could exist.

Absence of localization in interacting spin chains with a discrete symmetry

Novel paradigms of strong ergodicity breaking have recently attracted significant attention in condensed matter physics. Understanding the exact conditions required for their emergence or breakdown not only sheds more light on thermalization and its absence in closed quantum many-body systems, but it also has potential benefits for applications in quantum information technology. A case of particular interest is many-body localization whose conditions are not yet fully settled. Here, we prove that spin chains symmetric under a combination of mirror and spin-flip symmetries and with a non-degenerate spectrum show finite spin transport at zero total magnetization and infinite temperature. We demonstrate this numerically using two prominent examples: the Stark many-body localization system (Stark-MBL) and the symmetrized many-body localization system (symmetrized–MBL). We provide evidence of delocalization at all energy densities and show that delocalization persists when the symmetry is broken. We use our results to construct two localized systems which, when coupled, delocalize each other. Our work demonstrates the dramatic effect symmetries can have on disordered systems, proves that the existence of exact resonances is not a sufficient condition for delocalization, and opens the door to generalization to higher spatial dimensions and different conservation laws.

Dynamics and Origins of the Near-resonant Kepler Planets

Short-period super-Earths and mini-Neptunes encircle more than ∼50% of Sun-like stars and are relatively amenable to direct observational characterization. Despite this, environments in which these planets accrete are difficult to probe directly. Nevertheless, pairs of planets that are close to orbital resonances provide a unique window into the inner regions of protoplanetary disks, as they preserve the conditions of their formation, as well as the early evolution of their orbital architectures. In this work, we present a novel approach toward quantifying transit timing variations within multiplanetary systems and examine the near-resonant dynamics of over 100 planet pairs detected by Kepler. Using an integrable model for first-order resonances, we find a clear transition from libration to circulation of the resonant angle at a period ratio of ≈0.6% wide of exact resonance. The orbital properties of these systems indicate that they systematically lie far away from the resonant forced equilibrium. Cumulatively, our modeling indicates that while orbital architectures shaped by strong disk damping or tidal dissipation are inconsistent with observations, a scenario where stochastic stirring by turbulent eddies augments the dissipative effects of protoplanetary disks reproduces several features of the data.

Near resonant approximation of the rotating stratified Boussinesq system on a 3-torus

Based on a novel treatment of near resonances, we introduce a new approximation for the rotating stratified Boussinesq system on three-dimensional tori with arbitrary aspect ratios. The rotation and stratification parameters are arbitrary and not equal. We obtain global existence for the proposed nonlinear system for arbitrarily large initial data. This system is sufficiently accurate, with an important feature of coupling effects between slow and fast modes. The key to global existence is a sharp counting of the relevant number of nonlinear interactions. An additional regularity advantage arises from a careful examination of some mixed type interaction coefficients. In a wider context, the significance of our near resonant approach is a delicate balance between the inclusion of more interacting modes and the improvement of regularity properties, compared to the well-studied singular limit approach based on exact resonance.

Forward and inverse cascades by exact resonances in surface gravity waves.

We study the energy transfer by exact resonances for deep-water surface gravity waves in a finite periodic spatial domain. Based on a kinematic model simulating the generation of active wave modes in a finite discrete wave number space S_{R}, we examine the possibility of direct and inverse cascades. More specifically, we set an initially excited region which iteratively spreads energy to wave modes in S_{R} through exact resonances. At each iteration, we first activate new modes from scale resonances (which generate modes with new lengths), then consider two bounding situations for angle resonances (which transfer energy at the same length scale): the lower bound where no angle resonance is included and the upper bound where all modes with the same length as any active mode are excited. Such a strategy is essential to enable the computation for a large domain S_{R} with the maximum wave number R∼10^{3}. We show that for both direct and inverse cascades, the modal propagation to the boundaries of S_{R} can be established when the initially excited region is sufficiently large; otherwise a frozen turbulence state occurs, with a sharp transition between the two regimes especially for the direct cascade. Through a study on the structure of resonant quartets, the mechanism associated with the sharp transition and the role of angular energy transfer in the cascades are elucidated.

