Toroidal Waveguide Research Articles

Numerical proposal to solve Maxwell’s equations in a toroidal waveguide

In this contribution, we propose a numerical solution to the Maxwell equations to determine the electromagnetic fields in a toroidal dielectric wave-guide. Analyzing the relationship between the size of the cross-section of the toroid and its bending radius. We considered a sinusoidal time dependence of the electromagnetic field, then we just solve the Helmholtz equation in the waveguide. We propose a numerical way to solve this equation and analyze for to find the power radiation in each synchronous mode. We show a numerical method by calculating the frequencies and the loss factors for any mode in square, triangular, and round waveguides.

Analysis, Design, and Measurement of Directed-Beam Toroidal Waveguide-Based Leaky-Wave Antennas

Leaky-wave antennas (LWAs) have been widely investigated for wireless systems. Most LWAs reported to date are open-path based, i.e., their guided traveling waves follow a non-closed path. A substrate-integrated (SI) toroidal waveguide-based LWA is developed in this article. A coaxial-fed probe structure effectively excites traveling waves that propagate along a closed path in the toroidal waveguide. Inverted L- and planar helical-shaped radiators, whose pickup structures extract power from the waveguide through its top wall, are introduced to radiate, respectively, linearly-polarized (LP) and circularly-polarized (CP) directed beams. The dispersion properties of the closed waveguide’s traveling wave are determined and the associated propagation phase along circular paths with specific radii guides the placement of these radiators to achieve a directive beam at a specified angle. Prototypes of both the LP and CP toroidal LWA (TLWA) systems were fabricated and tested. Good agreement between the simulated and measured results was obtained. The measurements of the compact, low-cost LP and CP prototype systems confirm they radiate beams pointed in their distinctly different, specified directions with realized gains of 13.2 dBi and 13.9 dBic, respectively, at 9.75 GHz.

Effective technique for analyzing rectangular helical and toroidal waveguides with a hollow rectangle bounded by dielectrical material and metal boundary

The main objective of this research is to present an effective technique to solve discontinuous cross section with dielectric material between the hollow rectangle and the metal of rectangular helical and toroidal waveguides. The second objective is to examine the influence of the curved waveguide with the proposed discontinuous cross section on the output field. The proposed technique is based on subtracting a waveguide with dielectric material located at the center of the cross section from a waveguide entirely filled with dielectric material and by using the image method. The method is based on Laplace and Fourier transforms and the inverse Laplace and Fourier transforms. The application can be practical in the laboratory by connecting the rectangular helical and toroidal waveguides to the analyzer spectrum in order to analyze the effect of the proposed curved waveguide with the proposed discontinuous cross section on the behavior of the output field.

Acoustic wave propagation and reciprocity in a toroidal waveguide carrying a mean flow

Acoustic wave propagation and reciprocity in a toroidal waveguide carrying a mean flow

Waveguide platform for quantum anticentrifugal force.

This work is a proposition of an experimental platform to observe quantum fictitious anticentrifugal force. We present an analytical and numerical treatment of a rectangular toroidal dielectric waveguide. Solving the Helmholtz equation, we obtain analytical solutions for transverse spatial modes and estimate their number as a function of system characteristics. On top of that, the analysis of the structure is extended onto a real material platform, a thin-film lithium niobate on insulator rib waveguide. The framework presented here can be applied directly to analyze the phenomenon of quantum anticentrifugal force.

Acoustic wave propagation in a toroidal waveguide carrying a mean flow

This paper describes the analysis of acoustic wave propagation in an attenuating toroidal waveguide carrying a circumferentially directed mean flow. The disposition of the standing pressure waves driven into resonance by time harmonic excitation is of particular interest. The relationship between the mean flow velocity amplitude and location of peak pressure response relative to the source position is evaluated. The conditions required for non-reciprocal scattering behavior is given.

