Showing papers on "Normal mode published in 2020"

Interference traps waves in open system: Bound states in the continuum

Abstract: I review the four mechanisms of bound states in the continuum (BICs) in application to microwave and acoustic cavities open to directional waveguides. The most simple are the symmetry protected BICs which are localized inside the cavity because of the orthogonality of the eigenmodes to the propagating modes of waveguides. However, the most general and interesting is the Friedrich-Wintgen mechanism when the BICs are result of full destructive interference of outgoing resonant modes. The third type of the BICs, the Fabry-Perot BICs, occur in a double resonator system when each resonator can serve as an ideal mirror. At last, the accidental BICs can be realized in the open cavities with no symmetry like the open Sinai billiard in which the eigenmode of the resonator can become orthogonal to the continuum of the waveguide accidentally by a smooth deformation of the eigenmode. We also review the one-dimensional systems in which the BICs occur owing to full destructive interference of two waves separated by spin or polarization or by paths in the Aharonov-Bohm rings. We widely use the method of effective non-Hermitian Hamiltonian equivalent to the coupled mode theory which detects bound states in the continuum (BICs) by finding zero widths resonances.

Optomechanical detection of vibration modes of a single bacterium.

Abstract: Low-frequency vibration modes of biological particles, such as proteins, viruses and bacteria, involve coherent collective vibrations at frequencies in the terahertz and gigahertz domains. These vibration modes carry information on their structure and mechanical properties, which are good indicators of their biological state. In this work, we harnessed a particular regime in the physics of coupled mechanical resonators to directly measure these low-frequency mechanical resonances of a single bacterium. We deposit the bacterium on the surface of an ultrahigh frequency optomechanical disk resonator in ambient conditions. The vibration modes of the disk and bacterium hybridize when their associated frequencies are similar. We developed a general theoretical framework to describe this coupling, which allows us to retrieve the eigenfrequencies and mechanical loss of the bacterium low-frequency vibration modes (quality factor). Additionally, we analysed the effect of hydration on these vibrational modes. This work demonstrates that ultrahigh frequency optomechanical resonators can be used for vibrational spectrometry with the unique capability to obtain information on single biological entities.

Polaritonic normal modes in transition state theory.

Abstract: A series of experiments demonstrates that strong light–matter coupling between vibrational excitations in isotropic solutions of molecules and resonant infrared optical microcavity modes leads to modified thermally activated kinetics. However, Galego et al. [Phys. Rev. X 9, 021057 (2019)] recently demonstrated that, within transition state theory, effects of strong light–matter coupling with reactive modes are mostly electrostatic and essentially independent of light–matter resonance or even of the formation of vibrational polaritons. To analyze this puzzling theoretical result in further detail, we revisit it under a new light, invoking a normal mode analysis of the transition state and reactant configurations for an ensemble of an arbitrary number of molecules in a cavity, obtaining simple analytical expressions that produce similar conclusions as Feist. While these effects become relevant in optical microcavities if the molecular dipoles are anisotropically aligned, or in cavities with extreme confinement of the photon modes, they become negligible for isotropic solutions in microcavities. It is concluded that further studies are necessary to track the origin of the experimentally observed kinetics.

Dense active matter model of motion patterns in confluent cell monolayers.

Abstract: Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter. Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes. Here the authors show that cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce characteristic swirl-like correlations.

Photothermal excitation processes with refined multi dual phase-lags theory for semiconductor elastic medium

Abstract: The aim of this investigation is to study a refined multi-phase-lags generalized thermoelasticity theory and coupled plasma theory for a semi-infinite semiconductor elastic medium. The model is studied in context of the Photothermal transport process for isoropic homogenous two dimension medium. The governing equations describe the interaction between elastic-plasma-thermal waves. The normal mode technique is used to get the exact solutions analytically of main physical quantities under investigation. The thermal-plasma and mechanical loads are applied at the free surface of semiconductor medium to obtain the complete solution of the temperature, displacement, stresses and carrier density distributions. Some special cases have been obtained. Results will be displayed graphically and discussed. Comparisons are made between the different theories in thermoelasticity.

