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.     

Propagation Along Transversely Inhomogeneous Coaxial Transmission Lines (Short papers)

Numerical "shooting" methods are employed in obtaining the dispersion curves of a coaxial waveguide loaded with a radially inhomogeneous dielectric. The utility of this technique is tested by comparing results with known analytical solutions. The method is also used to find the dispersion curves of a coaxial waveguide loaded with a radially Gaussian-distributed plasma.     

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].     

Propagation in a Dielectric-Loaded Parallel Plane Waveguide

A theoretical analysis of wave propagation in a parallel plane waveguide partially filled with a dielectric is performed. This transmission line is a symmetrical three-region structure consisting of two infinite parallel conducting planes with a dielectric slab of rectangular cross section between and contacting each of the planes. It has been found that TEM and TM modes cannot propagate on this structure. This investigation is concerned with TE modes, although hybrid modes can also propagate on this line. The lowest order TE mode, which is the dominant mode, has no cutoff and hence is inherently suited to extremely wide bandwidth operation. Equations have been presented for the field components, guide wavelength, cutoff criteria, power handling capabilities, wall losses, and dielectric losses as a function of the operating wavelength, waveguide dimensions, and material constants. In the case of the dominant mode, design curves covering a large range of wavelengths, dimensions, and dielectric constants are presented. For a loosely bound wave, the losses are comparable or less than those of conventional rectangular waveguide and the power handling capacity is an order of magnitude greater.     

Computation of TM and TE modes in waveguides based on a surfaceintegral formulation

The surface integral formulation is used for the computation of TM and TE modes propagating in dielectric loaded waveguides. This formulation makes use of the surface equivalence principle whereby the field at any point internal or external to the waveguide can be expressed in terms of equivalent surface currents. This procedure reduces the original problem into a set of integro-differential equations which is then reduced to a matrix equation using the method of moments. The solution of this matrix equation provides the propagation characteristics of the waveguide and the equivalent surface currents existing on the waveguide walls. The equivalent surface currents can be used to compute the fields at all points, both inside and outside the waveguide. The surface integral method has been used to compute the propagation characteristics of waves propagating in dielectric loaded waveguides. The computed results agree very well with analytical and published data. A method that can be used to remove spurious modes is illustrated     

Impedance boundary method of moments for accurate and efficientanalysis of planar graded-index optical waveguides

An impedance boundary method of moments (IBMOM) is proposed to accurately and efficiently compute the propagation characteristics including the number of guided modes of general graded-index dielectric slab waveguide structures. The method is based on Galerkin's procedure in the method of moments and employs the exact impedance boundary condition at the interfaces between the graded-index region and constant-index cladding. Legendre polynomials are utilized in the field expansion. Computational results are shown for waveguides with various inhomogeneous refractive index profiles. The results indicate that typically five Legendre polynomials are sufficient for accurate solutions of the dominant TE and TM modes in optical waveguides having a finite region of inhomogeneous refractive index. Diffused optical waveguides with untruncated index profiles as well as coupled dielectric waveguides can be accurately analyzed using ten Legendre polynomials     

TE Modes of the Dielectric Loaded Trough Line

The properties of TE modes on a dielectric loaded trough waveguide have been investigated. In the case of the dominant mode of this line (TE/sub 20/), families of design curves giving the field distribution, guide wavelength, power handling capability, wall losses, and dielectric losses as a function of operating wavelength, waveguide dimensions and dielectric constant are presented. For a loosely bound wave, the losses are comparable to those of conventional rectangular waveguide and the power handling capability is an order of magnitude greater. The apparatus and procedure used to measure guide wavelength, rate of field decay in the transverse direction, and attenuation are described. The measured performance is in close agreement with the theoretically predicted characteristics.     

Propagation in a Rectangular Waveguide Partially Filled with a Linearly Varying Dielectric

A closed form solution for the TE/sub lo/ mode in a rectangular waveguide partially filled with a linearly inhomogeneous dielectric is obtained. The dielectric is assumed to vary linearly in one transverse direction. The theory developed for the partially filled waveguide is extended to consider the characteristic equation of the completely filled waveguide with a linearly inhomogeneous dielectric. The phase velocity of the fields in the waveguide is studied by considering the /spl omega/ / /spl beta/ diagrams.     

