Scattering of the TE/sub 01/ and TM/sub 01/ Modes on Transverse Discontinuities in a Rod Dielectric Waveguide-Application to the Dielectric Resonators

Our purpose is to determine the resonance frequency together with the radiation quality factor of dielectric resonators. To do that, the reflection and the scattering properties of the TE/sub 01/ and TM/sub 01/ modes, incident on an abruptly ended dielectric rod, are analyzed. After the building of the complete mode spectrum on each side of the discontinuity, the continuity relations in the discontinuity plane associated with the orthogonality properties lead to a coupled integral equation system. That one is solved by means of an iterative procedure, providing all the characteristics of the discontinuity (reflection or coupling coefficients, radiation losses). Then, these solutions are used to determine the resonant frequency and the radiation quality factor of cylindrical resonators which are considered as waveguide lengths between two interacting discontinuities.     

对称单负材料平面波导的波导模

基于经典电磁理论建立了芯层为单负材料的对称三层平板波导的导波方程,采用图解法研究了该波导中的TE和TM波导模,分析了TE波导模和TM波导模会受波导参数μ1/μ2和R的影响,给出TE模和TM模解的横向场分布图.结果显示,在单负材料的对称三层平板波导中只存在慢波导模,TE慢波模只能在磁负材料中传播,TM慢波模只能在电负材料...     

Finite-element analysis of the discontinuities in a dielectric slab waveguide bounded by parallel plates

A method for the solution of the discontinuity problem of TE modes and TM modes in a dielectric slab waveguide bounded by parallel plates is described. The approach is a combination of the finite-element and the analytical method. Results are compared with those given by previous authors.     

Phase matching in magneto-optic YIG films by waveguide temperature control

Demonstrates the tuning of linear birefringence in magneto-optic planar thin-film waveguides by temperature adjustment. Using this method, phase matching between coupled TE/sub 0/ and TM/sub 0/ modes, a necessary condition for the integrated optical isolator based on mode conversion, has been obtained at lambda =1.52 mu m in bilayer gadolinium gallium-substituted YIG films. The waveguide temperature was 85 degrees C. Moreover, the phase-matching temperature can be modified by a slight variation of gadolinium and gallium substitutions as shown by a phase matching observed in a waveguide at room temperature.<>     

含单负材料对称三层平板波导的模式特性

由电磁场的波动方程和边界条件建立了单负材料作为芯层的对称三层平板波导的模式本征方程,用图解法研究其色散特性。研究发现,单负介质波导不支持快波的传播,只支持表面波的传播。在负磁材料平板波导中只存在TE表面模,不存在TM表面模。分析了在负磁材料平板波导中TE模受磁导率的比值-μ2／μ1和波导参数的影响,给出了横向场分布图。在-μ2/μ1〈1时,偶对称只有TE0表面模存在,奇对称只有TE1表面模存在,高阶模式并不存在,且两种模式都没有低频截止;-μ2/μ1〉1时,TE1表面模始终不出现;TE0模的存在与否和波导参数有关,在一定条件下TE0模可出现双模并存。给出的结果可望对表面波器件的设计提供理论基础。     

Transmission Characteristics of Spherical TE and TM Modes in Conical Waveguides (Short Papers)

The transmission properties of spherical TE and TM modes in a perfectly conducting conical waveguide are treated in detail. To start with, an analytically simple and highly accurate digital-computer based iterative algorithm has been employed to evaluate the eigenvalues associated with the spherical TE and TM modes within the guide irrespective of the flare angle (2alpha/sub 0/) of the conical waveguide (theta < 2alpha/sub 0/ < 360/spl deg/). Subsequently, explicit expressions for the attenuation constant, phase constant, phase velocity, and wave impedance are obtained for the spherical modes transmitted within the guide. Accurate eigenvalues obtained numerically are used to study the variation of attenuation constant, phase constant, phase velocity, and wave impedance as a function of the radial distance from the apex with alpha/sub 0/ as a parameter. Measured data on the phase constant of a conical waveguide for the TE/sub 11/ mode have been compared with the analytical results obtained by calculation and an excellent agreement between the two justifies the validity of the analysis presented. Finally, a study of the phase coherence between the dominant spherical TE and TM modes within the guide is presented which may be fruitfully employed in the design of dual-mode conical waveguides.     