Polaritonic normal modes in Transition State Theory

Abstract: A series of experiments demonstrate that strong light-matter coupling between vibrational excitations in isotropic solutions of molecules and resonant infrared optical microcavity modes leads to modified thermally-activated kinetics. However, Feist and coworkers [\emph{Phys. Rev. X.}, \textbf{9}, 021057(2019)] have recently demonstrated that, within transition state theory, the effects of strong light-matter coupling with reactive modes are electrostatic and essentially independent of light-matter resonance or even of the formation of vibrational polaritons. To analyze this puzzling theoretical result in further detail, we revisit it under a new light, invoking a normal mode analysis of the transition state and reactant configurations for an ensemble of an arbitrary number of molecules in a cavity, obtaining simple analytical expressions that produce similar conclusions as Feist. While these effects become relevant in optical microcavities if the molecular dipoles are anisotropically aligned, or in cavities with extreme confinement of the photon modes, they become negligible for isotropic solutions in microcavities. It is concluded that further studies are necessary to track the origin of the experimentally observed kinetics.

Accurate Characterization and Design Guidelines of Glide-Symmetric Holey EBG

Abstract: The dispersion characteristics of a glide-symmetric holey periodic surface are investigated, with special emphasis on a detailed study of its stopbands. The unit cell is modeled as a multiport network associated with multiple modes at each of the lattice boundaries. Enforcing the periodic conditions, the real and imaginary parts of the wavenumbers of the Floquet modes are calculated through an eigenproblem posed in terms of the generalized multimodal transfer matrix, which is computed from the scattering parameters obtained with a full-wave simulator. This procedure allows us to take into account the higher order modal couplings between adjacent unit cells that are crucial for accurate dispersion analysis. The resulting simulation-assisted approach provides both a convenient computational tool and a very fruitful physical insight that reveals the existence of complex modes, the convergence of opposite-parity modes, and the anisotropy in both passband and stopband. This approach enables a precise calculation of the attenuation constant, which is not possible with conventional techniques as the eigenmode solvers of commercial software. Based on this approach, an extensive parametric study is carried out, rigorously establishing a set of critical criteria for the use of such a periodic surface as an electromagnetic bandgap structure in gap waveguide technology. Moreover, the analysis of the directional properties of the structure is applied to further suppress the leakage.

Gravitomagnetic tidal resonance in neutron-star binary inspirals

Abstract: A compact binary system implicating at least one rotating neutron star undergoes gravitomagnetic tidal resonances as it inspirals toward its final merger. These have a dynamical impact on the phasing of the emitted gravitational waves. The resonances are produced by the inertial modes of vibration of the rotating star. Four distinct modes are involved, and the resonances occur within the frequency band of interferometric gravitational-wave detectors when the star spins at a frequency that lies within this band. The resonances are driven by the gravitomagnetic tidal field created by the companion star; this is described by a post-Newtonian vector potential, which is produced by the mass currents associated with the orbital motion. These resonances were identified previously by Flanagan and Racine [Phys. Rev. D 75, 044001 (2007)], but these authors accounted only for the response of a single mode, the r-mode, a special case of inertial modes. All four relevant modes are included in the analysis presented in this paper. The total accumulated gravitational-wave phase shift is shown to range from approximately $10^{-2}$ radians when the spin and orbital angular momenta are aligned, to approximately $10^{-1}$ radians when they are anti-aligned. Such phase shifts will become measurable in the coming decades with the deployment of the next generation of gravitational-wave detectors (Cosmic Explorer, Einstein Telescope); they might even come to light within this decade, thanks to planned improvements in the current detectors. With good constraints on the binary masses and spins gathered from the inspiral waveform, the phase shifts deliver information regarding the internal structure of the rotating neutron star, and therefore on the equation of state of nuclear matter.

A primary model of THz and far-infrared signal generation and conduction in neuron systems based on the hypothesis of the ordered phase of water molecules on the neuron surface I: signal characteristics

Abstract: In this paper, we use the theory of quantum optics and electrodynamics to study the electromagnetic field problem in the nervous system based on the assumption of an ordered arrangement of water molecules on the neuronal surface. Using the Lagrangian of the water molecule-field ion, the dynamic equations for neural signal generation and transmission are derived. Perturbation theory and the numerical method are used to solve the dynamic equations, and the characteristics of high-frequency signals (the dispersion relation, the time domain of the field, the frequency domain waveform, etc.) are discussed. This model predicts some intrinsic vibration modes of electromagnetic radiation on the neuronal surface. The frequency range of these vibration modes is in the THz and far-infrared ranges.

