A General Approach to Guidance in General Two-Dimensionally Periodic Medium

Based on Floquet theorem and Maxwell equations, eigenvalue problem for general two-dimensionally periodic (2DP) medium is rigorously solved. The dispersion relation for piecewise uniform (PU) 2DP medium is derived in most general analytic formulations to suit all kinds of Dielectric Waveguide Array (DWA) configurations. Numerical results for a particular rectangular DWA are compared and shown to be in exact agreements with those obtained by previous different way, but recent method is much more universal and with much better simplicity and accuracy.     

Eigenvalue Spectrum of Rectangular Waveguide with Two Symmetrically Placed Double Ridges

The eigenvalue spectrum of rectangular waveguide with two symmetrically placed double ridges has been determined by formulating an integral eigenvalue problem and solving by Ritz-Galerkin method. The bandwidth characteristic is found to be adequate for varactor-tuned solid-state microwave oscillator applications requiring ridge structure for resonator. There remains some ambiguity in the designation of trough modes.     

介质波导阵列的横向传播特性分析

根据已提出的有关二维周期介质严格分析理论，针对介质波导阵列进行了大量的数值计算。对介质波导阵列中波的横向传播作了详细分析。首先，在给定纵向波矢量(k)的情况下，分析了在不同工作频率时的横向波矢量间布里渊区色散特性，对空间谐波的相互作用情况也进行了研究。其次，在给定工作频率的情况下，分析了不同纵向波矢量和不同调制系数时的横向波矢量间布里渊区色散特性。由于空间谐波的相互作用随纵向波数或调制系数的增大而增强，导致阻带能明显地表现出来，从而使介质波导阵列的横向传播特性能较为全面地得到分析。     

Longitudinal Wave Propagation in Dielectric Waveguide Array

Based on the established rigorous theory for two-dimensionally periodic (2DP) medium, Longitudinal propagation in Dielectric Waveguide Array (DWA) was analyzed in detail. Firstly, given longitudinal wave vector (k _z), Brillouin dispersion relations between transversal wave vectors were analyzed. Interactions between space harmonics were also studied. Secondly, on condition that transversal wave vector k _x equaled k _y, dispersion relations between longitudinal and transversal wave vectors were analyzed in detail. Because of interactions between space harmonics increasingly getting stronger with k _z or modulation coefficients increasing, stop-bands could be distinctly displayed and thus longitudinal propagation in DWA could be comprehensively analyzed. The applications about longitudinal propagation in DWA were also discussed.     

Analysis of a parallel resistive plate medium [EM scattering]

A half-space composed of parallel resistive sheets is studied by formulating an eigenvalue problem to find the characteristic modes of the medium. Two equivalent formulations of the eigenvalue problem are presented. The first approach is analytical in nature and provides greater insight into the physical behavior of the material, while the second is numerical and applicable to a wider class of problems. The eigenvalue problem is solved via the Muller method to find the complex modal wavenumbers and field distributions within the resistive sheet medium. The mode-matching procedure is used to study the medium's reflection and absorption properties     

On the Complete Eigenvalue Solution of Ridged Waveguide

The complete solution of the ridged waveguide eigen-value problem is presented. The solution is obtained by the formulation of an integral eigenvalue equation which is subsequently solved numerically by application of the Ritz-Galerkin method. The significance of the eigenvalue spectrum is discussed and the modes are classified as either hybrid or trough modes. Equations are given for the electric and magnetic fields and a brief discussion of the edge singularity is presented. The theory is illustrated by computing the dominant eigenvalues and characteristic impedances of various unsymmetrical ridged waveguides.     

介质波导阵列电磁特性分析

根据已提出的二维周期介质严格理论,比较详细地分析和研究了介质波导阵列的电磁特性．首先,对存在纵向波传播时(kz≠0)的空间谐波相互作用特征进行了分析,得出了横向波传播色散特性．其次,在横向平面上的两互相垂直方向的波数相等(kx=ky)时,对不同波频率下空间谐波相互作用特性及其产生的阻带分布特征作了详细研究,并对横向纵向波传播色散关系进行了分析和计算．最后,得出介质波导阵列存在纯纵向导波的十分有意义的结论,具有实用价值．     

Transverse Propagation in Dielectric Waveguide Array

Transverse propagation eigen equations for dielectric waveguide array (DWA) are derived and eigen solutions can be uncoupled into TE and TM modes. Numerical results shows that much stronger space harmonic interaction exists so that a series of interesting physical effect of canonical two-dimensionally periodic (2DP) medium can obviously be observed in DWA and related devices can be predicted, designed and realized much easier.     

