Nonuniform Waveguide Research Articles

Resonant excitation of radial modes in a nonuniform cylindrical plasma waveguide

Resonant excitation of radial modes in a nonuniform cylindrical plasma waveguide

A New Method for the Analysis of Perturbed-Wall Waveguide Mode Converters

An improved method for the analysis of the fields within a section of nonuniform cylindrical waveguide is presented. The technique uses the method of successive approximations to obtain consistent solutions to the Stratton-Chu equations and the cylindrical harmonic representations of the fields that satisfy the Maxwell equations and the boundary conditions of the nonuniform waveguide. As opposed to some recently reported methods, this new method is not restricted to oversized waveguide structures and can directly evaluate the fields within a tapered section of waveguide. The method is validated by evaluating the fields within two different mode converters for gyrotron launchers. The accuracy is seen to be competitive with the commercial method of moments code, Surf3d, and requires a fraction of the computational resources.

Synthesis of Microwave Filters by Inverse Scattering Using a Closed-Form Expression Valid for Rational Frequency Responses

In this paper, a novel technique to synthesize microwave filters by inverse scattering is proposed. It provides an exact solution for the synthesis problem, by means of a closed-form expression, with very low computational cost. The technique is valid when the target frequency response can be expressed as a rational function. The coupled-mode theory is used to model microwave propagation along the filter, and therefore, the synthesis technique is applicable to filters implemented in a wide range of technologies, such as planar and nonplanar transmission lines, and many waveguides. The synthesis method is exact for all the frequency range of interest, preventing the degradation of the frequency response that can be troublesome for wideband applications or to satisfy the out-of-band requirements of the filter. The resulting synthesized filter is, in general, a nonuniform transmission line or waveguide that features a continuously varying smooth profile, avoiding the presence of sharp discontinuities and their detrimental effects. To demonstrate the potential of the proposed synthesis technique, a multiband microwave filter, fulfilling stringent specifications, will be designed in rectangular waveguide technology. The prototype will be fabricated by electroforming and carefully measured with a vector network analyzer, confirming the accuracy of the novel synthesis method reported.

Analytic solutions for spectral properties of superstructure, Gaussian-apodized and phase shift gratings with short- or long-period

The analytic solutions (AS) for the spectral properties of short- and long-period waveguide gratings with the effects of discrete phase shift (PS), Gaussian-apodization (GA) and superstructure are presented in this paper, which are derived from the Fourier mode coupling (FMC) theory proposed recently. The spectral properties include the reflectivity of short-period gratings, and the transmission of long-period gratings. The calculated spectra based on the analytic solutions are achieved and compared with measured cases and that on the transfer matrix (TM) method, in the case of changing grating parameters. The AS-based calculation requires the average time of several milliseconds at common PC, and the AS-based efficiency is improved up to ~6700 times the TM-based one. The comparisons have confirmed that the FMC-based analytic solutions are suitable for the real-time and accurate analyses of some non-uniform waveguide gratings.

Optimization of Non-Uniform Optical Waveguide in MOEMS Accelerometer

Miniaturization is the rule of the day. This has even extended to optical domain where entire sensor arrays complete with laser or led source and pin photodiode are fabricated within a single chip. The device discussed and analyzed in this paper is a MOEMS accelerometer which consists of uniform micro cantilever on one arm of MZI structure. The refractive index is assumed to vary even along the direction of pulse propagation along with the frequently analyzed refractive index profile perpendicular to the light pulse path. The efficiency of device is increased by numerous optimization measures. A dual approach of optimal curved waveguide with increased difference is found to maximize power in waveguide core with minimal leakage to the cladding. This effectively translates to increased sensitivity as greater power is available for accurate detection process. The analysis is supported by appropriate simulations.