Quantum interactions with pulses of radiation

Abstract: This paper presents a general master equation formalism for the interaction between traveling pulses of quantum radiation and localized quantum systems. Traveling fields populate a continuum of free-space radiation modes and the Jaynes-Cummings model, valid for a discrete eigenmode of a cavity, does not apply. We develop a complete input-output theory to describe the driving of quantum systems by arbitrary incident pulses of radiation and the quantum state of the field emitted into any desired outgoing temporal mode. Our theory is applicable to the transformation and interaction of pulses of radiation by their coupling to a wide class of material quantum systems. We discuss the most essential differences between quantum interactions with pulses and with discrete radiative eigenmodes and present examples relevant to quantum information protocols with optical, microwave, and acoustic waves.

Nonlinear primary resonance analysis of nanoshells including vibrational mode interactions based on the surface elasticity theory

Abstract: The deviation from the classical elastic characteristics induced by the free surface energy can be considerable for nanostructures due to the high surface to volume ratio. Consequently, this type of size dependency should be accounted for in the mechanical behaviors of nanoscale structures. In the current investigation, the influence of free surface energy on the nonlinear primary resonance of silicon nanoshells under soft harmonic external excitation is studied. In order to obtain more accurate results, the interaction between the first, third, and fifth symmetric vibration modes with the main oscillation mode is taken into consideration. Through the implementation of the Gurtin-Murdoch theory of elasticity into the classical shell theory, a size-dependent shell model is developed incorporating the effect of surface free energy. With the aid of the variational approach, the governing differential equations of motion including both of the cubic and quadratic nonlinearities are derived. Thereafter, the multi-time-scale method is used to achieve an analytical solution for the nonlinear size-dependent problem. The frequency-response and amplitude-response of the soft harmonic excited nanoshells are presented corresponding to different values of shell thickness and surface elastic constants as well as various vibration mode interactions. It is depicted that through consideration of the interaction between the higher symmetric vibration modes and the main oscillation mode, the hardening response of nanoshell changes to the softening one. This pattern is observed corresponding to both of the positive and negative values of the surface elastic constants and the surface residual stress.

On the SN2 reactions modified in vibrational strong coupling experiments: reaction mechanisms and vibrational mode assignments

Abstract: Recent experiments have reported modified chemical reactivity under vibrational strong coupling (VSC) in microfluidic Fabry–Perot cavities. In particular, the reaction rate of nucleophilic substitution reactions at silicon centers (SN2@Si) has been altered when a vibrational mode of the reactant was coupled to a confined light mode in the strong coupling regime. In this situation, hybrid light–matter states known as polaritons are formed and seem to be responsible for the modified chemical kinetics. These results are very encouraging for future applications of polaritonic chemistry to catalyze chemical reactions, with the ability to manipulate chemical phenomena without any external excitation of the system. Still, there is no theory capable of explaining the mechanism behind these results. In this work we address two points that are crucial for the interpretation of these experiments. Firstly, by means of electronic structure calculations we report the reaction mechanism in normal conditions of the two recently modified SN2@Si reactions, obtaining in both cases a triple-well PES where the rate-determining step is due to the Si–C and Si–O bond cleavage. Secondly, we characterize in detail the normal modes of vibration of the reactants. In the VSC experiments, reaction rates were modified only when specific vibrations of the reactants were coupled to a cavity mode. We find that these vibrations are highly mixed among the different fragments of the reactants leading to a completely new assignment of the IR peaks coupled to cavity modes in the original experimental works. Our results are fundamental for the interpretation of the VSC experiments given that in the absence of a theory explaining these results, the current phenomenological understanding relies on the assignment of the character of the vibrational IR peaks.

Random vibrations of stress-driven nonlocal beams with external damping

Abstract: Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding environment. Loadings are modeled by accounting for their random nature. Such a dynamic problem is characterized by a stochastic partial differential equation in space and time governing time-evolution of the relevant displacement field. Differential eigenanalyses are performed to evaluate modal time coordinates and mode shapes, providing a complete stochastic description of response solutions. Closed-form expressions of power spectral density, correlation function, stationary and non-stationary variances of displacement fields are analytically detected. Size-dependent dynamic behaviour is assessed in terms of stiffness, variance and power spectral density of displacements. The outcomes can be useful for design and optimization of structural components of modern small-scale devices, such as Micro- and Nano-Electro-Mechanical-Systems (MEMS and NEMS).

