Properties Of Eigenmodes Research Articles

Eigenmode and eigenpropagation of the electromagnetic waves in Möbius and Klein networks

To explore the distribution of characteristic frequencies and the propagation properties of eigenmodes in topological networks at the zero-energy level, we design optical waveguide networks with two typical topologies: Möbius network and Klein network, inspired by the Möbius strip and Klein bottle, respectively. We investigate the degeneracy at characteristic frequencies and the propagation properties of the eigenmodes of these networks, both theoretically and experimentally. We discovered an intriguing eigenpropagation in the Möbius network and multiple degenerate eigenmodes in the Klein network, analyzing the propagation characteristics and distribution patterns of electromagnetic waves within them. In our experiments, we utilize coaxial cables as one-dimensional waveguides to construct transmission line networks for the two networks. We observe the distinct transmission paths of the Möbius network’s eigenmode and the two degenerate eigenmodes of the Klein network. Our findings provide a theoretical foundation for new optical modal transmission devices and novel nanoarrays, with potential implications for theoretical and experimental research in other quantum systems and topological networks.

EO nonlinear function generator.

An electro-optical programmable nonlinear function generator (PNFG) is developed on a multimode waveguide with four parallel thermal electrodes. The current on one electrode is chosen as the input, while the rest serve as function-defining units to modulate the multimode interference. The electro-thermo-optical effects are analyzed step by step and the impact on the eigenmode properties is derived. It shows that the optical output power variation by altered interference, in response to the input current, manifests as a complex ensemble of functions in general. The PNFG aims to find the special setting under which such relation can be simplified into some basic functions. Through an optimization program, a variety of such functions are found, including Sigmoid, SiLU, and Gaussian. Furthermore, the shape of these functions can be adjusted by finetuning the defining units. This device may be integrated in a large-scale photonic computing network that can tackle complex problems with nonlinear function adaptability.

Properties of eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry

We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational (${C}_{3}$) symmetry. Its band structure exhibits two Dirac points (DPs) that are separated by a nearly flat band. We present a procedure that we employed to identify eigenfrequencies and to separate the eigenstates according to their transformation properties under rotation by $\frac{2\ensuremath{\pi}}{3}$ into the three ${C}_{3}$ subspaces. This allows us to verify previous numerical results of Zhang and Dietz [Phys. Rev. B 104, 064310 (2021)], thus confirming that the properties of the eigenmodes coincide with those of artificial graphene around the lower DP, and they are well described by a tight-binding model for a honeycomb-kagome lattice of corresponding shape. Above all, we investigate the properties of the wave-function components in terms of the fluctuation properties of the measured scattering matrix, which are numerically not accessible. They are compared to random-matrix theory predictions for quantum-chaotic scattering systems exhibiting extended or localized states in the interaction region, that is, the DB. Even in regions where the wave functions are localized, the spectral properties coincide with those of typical quantum systems with chaotic classical counterparts.

Quantum dispersion properties of eigenmodes in semiconductor nanotubes with dielectric filling in dc magnetic field

Dispersion properties of electromagnetic eigenmodes in a semiconductor nanotube (with quadratic electron dispersion law) filled by a nonmagnetic dielectric and placed in a coaxial dc magnetic field are studied theoretically. A new quantum electrodynamical phenomenon is predicted. Namely, it is shown that increase in the electron density n02D in the nanotube results in the appearance of new branches in the eigenmodes spectrum. These branches arise in a bifurcation manner at some critical values of n02D, when a new electron energy subzone starts to fill in. The number of branches monotonously increases with growth n02D and oscillates with increase in the number of magnetic flux quanta through the nanotube (i.e., a peculiar Aharonov–Bohm effect takes place). We also found that the dispersion curves have parts with anomalous dispersion. The analytical expression for electron energy loss due to the excitation of eigenmodes under the Cherenkov resonance condition is derived and numerically analyzed.

