Intermode Interactions Research Articles

Wideband oscillation analysis of VSC-HVDC connected DFIG wind farm

This paper investigates the wideband oscillations of a doubly fed induction generator (DFIG)-based wind farm connected via a voltage source converter-based HVDC (VSC-HVDC) system across the full frequency band. A small signal model of the system is developed to facilitate this analysis. Oscillation mode characteristics are then examined through eigenvalue analysis and participation factors. The study further explores the impact of strongly correlated factors on typical wideband oscillation modes and their inter-mode interactions. Findings reveal that interactions between the DFIG wind farms and the VSC-HVDC system can induce new super-synchronous oscillations. Additionally, a damping coupling is observed between the medium-frequency oscillation interactive transformation mode and the stator-line mode.

Exact solutions of nonlinear dynamical equations for large-amplitude atomic vibrations in arbitrary monoatomic chains with fixed ends

Intermode interactions in one-dimensional nonlinear periodic structures have been studied by many authors, starting with the classical work by Fermi, Pasta, Ulam, and Tsingou (FPUT) in the middle of the last century. However, symmetry selection rules for the energy transfer between nonlinear vibrational modes of different symmetry, which lead to the possibility of excitation of some bushes of such modes, were not revealed. Each bush determines an exact solution of nonlinear dynamical equations of the considered system. The collection of modes of a given bush does not change in time, while there is a continuous energy exchange between these modes. Bushes of nonlinear normal modes (NNMs) are constructed with the aid of group-theoretical methods and therefore they can exist for the case of large amplitude atomic vibrations and for any type of interatomic interactions. In most publications, bushes of NNMs or similar dynamical objects in one-dimensional systems are investigated under periodic boundary conditions. In this paper, we present a detailed study of the bushes of NNMs in monoatomic chains for the case of fixed boundary conditions, which sheds light on a series of new properties of the intermode interactions in such systems. We prove some theorems that justify a method for constructing bushes of NNMs by continuation of conventional normal modes to the case of large atomic oscillations. Our study was carried out for FPUT chains, for the chains with the Lennard-Jones interatomic potential, as well as for the carbon chains (carbynes) in the framework of the density functional theory. For one-dimensional bushes (Rosenberg nonlinear normal modes), the amplitude–frequency diagrams are presented and the possibility of their modulational instability is briefly discussed. We also argue in favor of the fact that our methods and main results are valid for any monoatomic chain.

Optical microcombs in whispering gallery mode crystalline resonators with dispersive intermode interactions

Soliton microcombs have shown great potential in a variety of applications ranging from chip-scale frequency metrology to optical communications and photonic data center, in which light couplings among cavity transverse modes, termed as intermode interactions, are long-existing and usually give rise to localized impacts on the soliton state. Of particular interest are whispering gallery mode-based crystalline resonators, which with dense mode families, potentially feature interactions of all kinds. While effects of narrowband interactions such as spectral power spikes have been well recognized in crystalline resonators, those of broadband interactions remain unexplored. Here, we demonstrate microcombs with broadband and dispersive intermode interactions, in home-developed magnesium fluoride microresonators with an intrinsic Q -factor approaching 10 billion. In addition to conventional soliton comb generation in the single-mode pumping scheme, comb states with broadband spectral tailoring effect have been observed, via an intermode pumping scheme. Remarkably, footprints of both constructive and destructive interference on the comb spectrum have been observed, which as confirmed by simulations, are connected to the dispersive effects of the coupled mode family. Our results would not only contribute to the understanding of dissipative soliton dynamics in multi-mode or coupled resonator systems, but also extend the access to stable soliton combs in crystalline microresonators where mode control and dispersion engineering are usually challenging.