Solution of the Finite Length Septum Problem with Application to Periodic Mode Suppressors

A square waveguide with periodic septums is considered with a view towards determining the parameters of a structure which suppresses three of four possible propagating modes. The analysis is presented in two parts, the first of which is concerned with the isolated septum. Using available techniques, semi-infinite scattering matrices are determined for the semi-infinite septum for arbitrary TE/sub N0/, TE/sub N1/, and TM/sub N1/ incident modes. These are used to derive Fredholm matrix equations which yield the field everywhere near the finite length septum. The leading terms of the inverted equations are the far-field transmission and reflection coefficients. The solutions are evaluated for several frequencies, and fifth degree polynomials are fitted for the computation of S/sub 11/ and S/sub 12/. The analysis for the TE/sub 10/ mode is applicable to an arbitrary height waveguide and may be used without modification for the "finite length" septum in conventional waveguide. The second part is concerned with the periodic waveguide and assumes that the septums are far apart. A contour chart is introduced to visualize the performance of the periodic structure. The chart is especially useful when more than one propagating mode is involved and simplifies the design problem so that the parameters of practical structures may be obtained with little effort.     

Propagation in Rectangular Waveguide Containing Inhomogeneous, Anisotropic Dielectric

The Wentzel, Kramers and Brillouin (WKB) approximation is used to solve the wave equations for propagation of guided waves in rectangular waveguide containing an inhomogeneous dielectric. The simplest form of anisotropy is used to characterize the relative dielectric constant, i.e., it is assumed that the relative permittivity tensor is diagonalized with respect to the waveguide coordinants. Each of the elements of the relative permittivity tensor is allowed to vary continuously across the broad dimension of the waveguide. The TE/sub nm/ and TM/sub nm/ cases are analyzed for the instance of completely filled guide, while the TE/sub no/ modes are considered for slab-loaded guide.     

Generalized Coupled Dielectric Waveguide and its Variants for Millimeter-Wave Applications

The characteristic equations of hybrid TM and TE modes for a generalized coupled dielectric waveguide are derived using the mode-matching technique. From the characteristic equations of the generalized coupled dieketric waveguide, the phase constant, wave impedance, and field distribution can be evaluated. A variety of single and coupled dielectric waveguides can be obtained by assigning proper parameter values to the generalized coupled dielectric waveguide.     

Optimized overmoded TE01-to-TM11 mode converters for high-power millimeter wave applications at 70 and 140 GHz

Mode coupling in bent, oversized, smooth-wall circular waveguides was studied by means of numerical integration of coupled-mode differential equations in order to optimize high-power TE01-to-TM11 mode transducers at 70 GHz and 140 GHz. Such mode transformers are used in the mode conversion sequence TEOn to TE01 to TM11 to HE11 for generating the almost perfectly linearly polarized Gaussian-like HE11 mode from circular electric TEOn gyrotron modes. This quasi-optical HE11 hybrid mode is in many respects ideal for electron cyclotron resonance heating (ECRH) of magnetically confined plasmas in thermonuclear fusion research and for other technical applications. Curvature and ellipticity coupling as well as ohmic attenuation of 6 coupled modes (TE01, TM11, TE11, TE12, TE21, TM21) are included in the coupling matrices. Integral expressions were used for deriving the coupling coefficients for arbitrary modes in bent, smooth-wall waveguide. Lowest level of unwanted spurious modes together with highest transmission efficiency (shortest arc length) is achieved with sinusoidal curvature distribution instaed of constant curvature. The calculated conversion efficiencies of 98.0% at 70 GHz and 95.2% at 140 GHz (interior waveguide diameter D=27.8 mm for 200 kW transmission lines) are in excellent agreement with the measured values of (97.6±0.4)% and (95±1)%, respectively.     

Diffraction of a general surface wave mode by a surface reactance discontinuity

The scattering of a general hybrid surface wave mode at a reactance discontinuity, on a cylindrical surface waveguide, is considered both theoretically and experimentally. The theory leads to coupled Wiener-Hopf equations, which are solved approximately by assuming the hybrid modes to be mainly TE or TM. The theoretical expressions obtained are evaluated numerically for the symmetrical and dipole modes and compared with experimental results with which substantial agreement is obtained.     