Vibration Properties of a Concrete Structure with Symmetries Used in Civil Engineering

The paper aims to study a concrete structure, currently used in civil engineering, which has certain symmetries. This type of problem is common in engineering practice, especially in civil engineering. There are many reasons why structures with identical elements or certain symmetries are used in industry, related to economic considerations, shortening the design time, for constructive, simplicity, cost or logistical reasons. There are many reasons why the presence of symmetries has benefits for designers, builders, and beneficiaries. In the end, the result of these benefits materializes through short execution times and reduced costs. The paper studies the eigenvalue and eigenmode properties of vibration for components of the constructions’ structure, often encountered in current practice. The identification of such properties allows the simplification and easing of the effort necessary for the dynamic analysis of such a structure.

Microwave photonic crystals as an experimental realization of a combined honeycomb-kagome lattice

In 2015 experiments were performed with superconducting microwave photonic crystals emulating artificial graphene B. Dietz, T. Klaus, M. Miski-Oglu, and A. Richter, Phys. Rev. B 91, 035411 (2015)]. The associated density of states comprises two Dirac points with adjacent bands including van Hove singularities, thus exhibiting the characteristic features originating from the extraordinary electronic band structure of graphene. They are separated by a narrow region of particularly high resonance density corresponding to a nearly flatband in the band structure, which is reminiscent of that of a honome lattice -- a combination of two sublattices: honeycomb and kagome. We demonstrate that, indeed, the density of states, and also the eigenmode properties and the fluctuations in the resonance-frequency spectra are well reproduced by a tight-binding model based on the honome lattice. A good description was achieved by means of the reverse Monte-Carlo approach, thereby confirming our intepretation of the microwave photonic crystal as an experimental realization of a honome lattice and providing an answer to longstanding problem, namely the understanding of the origin of the flatband bordered by two Dirac points, generally observed in microwave photonic crystals of different shapes.

Dependence of the Volume of Eigenmodes of a One-Dimensional Random Laser on the Inverse Population of the Active Medium

A one-dimensional random laser consisting of a disordered system of layers with different permittivity values, some of which contain an active medium, has been considered. Such a system has been modeled as a chain of Fabry—Perot cavities separated by nonresonant layer subsystems. It has been assumed that light passing through such subsystems is weakened. The properties of partial eigenmodes of such cavities with increasing pump power of the active medium have been studied. It has been shown that the pulling of the mode frequencies that occurs with increasing pump power causes the formation of coupled cavity chains and an increase in the average volume of partial eigenmodes.

Geometry dependence of the fluctuation intensity in gyrokinetic turbulence

The findings of an investigation into the properties of the three dimensional (3D) saturated fluctuation intensity of the electric potential in gyrokinetic turbulence simulations is presented. Scans in flux surface elongation and Shafranov shift are used to isolate the tokamak geometric dependencies. The potential intensity required in order to compute exact fluxes by a quasilinear method is determined using linear eigenmodes computed with the gyrokinetic code. A model of this non-linear intensity is constructed using the linear eigenmode properties and the geometry shape functions obtained from the 3D intensity spectrum. The model computes the poloidal wavenumber spectrum of the electron and ion energy fluxes with unprecedented accuracy. New insights are gained into the way zonal flow mixing saturates ion-scale turbulence by controlling the radial wavenumber width of the turbulence spectrum.

Angle-Resolved Thermal Emission Spectroscopy Characterization of Non-Hermitian Metacrystals

We establish the angle-resolved thermal emission spectroscopy (ARTES) as a new platform to characterize the intrinsic eigenmode properties of non-Hermitian systems. This method can directly map the dispersion of meta-crystals within the light cone with a high angular resolution. To illustrate its usefulness, we demonstrate the existence of bound states in the continuum (BICs) and non-Hermitian Fermi arcs in a planar corrugated meta-crystal by measuring its angle-resolved thermal emission spectra. We show that change in the thickness of the meta-crystal can induce a band inversion between a BIC and a radiative state, and a pair of exceptional points emerge when the band inversion occurs. With this approach, the band mapping of non-Hermitian photonic systems can become a relatively straightforward task.

Mapping acoustical activity in 3D chiral mechanical metamaterials onto micropolar continuum elasticity

We compare the phonon band structures and chiral phonon eigenmodes of a recently experimentally realized three-dimensional (3D) cubic chiral metamaterial architecture to results from linear micropolar elasticity, an established generalization of classical linear Cauchy elasticity. We achieve very good qualitative agreement concerning the anisotropies of the eigenfrequencies, the anisotropies of the eigenmode properties of the acoustic branches, as well as with respect to the observed pronounced sample-size dependence of acoustical activity and of the static push-to-twist conversion effects. The size dependence of certain properties, that is, the loss of scale invariance, is a fingerprint of micropolar elasticity. We also discuss quantitative shortcomings and conceptual limitations of mapping the properties of finite-size 3D chiral mechanical metamaterials onto micropolar continuum elasticity.