Thermo-Optical Control of Raman Solitons in a Functionalized Silica Microsphere.

The investigation of optical microcavity solitons is in demand both for applications and basic science. Despite the tremendous progress in the study of microresonator solitons, there is still no complete understanding of all features of their nonlinear dynamics in various regimes. Controlling soliton properties is also of great interest. We proposed and investigated experimentally and theoretically a simple and easily reproducible way to generate Raman solitons with controllable spectral width in an anomalous dispersion region in a functionalized silica microsphere with whispering gallery modes (WGMs) driven in a normal dispersion regime. To functionalize the microsphere, coating (TiO2 + graphite powder) was applied at the pole. The coating is used for effective thermalization of the radiation of an auxiliary laser diode launched through the fiber stem holding the microsphere to control detuning of the pump frequency from exact resonance due to the thermo-optical shift of the WGM frequencies. We demonstrated that the thermo-optical control by changing the power of an auxiliary diode makes it possible to switch on/off the generation of Raman solitons and control their spectral width, as well as to switch Raman generation to multimode or single-mode. We also performed a detailed theoretical analysis based on the Raman-modified Lugiato–Lefever equation and explained peculiarities of intracavity nonlinear dynamics of Raman solitons. All experimental and numerically simulated results are in excellent agreement.

Detuned Resonances

Detuned resonance, that is, resonance with some nonzero frequency mismatch, is a topic of widespread multidisciplinary interest describing many physical, mechanical, biological, and other evolutionary dispersive PDE systems. In this paper, we attempt to introduce some systematic terminology to the field, and we also point out some counter-intuitive features: for instance, that a resonant mismatch, if nonzero, cannot be arbitrarily small (in some well-defined sense); and that zero-frequency modes, which may be omitted by studying only exact resonances, should be considered. We illustrate these points with specific examples of nonlinear wave systems. Our main goal is to lay down the common language and foundations for a subsequent study of detuned resonances in various application areas.

On the steady-state exactly resonant, nearly resonant, and non-resonant waves and their relationships

The steady-state exactly resonant, nearly resonant, and non-resonant waves in infinite water depth are investigated, and their relationships are revealed. In the framework of homotopy analysis method (HAM), the two primary wave components' amplitudes in the initial guess of the velocity potential are fixed and the actual frequencies of the primary waves are unknown. For different wavenumber ratio (k2/k1) values, three groups of steady-state wave systems are obtained with the proper auxiliary linear operator and the initial guess. It is found that when the third-order resonance occurs accurately, the energy of each wave group is mainly concentrated in the primary and third-order resonant wave components. When the value of the wavenumber ratio (k2/k1) moves away from the exact resonance, the energy of the whole wave system is either gradually transferred to the two primary or one resonant wave components that finally evolves into the trivial non-resonant wave system, or the energy is more evenly distributed among more wave components that evolves into multiple nearly resonant wave systems. In addition, the results obtained based on HAM are verified and confirmed by means of the Zakharov equation. This work illustrate that the steady-state wave systems are continuous in wavevector space, the normal non-resonant solution on either side of the resonance point comes from the different third-order resonant solutions, and the occurrence of multiple near resonances can significantly increase the nonlinearity of the wave system.

Spectral analysis of scattering resonances with application on high-contrast nanospheres

In this paper, we provide further spectral analysis of the general asymptotic scattering resonances formula of small 3D dielectrics of arbitrary shape with high contrast, already derived in other works to a first-order approximation. To investigate the components of a full expansion of such resonances, a breakdown is presented for the case of high-contrast nanospheres, in terms of its radius h in the interval [0, 1]. We also derive, for radially symmetric fields, an exact resonance formula for a spherical scatterer in terms of its radius, not necessarily small, and dielectric susceptibility coefficient, not necessarily high. This formula is further developed and simplified in the case of high contrast nanospheres. Such formulas are useful in imaging applications to identify objects’ properties from frequency measurements. Another application is the study of negative refractive index materials, such as metamaterials, and the anomalous localized resonance phenomenon (ALR) that is associated with cloaking and superlensing.