A modified wave approach for calculation of natural frequencies and mode shapes in arbitrary non-uniform one-dimensional waveguides

In this article, using the wave propagation method, the natural frequencies and mode shapes of an arbitrary non-uniform one-dimensional waveguide are calculated. The non-uniform rods and beams are partitioned into several continuous segments with constant cross-sections, for which there exists an exact analytical solution. At the end of each segment, waves in positive and negative directions are obtained in terms of waves at initial segment and subsequently, the calculations of the mode shapes become simple. By satisfying the boundary conditions, the characteristic equation is obtained and natural frequencies are calculated for both the arbitrary non-uniform rod and beam. Also, by adding waves in positive and negative directions at the end point of each segment, the mode shapes are obtained. To verify the modified wave method presented here, the frequencies and mode shapes of the rod and the beam with a polynomial cross-section having an exact analytical solution are compared and have been proven to be of high accuracy. Besides, comparisons of finite element method are also included. Therefore, this method can also be used to calculate the natural frequencies and mode shapes of rods and beams with any arbitrary variable cross-section for which no analytical solution is available. For the ‘Modified Wave Approach’ developed here, dimensions of transmission matrix remain constant if the number of segments is increased, while in general wave propagation method, dimensions of transmission matrix increase upon increasing the number of segments. Besides this novelty, this method has the advantage that it gives all the natural frequencies and mode shapes, unlike other approximate methods such as weighted residual, Rayleigh–Ritz, and finite difference methods which have their own shortcomings such as limited number of natural frequencies. Also, since each segment has an exact analytical solution, in contrast to other approximate methods, much higher accuracy is obtained even with only a few number of partitions.

Wave motions in non-uniform one-dimensional waveguides

Wave approach is used in the analysis of wave motions in one-dimensional non-uniform waveguides. Under assumptions of constant wave velocity and no wave conversion, one class of non-uniform rods including four different profiles results. The obtained results indicate kinetic energy is preserved as constant and wave amplitude is inversely proportional to square root of the cross-section area of the rod. The obtained spectrograms and dispersion relations indicate that under certain conditions there exists a cut-off frequency, below which waves do not propagate along the non-uniform waveguides. The conclusions are similar for high frequency longitudinal wave motions of arbitrary non-uniform rods. For a Euler-Bernoulli beam with exponent variation in geometry and material variation, the bending wave motion is also analyzed including its cut-off frequencies.

Studying spectral structures in the background ultralow-frequency noise at different latitudes

We numerically calculate the horizontal components of the magnetic field in the frequency range 0.1–15 Hz for reception points located at different geographical latitudes. For calculations, we used the solution of the problem on excitation of the Earth—vertically nonuniform anisotropic ionosphere waveguide by a source like a vertical electrical dipole [1]. Calculations were carried out for different numerical and analytical models of the ionospheric parameter profiles [2]. The results of modeling and experimental studies of the spectral resonant structure at the stations on Crete (35.15 N, 25.20 E), New Life (Nizhny Novgorod region, 55.97 N, 45.74 E), Lovozero (68 N, 35 E), and Barentsburg (78.09 N, 14.12 E) were compared. The degree of conformity of the different model profiles to the actual ones was revealed from a comparison of theoretical and experimental spectra. The studies were complemented by an analysis of calculated and experimental spectra of the magnetic noise polarization parameter.

Guiding Terahertz Waves by a Single Row of Periodic Holes on a Planar Metal Surface

In this paper, we show that surface plasmon polaritons (SPPs) can be sustained by a single row of holes periodically drilled on a perfect electric conductor surface. These SPPs can be strongly confined in the transverse plane and they possess an excellent modal shape. In the terahertz regime, large propagation length is available for highly confined SPPs on a real-metal surface waveguide. As the dispersion characteristics of such SPPs can be controlled by the surface geometry, unusual total reflection phenomenon occurs when waves travel along a nonuniform surface waveguide with gradually increasing hole depths.

Longitudinal waves in one dimensional non-uniform waveguides

Wave approach is used to analyze the longitudinal wave motion in one dimensional non-uniform waveguides. With assumptions of constant wave velocity and no wave conversion, there exist four types of non-uniform rods and corresponding traveling wave solutions are investigated. The obtained results indicate that the kinetic energy is preserved as a constant and the wave amplitude is inversely proportional to square root of the cross-sectional area of the rod. Under certain condition, there exists a cut-off frequency for the rod with variation in geometric or material properties, below which waves do not propagate along the non-uniform rod. For the rod with arbitrary variable cross-section, the conclusions are similar if the wave frequency is high enough. And a series solution of the wave motion is presented.