Three wire toroidal magnetic guide based on the vertical leads and ac current modulation

A new scheme to create a closed toroidal magnetic waveguide for deBroglie wave on a single layer atom chip is proposed and there is no zero magnetic field along the guide center. The guide is a two-dimensional magnetic trap for trapping weak-field seeking states of atoms with a magnetic dipole moment. The designed wire structure on the atom chip consists of three concentric and isometric ring wires, and six vertical current leads of the three ring wires. By using the through silicon via technology, the current leads can be made perpendicular to the atom chip surface instead of being generally arranged side by side on the chip surface. Compared with the general wiring way, the vertical lead way has two advantages. One is that each ring wire gap caused by the current leads is substantially smaller than the distance between the ring wires, which permits the generation of a closed toroidal magnetic guide near the atom chip surface when dc currents are supplied to the three ring wires. The other is that the distance between two leads of each ring wire is considerably reduced, resulting in the fact that the magnetic perturbation of the leads to the whole toroidal magnetic guide is negligible. We numerically calculate the magnetic field distribution generated by our wire layout when dc currents are applied, and it is shown that a closed and tight toroidal magnetic guide is formed near the atom chip surface. However, there are zero magnetic fields existing along the center of the toroidal guide, which leads to Majorana spin flips from trapped magnetic substate to an un-trapped magnetic sub-state. According to the time-orbiting-potential principle, we propose an ac current modulation method, which is simple and stable, to reduce the atom losses and suppress the atomic decoherence in the toroidal magnetic guide. We deduce the ac current expressions for the case of three isometric infinite straight wires and apply the ac modulation current expressions directly to our three ring wire structure. The numerical calculation results show that the closed toroidal guide does no longer have zero magnetic fields near the magnetic field minimum, and that the magnetic field fluctuation of the guide is smaller. Based on the vertical leads and ac current modulation, the closed toroidal wave guide with no zero magnetic field along the guide center can be generated near the atom chip surface. This scheme has important scientific significance and engineering value for developing the cold atomic chip gyroscope.

Cutoff frequency of toroidal plasma waveguide

The cutoff frequencies of E and H-modes of empty and plasma filled toroidal waveguides are evaluated. The effects of space curvature and plasma density on cutoff frequencies for both modes are investigated. Using a suitable variable change, a scalar wave equation in the direction of propagation was obtained. The study indicates that the curvature in the direction of wave propagation in toroidal waveguide has an analogous effect as a straight waveguide filled with anisotropic media. The Rayleigh-Schrodinger perturbation method was employed to solve for cutoff frequencies in the first order of approximation. In the limit of small space curvature, the toroidal waveguide cutoff frequencies for both E and H-modes approach those of TM and TE modes of empty cylindrical waveguide with a radius equal to toroidal waveguide minor radius. The analysis shows that the curvature in the direction of propagation in toroidal waveguides leads to the removal of the degeneracy between E and H-modes.

波导随机散射系统的激光发射

A random laser structure is proposed in which we symmetrically embed a toroidal waveguide in the randomly distributed scattering particles.The finite difference time domain(FDTD) method is used to numerically simulate the distribution of the optical filed in the random scattering system embedded with a toroidal waveguide and the corresponding comparative structures,and the modes spectra of each structure are obtained.The results show that there only exists a narrow linewidth lasing emission in the center of system,which verifies that the presence of the toroidal waveguide can influence the lasing emission of the random system,reduce the number of modes,and enhance the lasing intensity to a certain degree.

Demonstration of an inductively coupled ring trap for cold atoms

We report the first demonstration of an inductively coupled magnetic ring trap for cold atoms. A uniform, ac magnetic field is used to induce current in a copper ring, which creates an opposing magnetic field that is time-averaged to produce a smooth cylindrically symmetric ring trap of radius 5 mm. We use a laser-cooled atomic sample to characterize the loading efficiency and adiabaticity of the magnetic potential, achieving a vacuum-limited lifetime in the trap. This technique is suitable for creating scalable toroidal waveguides for applications in matter-wave interferometry, offering long interaction times and large enclosed areas.