A Complete Solution of the Inductive Iris with TE/sub k0/ Incidence in Rectangular Waveguide

A TE/sub k0/ wave incident on an inductive metal iris in a rectangular waveguide excites a reflected and a transmitted wave in the TE/sub k0/ mode. The reflection and transmission coefficients describing these waves are computed. In addition to the incident mode, a number of other modes are excited by the discontinuity. The amount of coupIing to these other modes, given by coupling coefficients, is determined using the variational technique. The method developed makes it possible to find the coupling to any desired mode without first finding the coupling to any other mode or group of modes. The analysis shows under what conditions certain modes can be suppressed or eliminated. The method should be applicable to other problems of interest where modes other than the incident one are excited. Since the reflection, transmission, and coupling coefficients are known, the total field at any point in the waveguide can be computed. As an example, the total field at the discontinuity when the TE/sub 10/ mode is incident is calculated. The result closely resembles the expected result (of zero electric field over the metal iris).     

Suppression of Higher Order Modes in Waveguide-Junction Circulators Using Coupled Open Dielectric Resonators (Letters)

It is well known that some waveguide circulators exhihit an unwanted spurious mode within their passband, which limits their insertion loss and bandwidth. This mode is identified as the TE/sub 0,1,delta/ one in the case of the waveguide junction which relies on the TM/sub 1,1delta,/ mode for its operation. The influence of the saturation magnetization on the separation between the two modes is studied in detail. A mode suppressor is also described which decouples the coupled TE/sub 0,1,delta/ mode without altering the frequency of the circulation ones. This suppressor consists of a thin metal ring placed on the open face of one of the ferrite disks.     

Parametric Equations for Surface Waves In Dielectric Slab (Short Paper)

For the dielectric slab it is shown that 1) the dispersion curve for the nth surface wave can be found using parametric equations in which the normalized inside wavenumber K/sub xl/ and the mode number are the parameters, 2) the dispersion curve for the nth surface wave mode can also be found by using parametric equations in which the mode number and a modified wavenumber x' with common domain [0, pi/2] are the parameters, and 3) an TE or all TM dispersion curves for surface waves are related to each other by a simple algebraic equation using the mode numbers and the normalized propagation constants K/sub 0/ and Beta as the variables.     

Propagation of TE Modes in Dielectric Loaded Waveguides

The propagation of TE/sub no/ modes in rectangular wave-guides that contain two dielectric slabs parallel to the narrow wall and extending over the full height of the guide is investigated. Waveguide and dielectric are assumed to be lossless and infinitely long. Apart from these restrictions, the dielectric slabs may have arbitrary thickness, position, and dielectric constant. The analysis is restricted to TE/sub no/ modes with the E-field parallel to the narrow guidewall. The guide containing only one dielectric slab is covered by this analysis. The even modes n = 2, 4, 6, . . . of the guide with two slabs correspond to the odd modes n' = n/2 = 1, 2, 3, . . . of the guide with one slab half the width of the guide with two slabs. For six relative dielectric constants (/spl epsilon/= 2.25, 4.00, 9.00, 12.25, 16.00, 25.00) the cutoff frequencies for TE 10, 20, 30, 40, 60 modes and the normalized propagation constants for TE 10 and TE 20 modes between their respective cutoff frequencies and a frequency slightly above the second- and fourth-order mode cutoff frequency for the empty guide, respectively, have been computed for a large range of slab thicknesses and slab positions. Selected results are presented graphically. These results are discussed. The parametric dependence of field distributions, of normalized characteristic impedances, of the ratio of cutoff frequencies (fractional bandwidth), and of the ratio of magnetic field components (ellipticity) are illustrated.     

Surface Waves on Symmetrical Three-Layer Sandwiches (Correspondence)

The theory of surface waves on plane dielectric slabs has been presented by Plummer and Hansen. Additional numerical results are shown in Figs. 1 and 2 for the lowest order TM and TE modes that can exist on a grounded dielectric slab. The slab has thickness d, and a relative dielectric constant of 4. It is separated by an air gap of thickness a from the ground plane. c/v represents the ratio of the velocity of light in free space and the phase velocity of the surface wave. By image theory, these modes (TM/sub 0/ and TE/sub 1/) can also exist on a symmetrical, three-layer, air-core sandwich to which the given numerical data also apply.     