Programming of inhomogeneous resonant guided wave networks

Photonic functions are programmed by designing the interference of local waves in inhomogeneous resonant guided wave networks composed of power-splitting elements arranged at the nodes of a nonuniform waveguide network. Using a compact, yet comprehensive, scattering matrix representation of the network, the desired photonic function is designed by fitting structural parameters according to an optimization procedure. This design scheme is demonstrated for plasmonic dichroic and trichroic routers in the infrared frequency range.

Theory of azimuthal surface waves propagating in non-uniform waveguides

AbstractThis paper is devoted to the theory of surface waves propagating across axis of symmetry in non-uniform cylindrical metal waveguides with plasma filling. The presented results are devoted to: first, studying an influence of plasma density non-uniformity on the features of these waves; second, studying an influence of an external magnetic fields' non-uniformity on their dispersion properties; third, studying possibility to sustain gas discharge by propagation of these waves under different operating regimes. The problems have been solved both analytically and numerically. Plasma particles are described in the framework of hydrodynamics; fields of the studied waves are determined by a set of Maxwell equations. Analytical research of the obtained equations is carried out by the method of successive approximation; adequacy of such approach is proved here as well. Numerical evaluations of the possibilities to observe experimentally the phenomena, which accompany propagation of these waves, are carried out.

A multimodal method for non-uniform open waveguides

We present an original method for the simulation of ultrasonic waves in a varying cross section elastic waveguide embedded in a homogeneous matrix. The so-called multimodal methods consist in expanding the acoustic field in each transverse section as a series which involves the modes of a perfectly cylindrical waveguide with this particular section. For such a cylindrical waveguide, the modal components of the acoustic field are uncoupled. But a varying cross section yields a coupling of these components. A multimodal approach consists in solving the system of differential equations which couples these components instead of the propagation equations.Such methods have been extensively studied for closed waveguides, that is, when no wave can radiate in the transverse direction. In our case, radiation waves occur, because of the presence of the matrix. Actually, such an open waveguide is characterized by a continuum of radiation modes together with a possible finite set of guided modes. The multimodal method proposed here does not take into account this continuum, but uses instead the concept of leaky modes. These modes appear naturally when the computational domain is artificially limited by Perfectly Matched Layers (PMLs). The main advantage of using leaky modes instead of radiation modes is that the formers compose a discrete set, which simplifies considerably the implementation of a multimodal method. In the case of a simple two-dimensional scalar model, the basic ideas of such a method are presented and illustrated by numerical results.

Light propagation in nonuniform plasmonic subwavelength waveguide arrays

We study light propagation in nanoscale periodic structures composed of dielectric and metal in the visible range. We demonstrate that diffraction curves of nonuniform waveguide arrays can be tailored by varying the geometric and dielectric features of the waveguides. The results obtained from a proper formulation of coupled mode theory for nonuniform arrays are validated through numerical solution of Maxwell equations in frequency domain.

An Analytical Design and Analysis Method for a High-Power Circular to Rectangular Waveguide Mode Converter and Its Applications

An analytical method to estimate the scattering of RF power into multiple modes inside a nonuniform waveguide using perturbation techniques is presented. This method is quite general, much faster than numerical methods, and may be applied to a wide variety of nonuniform waveguides. We have used this method to design and analyze a three-section mode transformer that converts a TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</sub> circular waveguide mode to a TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">20</sub> rectangular waveguide mode. This mode converter is specially suitable for use in ultra-high-power applications. Due to the complexity of the problem, we have used the symbolic solver Mathematica to produce most of our analytical results. The results match within reasonable accuracy with High Frequency Structure Simulator field solver simulations. We also present the application of this mode converter to variety of ultra-high-power microwave components and experimentally show the performance of these devices.

Effect of High-Frequency Electric Field on Propagation of Electrostatic Wave in a Non-Uniform Relativistic Plasma Waveguide

The effect of a high frequency (HF) electric field on the propagation of electrostatic wave in a 2D non-uniform relativistic plasma waveguide is investigated. A variable separation method is applied to the two-fluid plasma model. An analytical study of the reflection of electrostatic wave propagation along a magnetized non-uniform relativistic plasma slab subjected to an intense HF electric field is presented and compared with the case of a non relativistic plasma. It is found that, when the frequency of the incident wave is close to the relativistic electron plasma frequency, the plasma is less reflective due to the presence of both an HF field and the effect of relativistic electrons. On the other hand, for a low-frequency incident wave the reflection coefficient is directly proportional to the amplitude of the HF field. Also, it is shown that the relativistic electron plasma leads to a decrease in the value of reflection coefficient in comparison with the case of the non relativistic plasma.