Ultra-long-lived quasi-normal modes of neutron stars in massive scalar-tensor gravity

Abstract: The spectrum of frequencies and characteristic times that compose the ringdown phase of gravitational waves emitted by neutron stars carries information about the matter content (the equation of state) and the underlying theory of gravity. Typically, modified theories of gravity introduce additional degrees of freedom/fields, such as scalars, which result in new families of modes composing the ringdown spectrum. Simple but physically promising candidates are scalar-tensor theories, which effectively introduce an additional massive scalar field (i.e. , an ultra-light boson) that couples non-minimally to gravity, resulting in scalarized neutron stars. Here we present the first calculation of the full ringdown spectrum in such theories. We show that the ringdown spectrum of neutron stars with ultra-light bosons is much richer and fundamentally different from the spectrum in general relativity and that it possesses propagating ultra-long-lived modes.

Effect of large displacements on the linearized vibration of composite beams

Abstract: Natural frequencies and mode shapes are functions of the equilibrium state. In the large displacement regime, pre-stresses may modify significantly the modal behaviour of structures. In this work, a geometrical nonlinear total Lagrangian formulation that includes cross-sectional deformations is developed to analyse the vibration modes of composite beams structures in the nonlinear regime. Equations of motion are solved around nonlinear static equilibrium states, which are identified using a Newton–Raphson algorithm along with a path-following method of arc-length type. Different boundary conditions and stacking sequences are analysed. It is shown that vibration modes are strongly modified by nonlinear phenomena. Moreover, models that do not describe those effects accurately may results in misleading results, especially if compression is dominant. In fact, results show a crossing phenomenon in the post-buckling regime of an asymmetric cross-ply beam, whereas it is completely unforeseen by the linearized analysis.

Quantized quasinormal mode description of non-linear cavity QED effects from coupled resonators with a Fano-like resonance

Abstract: We employ a recently developed quantization scheme for quasinormal modes (QNMs) to study a nonperturbative open cavity-QED system consisting of a hybrid metal-dielectric resonator coupled to a quantum emitter. This hybrid cavity system allows one to explore the complex coupling between a low $Q$ (quality factor) resonance and a high $Q$ resonance, manifesting in a striking Fano resonance, an effect that is not captured by traditional quantization schemes using normal modes or a Jaynes-Cummings (JC) type model. The QNM quantization approach rigorously includes dissipative coupling between the QNMs, and is supplemented with generalized input-output relations for the output electric field operator for multiple modes in the system, and correlation functions outside the system. The role of the dissipation-induced mode coupling is explored in the strong coupling regime between the photons and emitter beyond the first rung of the JC dressed-state ladder. Important differences in the quantum master equation and input-output relations between the QNM quantum model and phenomenological dissipative JC models are found. In a second step, numerical results for the Fock distributions and system as well as output correlation functions obtained from the quantized QNM model for the hybrid structure are compared with results from a phenomenological approach. We demonstrate explicitly how the quantized QNM model manifests in multiphoton quantum correlations beyond what is predicted by the usual JC models.

A Critical Evaluation of Vibrational Stark Effect (VSE) Probes with the Local Vibrational Mode Theory.

Abstract: Over the past two decades, the vibrational Stark effect has become an important tool to measure and analyze the in situ electric field strength in various chemical environments with infrared spectroscopy. The underlying assumption of this effect is that the normal stretching mode of a target bond such as CO or CN of a reporter molecule (termed vibrational Stark effect probe) is localized and free from mass-coupling from other internal coordinates, so that its frequency shift directly reflects the influence of the vicinal electric field. However, the validity of this essential assumption has never been assessed. Given the fact that normal modes are generally delocalized because of mass-coupling, this analysis was overdue. Therefore, we carried out a comprehensive evaluation of 68 vibrational Stark effect probes and candidates to quantify the degree to which their target normal vibration of probe bond stretching is decoupled from local vibrations driven by other internal coordinates. The unique tool we used is the local mode analysis originally introduced by Konkoli and Cremer, in particular the decomposition of normal modes into local mode contributions. Based on our results, we recommend 31 polyatomic molecules with localized target bonds as ideal vibrational Stark effect probe candidates.

Subradiance-protected excitation spreading in the generation of collimated photon emission from an atomic array

Abstract: We show how an initial localized radiative excitation in a two-dimensional array of cold atoms can be converted into highly directional coherent emission of light by protecting the spreading of the excitation across the array in a subradiant collective eigenmode with a lifetime orders of magnitude longer than that of an isolated atom. We demonstrate how to reach two such strongly subradiant modes, a uniform one where all the dipoles are oscillating in phase normal to the plane and an antiferromagnetic mode where each dipole is π out of phase with its nearest neighbor. The excitation, which can consist of a single photon, is then released from the protected subradiant eigenmode by controlling the Zeeman level shifts of the atoms. Hence, an original localized excitation which emits in all directions is transferred to a delocalized subradiance-protected excitation, with a probabilistic emission of a photon only along the axis perpendicular to the plane of the atoms. This protected spreading and directional emission could potentially be used to link stages in a quantum information or quantum computing architecture.