Dispersion Characteristics of a Plasma Column in a Toroidal Waveguide

The dispersion characteristics of a toroidal waveguide in the presence of a plasma column are considered. The solution of the wave equation in a toroidal waveguide is presented using an analytical approximation method. In this method, the curvature of the axis of the waveguide is considered as a disturbance parameter to the straight circular cylinder approximation. The perturbed torus field for both the plasma and the vacuum regions is expanded in terms of the eigenfunctions of the unperturbed quantities. The effect of the plasma column in the toroidal waveguide is considered as the second perturbation factor in MHD equations. The perturbed Maxwell's equations along with the perturbed momentum transverse and the continuity equations lead to dispersion relation.

FLEXIBLE HOLLOW WAVEGUIDE WITH TWO BENDINGS FOR SMALL VALUES OF STEP ANGLES, AND APPLICATIONS

This paper presents an improved approach for the propagation of electromagnetic (EM) flelds in the case of the ∞exible hollow waveguide that consists of two bendings in the same direction. In this case, the objective is to develop a mode model for infrared (IR) wave propagation along the ∞exible hollow waveguide, in order to provide a numerical tool for the calculation of the output flelds, output power density and output power transmission. The main steps of the method for the two bendings will introduced in the derivation, in detail, for small values of step angles. The derivation for the flrst section and the second section of the waveguide with the two bendings is based on Maxwell's equations. The separation of variables is obtained by using the orthogonal-relations. The longitudinal components of the flelds are developed into the Fourier-Bessel series. The transverse components of the flelds are expressed as functions of the longitudinal components in the Laplace plane and are obtained by using the inverse Laplace transform by the residue method. This model can be a useful tool in all the cases of the hollow toroidal waveguides, e.g., in medical and industrial regimes.

Matter-wave vortices in cigar-shaped and toroidal waveguides

We study vortical states in a Bose-Einstein condensate (BEC) filling a cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) is derived in this setting, for the models with both repulsive and attractive interatomic interactions. Analytical formulas for the density profiles are obtained from the NPSE in the case of self-repulsion within the Thomas-Fermi approximation, and in the case of the self-attraction as exact solutions (bright solitons). A crucially important ingredient of the analysis is the comparison of these predictions with direct numerical solutions for the vortex states in the underlying 3D Gross-Pitaevskii equation. The comparison demonstrates that the NPSE provides for a very accurate approximation, in all the cases, including the prediction of the stability of the bright solitons and collapse threshold for them. In addition to the straight cigar-shaped trap, we also consider a torus-shaped configuration. In that case, we find a threshold for the transition from the axially uniform state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern, due to the instability in the self-attractive BEC filling the circular trap.

DETECTION OF HIGH-FREQUENCY GRAVITATIONAL WAVES BY SUPERCONDUCTORS

We present a detecting scheme of high-frequency gravitational waves (HFGWs) which is based upon coupling between superconducting open cavity and electromagnetic fields stored in the cavity. Utilizing zero resistance and perfect diamagnetism of the superconductors, one can obtain very large quality factor and high sensitivity for the cavity to detect the HFGWs in GHz band. In addition, we review other possible superconducting systems for detection of the HFGWs, such as superconducting resonant-mass detector, toroidal waveguide, coupled superconducting spherical cavities and superconducting quantum antennas.

Calculation of coherent synchrotron radiation in toroidal waveguides by paraxial wave equation

A new technique for the simulation of coherent synchrotron radiation (CSR) and space-charge fields from a single electron bunch in straight or toroidal rectangular waveguide sections has been developed. It is based on the integration of the paraxial approximation to the wave equations, using the perturbation technique where the bending radius is large compared to the dimension of the waveguide. We have implemented an unconditionally stable integration method in the time domain with transparent boundary conditions that allows the use of a minimally sized computational domain about the bunch. This technique explicitly enforces the causality condition so that no portion of the fields can propagate faster than the speed of light, can be used with arbitrary three-dimensional charge distributions, and contains corrections for finite energy. We have also developed a method for the calculation of the transverse forces within the bunch including space-charge. This method has been developed for incorporation with a particle-in-cell code so that we may self-consistently model CSR and space-charge in combinations of bending sections with a fully dynamic electron bunch in an efficient manner. In this paper we describe the model and methods for calculation of the fields in detail and compare results to theory wherever possible.