Edge reconstruction and emergent neutral modes in integer and fractional quantum Hall phases

This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the ν = 2/5 phase. QH states are topological phases of matter featuring chiral gapless modes at the edge. These edge modes may propagate downstream or upstream and may support either charge or charge-neutral excitations. From topological considerations, particle-like QH states are expected to support only downstream charge modes. However the interplay between the electronic repulsion and the boundary confining potential may drive certain quantum phase transitions (called reconstructions) at the edge, which are associated to the nucleation of additional pairs of counter-propagating modes. Employing variational methods, here we study edge reconstruction in the prototypical particle-like phases at ν = 1, 1/3, and 2/5 as a function of the slope of the confining potential. Our analysis shows that subsequent renormalization of the edge modes, driven by disorder-induced tunnelling and intermode interactions, may lead to the emergence of upstream neutral modes. These predictions may be tested in suitably designed transport experiments. Our results are also consistent with previous observations of upstream neutral modes in these QH phases and could explain the absence of anyonic interference in electronic Mach-Zehnder setups.

Soft modes condensation in Raman spectra of (Pb–La)(Zr–Sn–Ti)O3 ceramics

Low frequency Raman spectra of ([Formula: see text][Formula: see text]([Formula: see text][Formula: see text][Formula: see text]O3 ceramic samples have been studied near cubic to antiferroelectric phase transition at about 200∘C. A set of low frequency soft modes were observed restoring below the transition point, in addition to the known one above 100[Formula: see text]cm[Formula: see text]. These modes show strong damping anomalies at the transition point that supposes considerable intermode interactions via dampings.

Counterpropagating Fractional Hall States in Mirror-Symmetric Dirac Semimetals.

The Landau bands of mirror symmetric 2D Dirac semimetals (e.g., odd layers of ABA graphene) can be identified by their parity with respect to mirror symmetry. This symmetry facilitates a new class of counterpropagating Hall states. We predict the presence of a Laughlin-like correlated liquid state, at the charge neutrality point, with opposite but equal electron and hole filling factors |ν_{±}|=1/m (m odd). This state exhibits fractionally charged quasiparticle-hole pair excitations and counterpropagating edge states with opposite parity. Using a bosonized one-dimensional edge state theory, we show that the fractionally quantized two-terminal longitudinal conductance, σ_{xx}=2e^{2}/(mh), is robust to short-ranged intermode interactions.

Interacting Multiscale Acoustic Vortices as Coherent Excitations in Dust Acoustic Wave Turbulence.

In this work, using three-dimensional intermittent dust acoustic wave turbulence in a dusty plasma as a platform and multidimensional empirical mode decomposition into different-scale modes in the 2+1D spatiotemporal space, we demonstrate the experimental observation of the interacting multiscale acoustic vortices, winding around wormlike amplitude hole filaments coinciding with defect filaments, as the basic coherent excitations for acoustic-type wave turbulence. For different decomposed modes, the self-similar rescaled stretched exponential lifetime histograms of amplitude hole filaments, and the self-similar power spectra of dust density fluctuations, indicate that similar dynamical rules are followed over a wide range of scales. In addition to the intermode acoustic vortex pair generation, propagation, or annihilation, the intra- and intermode interactions of acoustic vortices with the same or opposite helicity, their entanglement and synchronization, are found to be the key dynamical processes in acoustic wave turbulence, akin to the interacting multiscale vortices around wormlike cores observed in hydrodynamic turbulence.

Intermode Breather Solitons in Optical Microresonators

The observation of temporal dissipative Kerr solitons in optical microresonators provides, on the applied side, compact sources of coherent optical frequency combs that have already been applied in coherent communications, dual comb spectroscopy and metrology. On a fundamental level, it enables the study of soliton physics in driven nonlinear cavities. Microresonators are commonly multimode and, as a result, inter-mode interactions inherently occur among mode families - a condition referred to as "avoided mode crossings". Avoided mode crossings can cause soliton decay, but can also modify the soliton spectrum, leading to e.g. the formation of dispersive wave and inducing a spectral recoil. Yet, to date, the entailing temporal soliton dynamics from inter-mode interactions has rarely been studied, but is critical to understand regimes of soliton-stability. Here we report the discovery of an inter-mode breather soliton. Such breathing dynamics occurs within a laser detuning range where conventionally stationary dissipative solitons are expected. We demonstrate experimentally the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators), and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We demonstrate experimentally that the breathing is associated with a periodic energy exchange between the soliton and another optical mode family. We further show that inter-mode interactions can be modeled by a response function acting on dissipative solitons. The observation of breathing dynamics in the conventionally stable soliton regime is critical to applications, ranging from low-noise microwave generation, frequency synthesis to spectroscopy. On a fundamental level, our results provide new understandings of the rich dissipative soliton dynamics in multimode nonlinear cavities.