Using the Symmetries in the Civil Engineering. An overview

Structural symmetries existing in real engineering systems can be used in a dynamic analysis to the calculus of vibrations of these systems. In this paper will be presented two types of mechanical systems, some with concentrated masses, others continuous. For these types of structure with symmetries, specific properties that could be used to facilitate analysis of such a system will be presented. Properties of eigenvalues and eigenmodes have been demonstrated to facilitate and simplify the design of a real structure. In the field of engineering, both in civil engineering and in other fields such as the machine or machinery industry, automotive industry, aerospace industry there are machines, and machine components with identical, repetitive elements, which have their composition with symmetries of different types.

Multifractality of the entanglement Hamiltonian eigenmodes

We study the fractal properties of single-particle eigen-modes of entanglement Hamiltonian in free fermion models. One of these modes that has the highest entanglement information and thus called maximally entangled mode (MEM) is specially considered. In free Fermion models with Anderson localization, fractality of MEM is obtained numerically and compared with the fractality of Hamiltonian eigen-mode at Fermi level. We show that both eigen-modes have similar fractal properties: both have same single fractal dimension in delocalized phase which equals the dimension of the system, and both show multi-fractality at phase transitio point. Therefore, we conclude that, fractal behavior of MEM -- in addition to the fractal behavior of Hamiltonian eigen-mode -- can be used as a quantum phase transition characterization.

An Efficient Mode-Based Domain Decomposition Hybrid 2-D/Q-2D Finite-Element Time-Domain Method for Power/Ground Plate-Pair Analysis

Generally, with a surface magnetic current excitation, only the $\mathrm {TM}_{\mathrm {zmn}}$ modes are activated between the power/ground plate pair. As a result, the magnetic field only has azimuthal component while the longitude component is zero. To make full use of this quasi-2-D (Q-2D) property, a Q-2D finite-element time-domain (FETD) method combined with the basic 3-D triangular prism mesh elements is firstly proposed to solve the magnetic field wave equation. It is further noted that the higher order modes are confined in the proximity of the antipads (labeled as via domain) due to the exponential attenuation property along the propagating direction. Therefore, in the region sufficiently far from the antipad (marked as plate-pair domain), only the fundamental mode needs to be considered. In this way, a Q-2D FETD analysis is required in the via domain while in the plate-pair domain, only a 2-D FETD solver is needed. As a result, the proposed algorithm is actually a hybrid 2-D and Q-2D FETD method. Besides, to handle arbitrarily shaped antipads, the wave-port excitation is implemented, and the corresponding mode-based S-parameter extraction methodology is developed according to the orthogonal property of different eigenmodes. The efficiency, accuracy, and generality of the proposed approach are verified by several representative examples.

Mode characteristics investigations on a side pumped electro-optic Q-switched Nd:YAG laser

The influence of representative aberration on the performance of a side pumped electro-optic Q-switched Nd:YAG lasers was demonstrated. The spatial and temporal behavior of the laser with intracavity disturbation was modeled using a numerical calculation of the diffraction integral equations and then experimentally characterized. The eigenmode properties, including the coaxial state with thermal effect of the active medium and geometric misalignment of the cavity OC mirror have been analyzed. Zernike polynomials are further adopted to describe beam distortions by combining the model wavefront reconstruction. Experiment illustrates that the lower-order Zernike aberration such as Z3, Z4 Z5 and Z10, etc. caused by the typical phase disturbation will significantly affect the mode characteristics and the uniform symmetry of wavefront. Other related beam properties e.g. PSF can also be acquired by further calculation. In addition, the proposed method has the merit of working stability and high efficiency. Corresponding strategies are suggested to consider active compensation of intracavity aberration in such lasers.