Scattering at Circular-to-Rectangular Waveguide Junctions

A formally exact solution is given for the problem of scattering at a circular-to-rectangular waveguide junction and at a thick diaphragm, with a centered circular aperture, in a rectangular waveguide. The method uses normal TE and TM mode expansions of the waveguide fields and traditional mode matching of the transverse electric and magnetic fields at the junction boundary. Exact closed-form expressions are obtained for the electric field mode-matching coefficients which couple the TE(TM) modes in the rectangular guide to the TE(TM) and TM(TE) modes in the circular guide. Numerical results are presented for the case of TE/sub 10/ mode propagation in the larger rectangular guide with all other modes cutoff. Convergent numerical results for the equivalent shunt susceptances of such junctions are obtained when about 12 modes (eight TE and four TM) are retained in the circular waveguide or in the circular aperture of the diaphragm. The results are graphically compared with formulas and curves due to the quasi-static theory of Bethe and the variational theory given in the Waveguide Handbook [2].     

Theory and Applications of Coupled Optical Waveguides Involving Anisotropic or Gyrotropic Materials

Coupled optical waveguides consisting of two isotropic dielectric slab waveguides coupled through anisotropic or gyrotropic materials inserted between them, are treated theoretically in detail. The properties of reciprocal and nonreciprocal TE-TM mode conversion and a nonreciprocal phase shift for TM modes are shown. As an example of application of this type of coupled waveguide, a nonreciprocal optical integrated circuit (IC) mode converter is proposed. It is shown that a circulator and an isolator which require neither mode separators nor mode filters can be constructed by utilizing the proposed nonreciprocal mode converter. The numerical design examples are also given.     

Mode Conversion in Tapered Waveguides At and Near Cutoff

The coupling coefficient between the TE/sub 11/ mode and the TM/sub 11/ mode in tapered circular waveguides is derived, and at cutoff frequency it tends to approach an infinity of the order of 0/sup -1/4/. It is surprising to discover that the corresponding coupling coefficient between the TE/sub 10/ mode and the TM/sub 12/ mode in tapered rectangular waveguides approaches instead a zero of the order of 0/sup 1/4/ at cutoff frequency. Accordingly, for the modes concerned, the choice of using circular or square waveguides as tapers for transition at and near cutoff frequency is significant in reducing mode conversion level. At and near cutoff frequency a "synthesized" square taper is better in that it is shorter than a "synthesized" circular taper for the same mode conversion levels. On the other hand, for frequencies far away from cutoff the choice is insignificant. Design procedures for "synthesized" waveguide tapers at and near cutoff are presented, and the results of measurements are in agreement with the theoretical calculations.     

Artificially integrated synthetic rectangular waveguide

A synthetic rectangular waveguide (SRW), which consists of two electrical sidewalls and two parallel periodical structures placed at the top and bottom surfaces of the waveguide, is presented. The SRW is made by multilayered integrated circuit processes, which typically have large ratios of SRW lateral dimensions to substrate thickness. Two theoretical methods, finite-element method and deembedding of composite structure consisting of SRW and mode converters, are applied to investigate the propagation characteristics of the SRW. Application of the dispersion characteristics of the two-dimensional periodical structures coupled with appropriate mode converter designs leads to results in SRW designs supporting TE/sub 10/, TM/sub 00/, and TM/sub 10/ modes. Measurements and the two theoretical approaches indicate that the slow-wave factor is 4.9 and Q-factor is 260 at 6.85 GHz for the TE/sub 10/ mode propagation with a cutoff frequency of 4.10 GHz (0.348 factor of cutoff frequency of conventional rectangular waveguide using the same material and dimensions). The theoretical data show the TM/sub 00/ mode to have a slow-wave factor of 1.8, Q-factor of 187.6 at 11.4 GHz, and cutoff frequency of 10.2 GHz. The TM/sub 10/ mode has a slow-wave factor of 1.98, Q-factor of 187.6 at 12.5 GHz, and cutoff frequency of 10.4 GHz.