Lamb-dip spectroscopy of the C-N stretching band of methylamine by using frequency-tunable microwave sidebands of CO2 laser lines.

Lamb-dip spectroscopy of the C−N stretching band of methylamine has been systematically extended to P-, Q-, and R-branch by using microwave sidebands of a large number of CO2 laser lines as frequency-tunable infrared sources in a sub-Doppler spectrometer. Lamb-dip signals of more than 150 spectral lines have been observed with a resolution of 0.4 MHz and their frequencies have been precisely measured with an accuracy of ±0.1 MHz. More than 30 closed combination loops have been formed, which unambiguously confirm the assignments. For over 150 vibrational excited levels in 27 substates, refined term values have been determined and expanded in J(J + 1) power-series to determine the substate origins and the effective rotational constants. For transitions with Aa torsion-inversion symmetry in torsional state υt = 0, 57 K-doublet lines displaying asymmetry splittings have been observed and the splitting constants for levels with K = 1, 2, and 3 in the excited states have been determined. Our results provide accurate experimental information for spectroscopic studies of the interesting vibrational perturbations and intermode interactions related to the C−N stretching mode, directly support astronomical surveys, and are very relevant in practice to identification and frequency determination of the CO2-laser-pumped far-infrared laser lines of methylamine.

Nonlinear resonance-assisted tunneling induced by microcavity deformation.

Noncircular two-dimensional microcavities support directional output and strong confinement of light, making them suitable for various photonics applications. It is now of primary interest to control the interactions among the cavity modes since novel functionality and enhanced light-matter coupling can be realized through intermode interactions. However, the interaction Hamiltonian induced by cavity deformation is basically unknown, limiting practical utilization of intermode interactions. Here we present the first experimental observation of resonance-assisted tunneling in a deformed two-dimensional microcavity. It is this tunneling mechanism that induces strong inter-mode interactions in mixed phase space as their strength can be directly obtained from a separatrix area in the phase space of intracavity ray dynamics. A selection rule for strong interactions is also found in terms of angular quantum numbers. Our findings, applicable to other physical systems in mixed phase space, make the interaction control more accessible.

Mode-coupling mechanisms in nanocontact spin-torque oscillators

Spin-torque oscillators (STOs) are devices that allow for the excitation of a variety of magnetodynamical modes at the nanoscale. Depending on both external conditions and intrinsic magnetic properties, STOs can exhibit regimes of mode hopping and even mode coexistence. Whereas mode hopping has been extensively studied in STOs patterned as nanopillars, coexistence has been only recently observed for localized modes in nanocontact STOs (NC-STOs), where the current is confined to flow through a NC fabricated on an extended pseudo spin valve. By means of electrical characterization and a multimode STO theory, we investigate the physical origin of the mode-coupling mechanisms favoring coexistence. Two coupling mechanisms are identified: (i) magnon-mediated scattering and (ii) intermode interactions. These mechanisms can be physically disentangled by fabricating devices where the NCs have an elliptical cross section. The generation power and linewidth from such devices are found to be in good qualitative agreement with the theoretical predictions, as well as provide evidence of the dominant mode-coupling mechanisms.

Experimental and theoretical study of absorption spectrum of the (CH3)2CO⋯HF complex. Influence of anharmonic interactions on the frequency and intensity of the C[dbnd]O and H–F stretching bands

IR absorption spectra of mixtures (CH3)2CO/HF and free (CH3)2CO molecules are recorded in the region of 4000–900cm−1 with a Bruker IFS-125 HR vacuum Fourier spectrometer at room temperature with a resolution up to 0.02cm−1. Spectral characteristics of the 2ν(CO) overtone band of free acetone are reliably measured. The ν1(HF) and ν(CO) absorption bands of the (CH3)2CO⋯HF complex are obtained by subtracting the absorption bands of free HF and acetone and absorption lines of atmospheric water from the experimental spectrum of mixtures. The experimental data are compared with theoretical results obtained from variational solutions of 1D–4D vibrational Schrödinger equations. The anharmonic potential energy and dipole moment surfaces used in the calculations were computed in the MP2/6-311++G(2d,2p) approximation with corrections for the basis set superposition error. Comparison of the data derived from solutions for different combinations of vibrational degrees of freedom shows that taking the inter-mode anharmonic interactions into account has different effects on the transition frequencies and intensities. Particular attention has been given to elucidation of the influence of anharmonic coupling of the H–F and CO stretches with the low-frequency intermolecular modes on their frequencies and intensities and the strength of resonance between the fundamental H–F and the first overtone CO transitions.