Nonlinear vibration of axially moving simply-supported circular cylindrical shell

Abstract: This paper investigates the nonlinear free and forced vibration of axially moving simply-supported thin circular cylindrical shells in the sub-harmonic region, considering the effect of viscous structure damping Motion equations of axially moving circular cylindrical shells in cylindrical coordinates are derived with the aid of the Hamilton principle and employing the Donnell–Mushtari nonlinear shells’ theory Three nonhomogeneous nonlinear partial differential equilibrium equations concerning displacements across the three directions of cylindrical coordinate are reduced to two equations as a result of using the definition of the airy function The particular and private solution of airy stress function is obtained utilizing the assumption of the form of the displacement in the radial direction based on the simply-supported boundary conditions and combination of axisymmetric and asymmetric driven and companion modes By gaining the airy function, the third motion equation is discretized using the Galerkin method into the set of coupled nonlinear nonhomogeneous ordinary differential equations The perturbation method and Runge–Kutta 4th order are employed as a semi-analytical and a numerical solution method, which in practice leads to the prediction of the nonlinear frequencies and amplitudes of various modes of vibration at different velocities and external excitation fluctuation domain and frequency The bifurcation analysis of the velocity and external excitation parameters in sub-harmonic regions shows the changes in the instability condition of the system It causes the appearance of the pitchfork bifurcation and the Neimark–Sacker bifurcation points The accuracy of both, the direct normal form and numerical method results are compared against each other and validated in the particular case in the absence of the velocity with available data The system would be more stable at a higher speed near 1:1 external resonance due to the activation of more asymmetric vibration modes and the growth of the nonlinear softening characteristic in the absence of companion vibration modes

Quantum information preserving computational electromagnetics

Abstract: We present a computational framework for canonical quantization in arbitrary inhomogeneous dielectric media by incorporating quantum electromagnetic effects into complex solutions of quantum Maxwell's equations. To do so, the proposed algorithm integrates and performs (1) numerical computation of normal modes and (2) evaluation of arbitrary products of ladder operators acting on multimode Fock states. The former is associated with Hermitian-Helmholtz linear systems using finite-element or finite-difference methods; consequently, the complete set of numerical normal modes diagonalizes the Hamiltonian operators up to floating-point precision. Its Hermiticity is retained, allowing its quantization. Then, we perform quantum numerical simulations of two-photon interference occurring in a 50:50 beam splitter to observe the Hong-Ou-Mandel effect. Our prototype model is useful for numerical analyses on various narrow-band quantum-optical multiphoton systems such as quantum metasurfaces, quantum-optical filters, and quantum electrodynamics in open optical cavities.

Generation Mechanism and Development Characteristics of Rail Corrugation of Cologne Egg Fastener Track in Metro

Abstract: By establishing vehicle-track space coupled model and rail corrugation evaluation model, the generation mechanism of rail corrugation was analyzed in frequency domain and time domain, and development characteristics of corrugation were studied by using corrugation growth rate. Analysis based on frequency domain: through modal analysis and frequency response analysis on the finite element model of track structure, it is found that there are natural frequencies of track structure close to measured corrugation passing frequencies. It shows that the vibration modes corresponding to these frequencies can be more easily excited, which can cause the resonance phenomenon of track structure and form the rail corrugation at corresponding frequencies. Analysis based on time domain: the time-history curves of rail vertical vibration acceleration and rail vertical displacement are calculated by using vehicle-track coupled model and the frequency domain transformation of the time-history data is carried out. It is found that there are characteristic frequencies close to the measured corrugation passing frequencies, which indicates that the vibration of track structure at corresponding frequencies is an important reason to promote the formation of corrugation. The change of vehicle speed has no effect on characteristic frequencies of corrugation growth rate curves, which reflects the fixed frequency characteristic of corrugation. With the increase of train operation times, the corrugation corresponding to characteristic frequencies will gradually form and develop, and the increase of vehicle speed will increase the wavelength range and development speed of rail corrugation.