Scaling Laws for Perovskite Nanolasers With Photonic and Hybrid Plasmonic Modes

AbstractSurface plasmons exhibit an extraordinary capability to reduce the structural size and improve light−matter interaction. However, for small‐sized plasmonic cavities, the optical diffraction limit makes the near‐field difficult to observe, complicating the analysis of exact lasing characteristics. In this study, a 4f measurement system is used to extract the mode parity from the interference pattern and reconstruct the near‐field of the hybrid plasmonic perovskite nanolasers. In conjunction with other measurements, a series of rigorous methods for determining the exact resonance mode and obtaining the precise lasing characteristics of perovskite nanolasers are described. By applying these methods, the scaling laws for wire‐type hybrid plasmonic perovskite lasers are successfully determined and an appropriate size is selected for achieving outstanding lasing performance with low threshold power consumption and a high group index. These methods can be applied to nanowire plasmon‐based lasers to advance the development of plasmonic devices.

Dynamics of Polar Resonances and Their Effects on Kozai–Lidov Mechanism

The research on highly inclined mean motion resonances (MMRs), even retrograde resonances, has drawn more attention in recent years. However, the dynamics of polar resonance with inclination i≈90∘ have received much less attention. This paper systematically studies the dynamics of polar resonance and their effects on the Kozai–Lidov mechanism in the circular restricted three-body problem (CRTBP). The maps of dynamics are obtained through the numerical method and semi-analytical method, by mutual authenticating. We investigate the secular dynamics inside polar resonance. The phase-space portraits on the e−ω plane are plotted under exact polar resonance and considering libration amplitude of critical angle σ. Simultaneously, we investigate the evolution of 5000 particles in polar resonance by numerical integrations. We confirm that the e−ω portraits can entirely explain the results of numerical experiments, which demonstrate that the phase-space portraits on the e−ω plane obtained through the semi-analytical method can represent the real Kozai–Lidov dynamics inside polar resonance. The resonant secular dynamical maps can provide meaningful guidance for predicting the long-term evolution of polar resonant particles. As a supplement, in the polar 2/1 case, we analyze the pure secular dynamics outside resonance, and confirm that the effect of polar resonance on secular dynamics is pronounced and cannot be ignored. Our work is a meaningful supplement to the general inclined cases and can help us understand the evolution of asteroids in polar resonance with the planet.

On bi-chromatic steady-state gravity waves with an arbitrary included angle

Being encouraged by the recent study by Yang et al. [“On collinear steady-state gravity waves with an infinite number of exact resonances,” Phys. Fluids 31, 122109 (2019)] on two primary waves traveling in the same/opposite direction, we investigate two primary waves traveling with an arbitrary included angle by solving the water-wave equations as a nonlinear boundary-value problem. When the included angle is small, there exists an infinite number of nearly resonant wave components corresponding to an infinite number of small denominators in the framework of the classical analytic approximation methods, like perturbation methods. At a certain included angle, it will cause the classical third-order resonance, corresponding to a singularity. Fortunately, based on the homotopy analysis method (HAM), this type of problem can be solved uniformly by choosing a proper auxiliary linear operator with which the small denominators and singularity can be avoided once and for all. Approximate homotopy-series solutions can be obtained for the two primary waves traveling with an arbitrary included angle. The solutions bifurcate at the angle of classical third-order resonance. Regardless of the resonance at the third-order, it is found that when the acute angle between the two primary wave components becomes smaller, the wave energy slowly shifts from the primary wave components to the high-order wave components, and the increase in wave amplitude strengthens this energy transfer. Moreover, when the included angle is close to or smaller than the third-order resonant angle, the third-order quasi-resonant interaction has a greater influence on the energy distribution, especially if the overall amplitude is relatively large. All of this illustrates the validity and potential of the HAM to be applied to rather complicated nonlinear problems that may have an infinite number of singularities or small denominators.