Expressions for the nonlinear transmission performance of multi-mode optical fiber

We develop an analytical theory which allows us to identify the information spectral density limits of multimode optical fiber transmission systems. Our approach takes into account the Kerr-effect induced interactions of the propagating spatial modes and derives closed-form expressions for the spectral density of the corresponding nonlinear distortion. Experimental characterization results have confirmed the accuracy of the proposed models. Application of our theory in different FMF transmission scenarios has predicted a ~10% variation in total system throughput due to changes associated with inter-mode nonlinear interactions, in agreement with an observed 3dB increase in nonlinear noise power spectral density for a graded index four LP mode fiber.

Mean-field dynamics of two-mode Bose–Einstein condensates in highly anisotropic potentials: interference, dimensionality and entanglement

We study the mean-field dynamics and the reduced-dimension character of two-mode Bose–Einstein condensates (BECs) in highly anisotropic traps. By means of perturbative techniques, we show that the tightly confined (transverse) degrees of freedom can be decoupled from the dynamical equations at the expense of introducing additional effective three-body, attractive, intra- and inter-mode interactions into the dynamics of the loosely confined (longitudinal) degrees of freedom. These effective interactions are mediated by changes in the transverse wave function. The perturbation theory is valid as long as the nonlinear scattering energy is small compared to the transverse energy scales. This approach leads to reduced-dimension mean-field equations that optimally describe the evolution of a two-mode condensate in general quasi-one-dimensional (1D) and quasi-two-dimensional geometries. We use this model to investigate the relative phase and density dynamics of a two-mode, cigar-shaped 87Rb BEC. We study the relative-phase dynamics in the context of a nonlinear Ramsey interferometry scheme, which has recently been proposed as a novel platform for high-precision interferometry. Numerical integration of the coupled, time-dependent, three-dimensional, two-mode Gross–Pitaevskii equations for various atom numbers shows that this model gives a considerably more refined analytical account of the mean-field evolution than an idealized quasi-1D description.

Energy types

This paper presents a novel type system to promote and facilitate energy-aware programming. Energy Types is built upon a key insight into today's energy-efficient systems and applications: despite the popular perception that energy and power can only be described in joules and watts, real-world energy management is often based on discrete phases and modes, which in turn can be reasoned about by type systems very effectively. A phase characterizes a distinct pattern of program workload, and a mode represents an energy state the program is expected to execute in. This paper describes a programming model where phases and modes can be intuitively specified by programmers or inferred by the compiler as type information. It demonstrates how a type-based approach to reasoning about phases and modes can help promote energy efficiency. The soundness of our type system and the invariants related to inter-phase and inter-mode interactions are rigorously proved. Energy Types is implemented as the core of a prototyped object-oriented language ET for smartphone programming. Preliminary studies show ET can lead to significant energy savings for Android Apps.

Excitation, relaxation, and quantum diffusion of CO on copper

We investigate the effect of intermode coupling and anharmonicity on the excitation and relaxation dynamics of CO on Cu(100). The nonadiabatic coupling of the adsorbate to the surface is treated perturbatively using a position-dependent state-resolved transition rate model. Using the potential energy surface of Marquardt et al. [J. Chem. Phys. 132, 074108 (2010)], which provides an accurate description of intermode interactions, we propose a four-dimensional model that represents simultaneously the diffusion and the desorption of the adsorbate. The system is driven by both rational and optimized infrared laser pulses to favor either selective mode and state excitations or lateral displacement along the diffusion coordinate. The dissipative dynamics is simulated using the reduced density matrix in its Lindblad form. We show that coupling between the degrees of freedom, mediated by the creation and annihilation of electron-hole pairs in the metal substrate, significantly affects the system excitation and relaxation dynamics. In particular, the angular degrees of freedom appear to play an important role in the energy redistribution among the molecule-surface vibrations. We also show that coherent excitation using simple IR pulses can achieve population transfer to a specific target to some extent but does not allow enforcement of the directionality to the diffusion motion.