有耗介质导波结构的高次杂交四边形边缘元分析

本文提出了一种高次杂交四边形边缘元方法。讨论了这种高次杂交边缘元的有限元空间构造，给出了其形函数的显形表达式。这种方法不仅消除了伪解而且能直接求解传播常数，从而无需迭代便能分析有耗介质导波结构的传输特性。对矩形导和条形介质填充波导本征模传播常数的计算表明这种高次杂交边缘元的计算精度比低次杂交边缘元要高出一个量级。     

Electrooptic polymer modulators operating in both TE and TM modes incorporating a vertically tapered cladding

We propose a modified electrooptic (EO) PMMA polymer waveguide structure supporting both TE and TM modes in spite of the large birefringence induced by the poling. A vertically tapered structure is employed to connect a single-mode rib waveguide and a confinement-enhanced rectangular buried waveguide. This waveguide structure can be easily fabricated by a two-step reactive ion etching (RIE) process with a shadow mask. To demonstrate TE/TM confinement and single-mode operation, Mach-Zehnder intensity modulators are fabricated by incorporating the proposed waveguide structure. The extinction ratio is better than -15 dB, which proves the single-mode operation. Half-wave voltages for TM and TE modes are 6 and 24 V, respectively.     

Spontaneous emission coupling to radiation and guided modes ofplanar waveguide structures

A general analysis of spontaneous emission in the vicinity of a symmetric slab dielectric waveguide is presented using explicit energy-normalized functions for the complete set of bound and radiating TE and TM modes. Expressions for the spontaneous emission rates are derived for each mode type, and calculated results are presented illustrating the emission behavior as a function of the position of the radiating atom, for various slab waveguides. The model is used to analyze the spontaneous emission coupling efficiency to guided modes in planar erbium-doped amplifier structures. Spontaneous emission factors for the TE and TM modes are calculated for the cases of erbium doping of the core and of the cladding     

A TE/TM modal solution for rectangular hard waveguides

A TE/TM modal solution for a longitudinally corrugated rectangular waveguide is developed. These longitudinal corrugations can be used to excite a quasi-TEM wave and form a hard waveguide by correctly choosing the impedance at the guide wall. The correctly chosen impedance is referred to as the hard boundary condition. The modal solution developed here solves the problem of longitudinal corrugations filled with a dielectric material by first finding and solving the characteristic equation for a complete TE/TM modal set. It is shown that this TE/TM mode solution can be used to achieve the hard boundary condition resulting in the quasi-TEM wave in a hard waveguide for discrete values of corrugation depth. Beyond each of these depths, a mode becomes a surface wave. The theoretical mode set is amenable to the solution of problems using the mode-matching method. A combination of the mode-matching method and the TE/TM modal solution will allow the solution of larger problems.     

An efficient full-vectorial finite-element modal analysis ofdielectric waveguides incorporating inhomogeneous elements acrossdielectric discontinuities

A new vectorial finite-element method (FEM) free of spurious modes is proposed for analyzing optical waveguides with sharp corners in the cross section. The method is formulated in terms of the transverse field components H_x and H_y or E_x and E_y , and it explicitly shows the relationships between the semivectorial and the full-vectorial wave equations. In this method, we introduce the distribution concept and an inhomogeneous element to describe the field across the dielectric interface, and the error in the numerical solution caused by the dielectric discontinuity is reduced. We show how the width of such inhomogeneous elements and the number of nodes would affect the numerical result and its convergent rate using the dielectric-loaded rectangular waveguide, the channel waveguide, and the rib waveguide as analysis examples. For the dielectric-loaded rectangular waveguide, we compare our results with the exact solutions. For the rib waveguide, we compare our results with previously published data based on other methods. Also, field convergence near the corners is discussed     

Analysis of dielectric loaded hybrid mode coaxial horns

This article presents a numerical solution for radiation from a novel coaxial horn with a partial dielectric loading. The horn is represented as a set of three-layer dielectric loaded coaxial waveguide sections. Characteristic equation has been obtained to calculate phase coefficients for hybrid modes in each section. Applying mode matching technique generalised scattering matrices for each junction between the sections have been obtained, besides that power coupling integrals for each of three different type of junctions have been found in closed-form solutions. Cascading these scattering matrices with transmission matrices of each section yields a generalised scattering matrix of the horn. For the given excitation at the throat of the horn, amplitude and phase of eigenmodes at the aperture of the horn have been determined. Finally, Fourier transform integral of the aperture electric field has been applied to solve radiation problem of the horn. Numerical results on propagation and radiation characteristics of the first four hybrid modes of the horn are presented and it is validated that this solution can be successfully used for full-wave electromagnetic analysis and optimisation of multiband dielectric loaded coaxial feeds.     