Features of the dispersion characteristics of nonuniform plasma waveguides in a longitudinal magnetic field

We study the features of the dispersion curves and field structures of the fundamental axisymmetric mode of nonuniform layered plasma waveguides in a longitudinal magnetic field. It is shown that the presence of sharp boundaries between layers leads to the appearance of additional branches of the dispersion curves in the frequency range ω Be < ω < ωUH(0), where ωBe is the electron gyrofrequency and ωUH(0) is the upper-hybrid resonance frequency for the near-axis region of a nonuniform waveguide. The fields of eigenmodes corresponding to these branches comprise resonance structures near the sharp plasma-density variation at which the upper-hybrid resonance conditions are satisfied and plasma waves are excited. The frequency interval of such a branch is limited by the resonant frequencies of the neighboring uniform layers. It turns out that in the case of a strong magnetic field ({ie392-01}, where ωp is the plasma frequency having the value {ie392-02} in the near-axis region of a nonuniform waveguide), the fundamental-mode field is localized in the near-axis region of a nonuniform waveguide, whereas in the opposite case {ie392-03}, the maximum wave fields are localized in either the upper-hybrid resonance region or the outer (near-boundary) layer of the waveguide if there is no resonance region. It is found that the whistler (helicon) contribution to the field structure of the fundamental axisymmetric mode is very small for narrow nonuniform waveguides (b < λ0, where b is the waveguide radius and λ0 is the wavelength in free space) if the plasma density on the axis is high compared with the cutoff density {ie392-04}. We present one of the possible explanations for the effect of narrowing of the plasma channel of a high-frequency whistler-range discharge with distance from a source in the increasing magnetic field.

Modeling of sound propagation in nonuniform waveguides

Sound propagation in waveguides is modeled by a Multimodal Method. The waveguides geometries may involve bends, variable cross-sections, or their combinations. The waveguide boundaries may involve axially or circumferentially nonuniform impedance conditions or acoustically rigid conditions. Uniform flow may also be included for a simple uniform geometry. The pressure (displacement potential for uniform flow) is expanded in terms of the modes of acoustically rigid waveguides and an additional function that carries the information about the impedance boundary. The rigid waveguide modes and the additional function are known a priori so that calculations of the true modes of waveguides with impedance boundary, which are difficult, are avoided. By matching the pressure and axial velocity (displacement potential and axial derivative for uniform flow) at the interface between different axially uniform segments, scattering matrices are obtained for each individual segment; these are then combined to construct a global scattering matrix for multiple segments. After calculating the scattering matrix, the transmitted and reflected sound fields or intensities may be obtained for any kind of modal sources. The method allows modeling sound propagation in waveguides with axially and circumferentially nonuniform impedance boundaries up to dimensionless frequency K=70 in just hours on a personal computer, which advantageously compares with other techniques.

Investigation of ultrasonic pulse propagation in a nonuniform jet waveguide

An acoustic channel corresponding to the through transmission method with an acoustic contact ensured using liquid jets is considered. An equation for the acoustic channel is obtained for the case of long pulses. In the case of short pulses, a technique for selecting the optimal parameters of the acoustic channel is described.

A Series Solution for the Single-Mode Synthesis Problem Based on the Coupled-Mode Theory

In this paper, we present an exact analytical solution for the inverse scattering problem formulated by using the coupled-mode theory in the microwave range, assuming single-mode operation. The solution is a series that gives the required coupling coefficient for the microwave device as a function of the target frequency response. A clear physical meaning for the terms of the series is discussed, and several useful properties for the synthesis are given, thus providing a deep understanding of the synthesis mechanics. The method allows for the design of microwave devices with arbitrary frequency response only constrained by principles of causality, passivity, and stability. The resulting device is, in general, a nonuniform waveguide that features a continuously varying profile, e.g., a nonuniform microstrip line with continuously varying strip width. As an example of the potential of the synthesis method, a matched filter for ultra-wideband applications is finally designed in microstrip technology and successfully tested.