Quantum memory node based on a semiconductor double quantum dot in a laser-controlled optical resonator

The concept of a quantum node consisting of a memory qubit and a frequency convertor is proposed and analysed. The memory qubit is presented by a semiconductor four-level double quantum dot (DQD) placed in an optical microresonator (MR). The DQD contains an electron in the quantised part of the conduction band and the MR can be populated by a certain number of photons. The DQD and MR states are controlled be applying the laser and electrostatic fields. The difference between the telecommunication frequency of the photon (transport qubit) supplied to the system through a waveguide and the frequency of the electronic transition in the DQD is compensated for using an auxiliary element, i.e. a frequency convertor based on a single quantum dot (QD). This design allows the electron – photon state of the hybrid system to be controlled by an appropriate variation of the field parameters and the switching between resonance and nonresonance DQD and MR interaction regimes. As an example, a GaAs DQD placed in a microdisk MR is studied. A numerical technique for modelling an optical spectrum of a microdisk MR with an additional layer (AL) deposited on its surface is developed. Using this technique, the effect of the AL on the MR eigenmode properties is investigated and the possibility of tuning its frequency to the QD electronic transition frequency by depositing an AL on the disk surface is demonstrated.

Intrinsic transverse spin angular momentum of fiber eigenmodes

We study the transverse spin angular momentum of fiber eigenmodes. As an intrinsic property of fiber eigenmodes, it becomes considerable in optical nanofibers and, especially, increases sharply in the evanescent field. We derive analytical expressions of this angular momentum, and present its density distribution inside andoutside nanofibers. Significantly, we find the optimal ratio of the fiber core radius to the wavelength to obtain the maximum surface transverse spin. For instance, the optimal fiber radius is one fourth of the wavelength for the fundamental mode. Furthermore, we investigate the spin flow of each guided mode on the nanofiber surface and the transverse mechanical effects originated from the transverse spin on small particles.

The Origin and Limit of Asymmetric Transmission in Chiral Resonators.

We observe that the asymmetric transmission (AT) through photonic systems with a resonant chiral response is strongly related to the far-field properties of eigenmodes of the system. This understanding can be used to predict the AT for any resonant system from its complex eigenmodes. We find that the resonant chiral phenomenon of AT is related to, and is bounded by, the nonresonant scattering properties of the system. Using the principle of reciprocity, we determine a fundamental limit to the maximum AT possible for a single mode in any chiral resonator. We propose and follow a design route for a highly chiral dielectric photonic crystal structure that reaches this fundamental limit for AT.

Correlation between the properties of eigenfrequencies and eigenmodes in a chain of rigid bodies with torque connections

A chain of N rigid bodies with elastic connections transmitting a torque interaction is considered. Similar individual inertial elements of the chain have one degree of freedom. An exact analytical solution of the problem of oscillation eigenfrequencies and eigenmodes is constructed for an arbitrary value of N. The properties of frequencies and modes of such a chain are compared with those of a canonical Newton chain. It is established that the correlation between eigenfrequencies and the properties of the corresponding eigenmodes fundamentally differs from that for a canonical Newton chain. Lower eigenfrequencies of a chain of rigid bodies with inertialess torque connections correspond to modes with a larger number of nodes, while higher eigenfrequencies correspond to the smoother modes. The nontypical correlation between the oscillation eigenfrequencies and eigenmodes discovered based on the exact analytical solution to the problem of free oscillations of a chain of N rotating rigid bodies contradicts the ideas underlying theoretical studies in the field of solid state physics devoted to simulation of mechanical and thermal dynamic processes in crystalline lattices.

Correlation between properties of eigenfrequencies and eigenmodes in a chain of rigid bodies with inertialess moment connections

Correlation between properties of eigenfrequencies and eigenmodes in a chain of rigid bodies with inertialess moment connections

Eigenmodes of a periodic array of coupled waveguides

General properties of eigenmodes in periodic arrays of coupled waveguides are considered. The Floquet channel model is used to analyze arrays operating in the quasi-periodic mode. Relationships for the orthogonality of different types of eigenmodes are obtained on the basis of the Lorentz lemma and the active power theorem. The problem of excitation of array eigenmodes by given currents is solved. The relation between two representations of the array field, by means of the eigenmode expansion and in the form of the Fourier integral, is shown by the example of an array of coupled slot lines.