Effects of high-order mode coupling in dielectric covered finitearray of dissimilar rectangular waveguides

Expressions are presented for the computation of mutual admittance between rectangular apertures of different size, in a finite planar array. The equations allow any orientation for any of the apertures, with any number of transverse electric (TE) and transverse magnetic (TM) waveguide modes. Furthermore, the expressions also include the effect of dielectric covering of these apertures. A versatile software package, useful for the design and analysis of finite phased arrays, is produced incorporating these features, and its extensive validation is provided     

On Inhomogeneously Filled Rectangular Waveguides (Short Papers)

A method is given for determining the characteristic equations and field components of the LSE and LSM modes in rectangular waveguides filled with a dielectric which is inhomogeneous in one transverse dimension. The method is exact and yields solutions for a nearly arbitrary variation in permittivity across the waveguide.     

Series solutions to the arbitrary profile 1-D waveguide andquantum-well problems

The 1D waveguide of arbitrary dielectric profile is solved for TE and TM modes by a method based on series solutions. It is a guess-propagate-iterate scheme. The profile is approximated by small segments of either constant or linearly changing dielectric constant. The method is accurate, generally significantly faster than other methods, and can cope with modes near cutoff; and with lossy, or gain-guided modes. Series solutions are also given to solve the 1D Schrodinger equation     

Cutoff Frequencies of Eccentric Waveguides

This paper discusses the uniform cylindrical waveguide formed by placing one conductor inside a conducting tube. Because of the complexity of the guide's cross section, the numerical technique of the point-matching method is adopted to solve the boundary-value problem. The formulations are carried out for the case when each of the conductors has an arbitrary cross section and also for the case when one of the conductors has a circular cross section. The coaxial waveguide modes, in which the field components have angular variations, split into odd and even modes when the center conductor begins to shift axis to form the uniform eccentric waveguide. However, only even modes in the eccentric guide correspond to the coaxial modes with no angular variations. The dependence of the cutoff frequency on the eccentricity of the guide is determined numerically for even and odd TE and TM modes. Experimental results verify the theoretical calculations for TE modes.     

Rigorous Analysis of the Scattering of Surface Waves in an Abruptly Ended Slab Dielectric Waveguide

The reflection and the scattering properties of even TE and TM surface waves incident in an abruptly ended dielectric slab waveguide are analyzed. The discontinuity is regarded as a junction between two open waveguides namely the dielectric slab waveguide and the free space waveguide. The boundary conditions acting together with the orthogonality provide singular coupled integral equations on the discrete and the continuous wave amplitudes at the discontinuity. These singular coupled intergral equations with Cauchy kernels and infinite limits of integration are solved by iteration via the Neuman series. Numerical results are presented for the reflectivity of the even TE/sub 0/ and TM/sub 0/ fundamental modes, together with their mode conversion on even TE/sub 2/ and TM/sub 2/ in a slab where two guided modes can propagate. Reflectivity and mode conversion of higher order excitations are also investigated     

Analysis of dispersion characteristics for a circular dielectric waveguide with periodic metallic strips by using the method of lines

The dispersion characteristics of circular dielectric waveguide with periodic metallic strips are analyzed by the method of lines. The filter property of the metallic strip loaded structure is carefully investigated for both TE and TM modes. The brillioum diagrams for both TE₀₁ and TM₀₁ modes are given. A comparison is made between the results obtained by Galerkin's method and those calculated with the method of lines, and very good agreement has been found; the accuracy of the present method is thus justified. On the basis of the analysis, some useful guidelines for the design of the bandreject filters are suggested.