The design and optimization of a new microwave plasma source by numerical simulation

The aim of the work is to design a new compact microwave plasma source with a homogeneous circumferential distribution of the electric field intensity. The software for electromagnetic field simulation combined with design-of-experiments techniques was used to design and optimize the source geometry in terms of energy efficiency and field homogeneity. The basic assumption is that plasma can be described by an equivalent dielectric load. Two relatively simple microwave waveguide plasma sources have been simulated to study the effect of impedance-matching devices on the energy efficiency of the whole system. A microwave waveguide plasma source based on the WR340 waveguide geometry has been assembled to validate the model experimentally. A completely new compact plasma source, which is a toroidal waveguide and an innovative ‘self-adapting’ coupling slot, has been numerically simulated, designed and built. Preliminary tests confirmed the existence of a sufficiently homogeneous five-lobe distribution of the electric field.

Controllable Persistent Atom Current of Bose–Einstein Condensatesin an Optical Lattice Ring

In this paper the macroscopic quantum state ofBose–Einstein condensates in optical lattices is studied by solving theperiodic Gross–Pitaevskii equation in one-dimensional geometry. It is shownthat an exact solution seen to be a travelling wave of excited macroscopicquantum states resultes in a persistent atom current, which can be controlledby adjusting of the barrier height of the optical periodic potential. Acritical condition to generate the travelling wave is demonstrated and wemoreover propose a practical experiment to realize the persistent atomcurrent in a toroidal atom waveguide.

Transient unidirectional acoustic streaming in annular resonators

Theoretical description of the transient process of the acoustic streaming excitation in a toroidal waveguide with driven walls is developed. Particular attention is paid to the analysis of the closed-loop (unidirectional) streaming excitation by purely propagating acoustic mode. This mode might be excited by proper phasing of the two localized acoustic sources. It is demonstrated that the evolution of the local streaming velocity can be non-monotonous in some points of the resonator cross-section. A numerical evaluation of the analytical solutions highlights the influence of the ratio of the acoustic boundary layer thickness to the waveguide width on the acoustic-streaming stabilization time. The results obtained for the acoustic streaming in the annular resonator can be useful for the analysis of the annular thermoacoustic engines and refrigerators. They might be also applied in microfluidics where there is a growing interest to different possible physical mechanisms of fluid pumping in microscale channels.

Shielding and synchrotron radiation in toroidal waveguide

We develop a new approach to the calculation of the synchrotron radiation in a toroidal vacuum chamber. Using a small parameter $ϵ=\sqrt{a/R}$, where $a$ is the characteristic size of the cross section of the toroid and $R$ is the bending radius, we simplify Maxwell's equations assuming that the characteristic frequency of the modes $\ensuremath{\omega}\ensuremath{\sim}c/aϵ$ and neglect terms of higher order in $ϵ$. For a rectangular cross section of the waveguide, we find an analytical solution of the equations and analyze their asymptotics at very high frequency. We then obtain an equation which gives radiation into each synchronous mode. We demonstrate the flexibility of the new method by calculating the frequencies and the loss factors for the lowest modes in square and round waveguides.

Improved mode model for infrared wave propagation in a toroidal dielectric waveguide and applications

An improved approach is derived for the propagation of electromagnetic (EM) fields along a curved dielectric waveguide. The objective is to develop a mode model to provide a numerical tool for the calculation of the output fields also for intermediate radius of curvature (R~ 0.5 m). Therefore we take into account all the terms in the calculations, without neglecting the terms of the bending. The longitudinal components of the fields are developed into Fourier-Bessel series. The transverse components of the fields are expressed as functions of the longitudinal components in the Laplace plane and are obtained using the inverse Laplace transform. The separation of variables is obtained using the orthogonal relations. The metal boundaries of the waveguides are modeled as a lossy dielectric media. This model is applicable for hollow waveguide tubes where the wall of the bore is covered with a metal layer and dielectric overlayer.