Analysis of dielectric waveguide structure of arbitrary cross section

A class of dielectric waveguide structures of arbitrary cross section in conjuction with one or more layer dielectrics is ana lysis with the Method of Lines(MOL). This leads to an eigenvalue problem where the nonphysical and spurious modes do not appear. Dispersion characteristic examples are calculated for structures suitable for mm waves and optical integrated circuits. Such as ridge guides, guide, and so on. The numerical examples are verified by results available from other methods.     

Coaxial cavities with corrugated inner conductor for gyrotrons

This paper investigates coaxial gyrotron cavities with longitudinal slots on the inner conductor as a means to reduce the number of possible competing modes. In the analytic theory the corrugated surface is treated as a homogeneous impedance surface (“impedance corrugation”) to obtain simple formulas for the characteristic equation of the eigenmodes, for the electromagnetic fields and the wall losses. The developed model applies if the number of slots is sufficiently high (cutoff wavelength much larger than the corruption period). The characteristic equation in terms of the ratio C of the outer wall radius to the inner conductor radius is solved numerically to determine a range of eigenvalues and C where the eigenvalue curves are monotonically decreasing. In such a region a cavity having its inner conductor downtapered (radius decreasing toward the cavity output) can be used to reduce the diffractive quality factors of several modes, leaving the working mode undisturbed and without favoring other modes. In addition the electromagnetic field profiles are investigated, and in particular it is shown that for certain cavity parameters a mode could have its energy concentrated close to the inner conductor. As a check on the validity of the theoretical approximations, simulations with the MAFIA code are carried out. These give good agreement with the results of the analytic equations     

Analysis of guided modes in multilayer/multiconductor structures bythe “boundary integral-resonant mode expansion method”

This paper describes a new method for the analysis of modes propagating in shielded waveguides consisting of many dielectric and perfectly conducting layers of different widths. The eigenvalue problem inherent to the mode determination is formulated subdividing the structure into layered elementary wave-guides EWGs and matching the fields generated in adjacent EWGs by unknown equivalent sources placed at the interfaces. The special representation of the EWG field, consisting of boundary integrals and mode expansions, leads to a linear matrix eigenvalue problem involving a limited number of variables. Thanks to this peculiarity the method permits one to determine many modes in short computing times. The method was implemented in a flexible and fully automatic computer code, whose reliability and efficiency has been confirmed by many tests     

Waves and Evanescent Fields in Rectangular Waveguides Filled with a Transversely Inhomogeneous Dielectric

A numerical-calculation method for rectangular waveguides containing a transversely inhomogeneous dielectric is presented. The method is not restricted to the cutoff case or to special inhomogeneities. The relative permittivity of the dielectric can be an arbitrary function of the cross-sectional coordinates. The electric-and magnetic-field strengths, the dispersion characteristics of the propagating modes, and the attenuation constants of the evanescent modes result from the solution of a matrix eigenvalue problem with typically 8000 matrix elements. Propagating and evanescent modes in a waveguide containing a longitudinal semicircular dielectric rod are calculated as examples. The accuracy of the calculation method is confirmed by measurements and by calculating a special example with an exactly known solution. The error of the field intensities is typically 5 percent; the error of the dispersion characteristics and of the attenuation constants is typically 0.5 percent.     

Waveguides of Arbitrary Cross Section by Solution of a Nonlinear Integral Eigenvalue Equation

The problem of electromagnetic wave propagation in hollow conducting waveguides of arbitrary cross section is formulated as an integro-differential equation in terms of fields at the waveguide boundary. Cutoff wave numbers and wall currents appear as eigenvalues and eigenfunctions of a nonlinear eigenvalue problem involving an integro-differential operator. A variational solution is effected by reducing the problem to matrix form using the method of moments. A specific solution of the problem is developed using triangle expansion functions in the method of moments. The solution is simplified by symmetry considerations and is implemented by two digital computer programs. Listings and full documentation of these programs are available. This solution yields accurate determinations of cutoff wave numbers, wall currents, and distributions of both longitudinal and transverse modal field components for the first several modes. Illustrative computations are presented for the single-ridge waveguide, which has a complicated boundary shape that does not lend itself to exact solution.     