Quantum equations of motion for multimode laser generation with a spatial dependence of the atom interaction with the field taken into account

We derive equations of motion for the electromagnetic field operators a + aq for a three-level multimode laser with a spatial dependence of the interaction of atoms with the field of a standing wave in a cavity taken into account. We calculate and analyze the dynamics of means of photon numbers in the field modes and of the correlation function of field modes. We explore the effect of intermode correlations on the dynamics of establishing stationary laser generation. We find that taking the spatial dependence of the interaction of atoms with the field and the intermode correlation into account in investigating the means of photon numbers leads to revealing new properties of laser generation, such as saturation of the laser radiation intensity in a single-mode regime and generation of short light pulses of side below-threshold modes with the amplitudes depending on the initial state of the field in a cavity. Under the condition that the width of a laser amplification line (the rate of damping of the active medium polarization) is of the order of or greater than the intermode gap of eigenfrequencies in a cavity, laser generation has a multimode (multifrequency) nature. In real conditions, a small increase above the generation threshold, when the pumping is relatively small, can already lead to excitation of several eigen- modes of the laser cavity. With an increase in pumping, the number of modes involved in the generation and having intensities comparable to each other rapidly increases and can attain large values (up to sev- eral hundreds). The complicated dynamics of the multimode generation of different lasers are currently widely investigated both theoretically and experimentally. The theoretical analysis of multimode genera- tion encounters major complications because we must take intermode interactions into account, together with the spatial dependence of the interaction of the active medium atoms with a spatially inhomogeneous electromagnetic (EM) field in the cavity, which shows up, in particular, in the effect of spatial burning of a hole. The semiclassical theory of multimode (multifrequency) laser generation was developed in (1)-(10), where the Maxwell equations for a classical EM field were considered and the active medium was described quantum-mechanically in terms of a density matrix (operator) and an ensemble of two-level atoms. A full quantum mechanical theory of multimode generation was considered in (1), (11)-(16). The approximation of identical modes was used in (12)-(16). We note that in (1)-(4) in the semiclassical theory, the phenomenon of spatial burning of a hole in the population inversion of an active medium was regarded as the main reason and the necessary condition for the occurrence of stable multimode laser generation with a homogeneously broadened line. The approximation of identical modes, broadly used in the theory of multimode laser generation (12)- (16), in some cases allows assessing the generation dynamics qualitatively, but in the general case and for a

Comparative analysis of the H–F stretching band in absorption spectra of gas-phase complexes of HF with water, dimethyl ether, and acetone

Comparative analysis of the ν 1(H–F) stretching band shapes in the absorption spectra of complexes of HF with water, dimethyl ether, and acetone and the mechanisms of formation of this band is performed by comparing the experimental spectra and results of nonempirical quantum–mechanical calculations. The experimental spectra of complexes considered were obtained by subtracting the spectra of monomers from the experimental spectra of gaseous mixtures recorded at different temperatures in the region of the ν 1(H–F) band at a high resolution with Bruker IFS-113v and Вruker IFS-125 HR vacuum Fourier spectrometers. These spectra are compared with the band shapes reconstructed theoretically with the use of electro-optical parameters obtained from variational solutions of multidimensional anharmonic vibrational problems. The equilibrium geometries of the complexes, their potential energy and dipole moment surfaces necessary for solving these problems were calculated ab initio at a high level of theory. In this approach the internal anharmonicity of the ν 1(H–F) mode and its interaction with all low-frequency intermolecular modes are considered explicitly. Anharmonic interactions between different intermolecular motions are also analyzed in detail. The inter-mode interactions are found to have different effects on the frequency and absolute intensity of the ν 1(H–F) fundamental transition. Comparison of the data for different complexes shows that the resulting spectral manifestations of the anharmonic effects depend on the interplay between the H-bond strength, the barrier height for tunneling, the magnitudes of frequencies of intermolecular vibrations, rotational constants, etc. The reconstruction of spectra as a superposition of rovibrational bands of the fundamental, hot, and combination transitions with calculated values of absolute intensities can reproduce the shape and separate details of the experimental spectra. Analysis of the experimental and calculated data provides reliable values of the fundamental ν 1(H–F) transition frequency, indicates its position in the spectrum, and elucidates the nature of different structural features.