Variational Analysis of Ridged Waveguide Modes

Brief expressions of eigenvalue problems, nornral modes, and electric-field profiles for all odd TE and TM modes of ridged waveguides, and the guide wavelength and characteristic impedance for the TE/sub 10/ dominant mode, are presented in this paper. In this analysis, the computation time can be reduced by getting simple approximated variational expressions for eigenvalue equations by using a trial function which satisfies the right-angled edge condition of a ridge. These theoretical results are in good agreement with the experimental results and the several references employed.     

Purely Longitudinal Guidance in Dielectric Waveguide Array

Rigorous analysis shows that independent longitudinally guided TE and TM modes are possible in dielectric waveguide array (DWA) as a two dimensionally periodic medium. Especially, purely longitudinally guidance is also possible and investigated in detail.     

Calculating the Characteristic Impedance of Finlines by Transverse Resonance Method

The characteristic impedance of finlines with up to three slots is calculated by a rigorous hybrid-mode analysis which includes the finite metallization thickness and finite depth of the mounting grooves. The transverse resonance principle utilized reduces considerably the order of the involved matrix eigenvalue problem. The propagation constants for the fundamental HE/sub 1/ mode (and EH/sub 0/ mode at related structures), as well as for the higher order modes (up to HE/sub 7/), and the characteristic impedances for the fundamental modes are computed as a function of frequency for the bilateral and unilateral finline, as well as for the unilateral finline with two coupled slots, and an additional slot on the opposite side of the substrate surface. The finite metallization thickness and mounting groove depth considered show significant influence on the behavior of the characteristic impedance.     

Ag-coated Long-period Fiber Grating

Based on coupled-mode theory, the eigenvalue equation of five-layered long-period fiber grating （LPFG） sensor with Ag film and gas-sensitive film overlays are firstly studied. The problem of resolving complex eigenvalue equation on five-layered LPFG is analyzed, and the method of resolution is also given. Then the eigenvalue equation of three-layered metal cladding LPFG is analyzed, and the complex transcendental equation is also discussed. The computing result shows that the coupling between the low order EH modes and the core mode is much stronger than that between the low-order HE modes and the core mode.     

Comments, on `Three-dimensional finite, boundary, and hybridelement solutions of the Maxwell equations for lossy dielectric media'[and reply]

For the original article see ibid., vol.36, no.4, p.682-93 (1988). The commenters point out a potential source of error with the finite-element analysis of the vector wave equation in the paper of K.D. Paulsen, et al. Specifically, this error source is connected with the finding that, if spurious modes exist in the finite-element solution of the eigenvalue problem, the corresponding solution to the externally driven problem may consist of some linear combination of the nonphysical spurious modes in addition to the physical modes. In replying, the author acknowledges the importance of the question of spurious modes     

Characteristic Electromagnetic Fields in Dielectric Waveguide Array

Based on the modal solution of one dimensionally periodic structure with piecewise uniform dielectric constant distribution, characteristic solutions for two dimensionally Dielectric Waveguide Array (DWA) are rigorously formulated. By satisfying periodic boundary conditions in the interfaces inside a unit cell, semi-closed-form dispersion relation for DWA can be established. Numerical results are presented and compared with a previous method. A class of guidance and radiation problems can be solved with much more simplicity and accuracy.     

过尺寸毫米波铁氧体移相器的工程设计

旋磁波导问题一般是利用驻波展开法导出耦合波方程组再求解。但这种方法由于数值实现比较困难，处理高次模问题有一定的局限性。文中提出利用Galerkin法求解本征模问题，即把波导中的电磁波用矩形波导基本波型函数展开，把波导模式问题进一步转化为矩阵特征值问题。在此基础上计算了过尺寸铁氧体移相器各阶传播模式场型分布，并给出了有关工程设计曲线。