Quasiclassical Trajectory Simulations of OH(v) + NO2 → HONO2* → OH(v‘) + NO2: Capture and Vibrational Deactivation Rate Constants

Quasiclassical trajectory calculations are used to investigate the dynamics of the OH(v) + NO(2) --> HONO(2) --> OH(v') + NO(2) recombination/dissociation reaction on an analytic potential energy surface (PES) that gives good agreement with the known structure and vibrational frequencies of nitric acid. The calculated recombination rate constants depend only weakly on temperature and on the initial vibrational energy level of OH(v). The magnitude of the recombination rate constant is sensitive to the potential function describing the newly formed bond and to the switching functions in the PES that attenuate inter-mode interactions at long range. The lifetime of the nascent excited HONO(2) depends strongly not only on its internal energy but also on the identity of the initial state, in disagreement with statistical theory. This disagreement is probably due to the effects of slow intramolecular vibrational energy redistribution (IVR) from the initially excited OH stretching mode. The vibrational energy distribution of product OH(v') radicals is different from statistical distributions, a result consistent with the effects of slow IVR. Nonetheless, the trajectory results predict that vibrational deactivation of OH(v) via the HONO(2) transient complex is approximately 90% efficient, almost independent of initial OH(v) vibrational level, in qualitative agreement with recent experiments. Tests are also carried out using the HONO(2) PES, but assuming the weaker O-O bond strength found in HOONO (peroxynitrous acid). In this case, the predicted vibrational deactivation efficiencies are significantly lower and depend strongly on the initial vibrational state of OH(v), in disagreement with experiments. This disagreement suggests that the actual HOONO PES may contain more inter-mode coupling than found in the present model PES, which is based on HONO(2). For nitric acid, the measured vibrational deactivation rate constant is a useful proxy for the recombination rate, but IVR randomization of energy is not complete, suggesting that the efficacy of the proxy method must be evaluated on a case-by-case basis.

Fourier Transform Infrared Spectroscopy and Vibrational Coupling in the OH-Bending Band of13CH3OH

We present in this work a high-resolution Fourier transform infrared study of the OH-bending vibrational band of13CH3OH. We have investigated the 1070–1400 cm−1spectral region at 0.002 cm−1resolution using the modified Bomem DA3.002 Fourier transform spectrometer at the Steacie Institute for Molecular Sciences at the National Research Council of Canada in Ottawa. This study has led to (i) determination of excited-state J(J + 1) subband expansion coefficients and (ii) characterization of a variety of interactions coupling the different vibrational modes, notably a strong Fermi resonance between the OH bend and the torsionally excited CH3-rocking mode. The OH-bending band is widely spread withQsubbranches grouped in two peaks at about 1312 and 1338 cm−1. The lower levels for all assigned subbands were confirmed using closed loops of IR and FIR transitions. The subbands have been fitted toJ(J+ 1) power-series expansions in order to obtain the subband origins and the state-specific energy expansion coefficients for both the OH-bending and excited torsional CH3-rocking states. The strong interaction between the OH-bending state and the first excited torsional CH3-rocking state gives rise to several “extra” forbidden subbands due to intensity borrowing. The asymmetry splitting of the (nτK)v= (122)OHA OH-bending doublet was found to be anomalously small, and the splitting of the (122)rA CH3-rocking doublet is observed to be enhanced. We have identified a network of intermode interactions causing this unusual behavior, but a quantitative analysis of the vibrational coupling is restricted by limited knowledge of the unperturbed positions of the interacting levels. All these interactions provide relaxation channels for intramolecular vibrational redistribution among the lower vibrational modes in13CH3OH. Another important finding is that the torsion–K–rotation energy curves in the OH-bending state display an inverted pattern compared to the ground state.