Analysis of guided waves in inhomogeneous bianisotropic cylindricalwaveguides

Electromagnetic fields in structures composed of inhomogeneous cylindrical layers are analyzed using a propagator matrix approach. The presented formulation is capable of analyzing fully bianisotropic media, where the involved propagator matrix for bianisotropic media is derived in cylindrical coordinates. The applicability of the method is demonstrated by calculating the dispersion characteristics of surface waves as well as fundamental and higher order modes on cylindrical microstrip lines on top of an inhomogeneous bianisotropic substrate     

A linear-operator formalism for bianisotropic waveguides

A bianisotropic waveguide can be defined as a cylindrical waveguide filled with bianisotropic materials, and all the conventional waveguides are special cases of the bianisotropic waveguide. In this paper, guided wave propagation in bianisotropic waveguide is analyzed by the theory of linear operators, and two types of adjoint waveguides and inner products are introduced respectively. Based on the concept of adjoint waveguides, the functional expressions of the field equations can be obtained, and from which the eigenvalue problem of the bianisotropic waveguide can be solved. Also, bi-orthogonality relations of guided modes are derived. These biorthogonality relations reported here can be used to expand electromagnetic fields in terms of a complete set of modes in straight bianisotropic waveguide. As an example of application, mode matching formulae for a discontinuity problem are given.     

A Study of Backscattering and Emission from Closely Packed Inhomogeneous Media

The effects of close spacing between small scattering spheres were examined by keeping the distance-dependent terms in the expressions for the transverse scattered fields. The phase matrix was then derived from these fields and was used in the radiative transfer formulation to model scattering and emission from a densely populated, inhomogeneous layer. Computed results were compared with those obtained when the phase matrix was specialized to the far-field condition. It was found that the use of the far-zone condition tended to underestimate both the level of the copolarized backscattering and the cross-polarized backscattering. In emission computations, the use of the far-zone condition overestimated the level of the brightness temperature. hese effecit decreased with a decrease in the volume fraction or an increase in the exploring frequency, as expected. An improvement on the snow parameter (density and crystal size) estimation was shown to be possible when this new phase matrix was used.     

Integral equation based analysis of scattering from 3-D inhomogeneous anisotropic bodies

This paper presents an integral equation based scheme to analyze scattering from inhomogeneous bodies with anisotropic electromagnetic properties. Both the permittivity and permeability are assumed to be generalized tensors. Requisite integral equations are derived using volume equivalence theorem with the electric and magnetic flux densities being the unknown quantities. Matrix equations are derived by discretizing these unknowns using three dimensional Rao-Wilton-Glisson basis functions. Reduction of the integral equation to a corresponding matrix equation is considerably more involved due to the presence of anisotropy and the use of vector basis function; methods for evaluation of the integrals involved in the construction of this matrix is elucidated in detail. The method of moments technique is augmented with the fast multipole method and a compression scheme. The latter two enable large scale analysis. Finally, several numerical results are presented and compared against analytical solutions to validate the proposed scheme. An appendix provides analytical derivations for the formulae that are used to validate numerical method, and the necessary formulae that extends the approach presented herein to the analysis of scattering bianisotropic bodies.     

Field representations in uniaxial bianisotropic medium bycylindrical vector wave functions

Field representations are presented in a uniaxial bianisotropic material region. The results reveal that the solution of a source-free vector wave equation is the sum-integral form of the circular cylindrical vector wave functions in isotropic media. The application of the proposed theory to scattering is considered     

Analysis of bianisotropic layered structures with laterallyperiodic inhomogeneities-an eigenoperator formulation

A method of analysis for electromagnetic wave phenomena in multilayered media consisting of bianisotropic slabs with periodically inhomogeneous material parameters is presented. The analysis relies on a transformation of Maxwell's equations into an equivalent eigenoperator equation for the transverse components of the field vectors, which is Fourier transformed into an algebraic eigenvalue equation in the spectral domain. The fields in the inhomogeneous layers are then expressed in terms of eigenmodes, where the expansion coefficients are determined by imposing internal and external boundary conditions. The proposed method is verified by comparing numerical results for ordinary isotropic-media problems with corresponding results obtained previously by different methods. The applicability and convergence behavior of the approach is illustrated for typical sample applications involving scattering- and guided-wave problems     

Scattering from a periodic array of thin planar chiralstructures-calculations and measurements

In this paper, as a first approach toward modeling inhomogeneous bianisotropic slabs, the electromagnetic scattering by an infinite regular array of thin planar chiral structures disposed on grounded or ungrounded dielectric slabs is studied. The electromagnetic analysis is based on the Floquet's theorem and the method of moments associated to quadratic wire segments. Experimental results concerning copolarized and cross-polarized reflection coefficients from both grounded and ungrounded finite grids of novel planar chiral particles are reported. Comparisons are made between numerical and experimental results     

Radiation and scattering features of patch antennas with bianisotropic substrates

The analysis of patch antennas residing in cavities filled by general inhomogeneous and lossy bianisotropic substrates is presented. The theoretical study is based on a variational formulation associated with the boundary value problem under analysis, and a hybrid finite element-boundary integral method is employed to solve the electromagnetic field inside and outside cavities numerically. Initially, the general formulation presented is applied to some particular cases known in the literature. Then, the main scattering and radiation features of cavity backed patch antennas with chiral, anisotropic, and bianisotropic materials are presented. Particularly, it is shown that complex media allow for frequency control and for a reduced antenna size at a given operating frequency.     

Electromagnetic waves scattering by cylindrical dielectric structures: Application to microwave devices design

A method which allows us to analyze the electromagnetic scattering characteristics of multiple discontinuities in shielded dielectric waveguides is presented. There are not restrictions both geometry of the cross section and electrical parameters of the dielectrics which are assumed to be linear, inhomogeneous, isotropic and free from losses. Each discontinuity is analyzed combining a modal matching technique with a generalized telegraphist's equations formulation; in this way, we obtain its scattering matrix. By using the concept of the generalized scattering matrix of two discontinuities, the equivalent generalized scattering matrix (EGSM) of the cascaded set is calculated. Theoretical and experimental results were obtained for different dielectric structures such as dielectric posts, isolated and coupled, as well as dielectric waveguides with circular cross section connected by means of abrupt and gradual transitions. The experimental values for the scattering properties show a good agrement with the theoretical ones. This study has shown the possibility of using cylindrical dielectric structures to design microwave devices such as: resonators, power-dividers and filters.     

Scattering by a cylindrical dielectric shell with inhomogeneous permittivity profile

The scattering by a plane wave incident on an infinitely long cylindrical shell is derived using the boundary-value method. The cylindrical shell is assumed to have an inhomogeneous dielectric profile in both the radial and azimuthal directions or a circular cylindrical coordinate system. The validity of the solution is verified by comparison with the method of moments. Different types of inhomogeneities are investigated and the resulting echo width as well as the scattered field pattern indicate significant variations which could be used to improve the radiation characteristics of antennas and the reradiation behaviour of scattering objects.     

A rigorous analysis of a cross waveguide to large circularwaveguide junction and its application in waveguide filter design

A rigorous analysis is obtained for the problem of scattering at the junction of a cross-shaped waveguide and a larger circular waveguide. The general case of an arbitrary offset and orientation of the cross waveguide axes is considered. The fields matching over the cross aperture of the smaller guide is facilitated by using the transformation of the circular cylindrical Bessel-Fourier modal fields of the circular guide into a finite series of exponential plane wave functions. This permits an analytical finite series solution for the elements of the fields mode matching matrix, from which the general scattering matrix of the junction is obtained. The application of the formulation to circular waveguide filter design is emphasized in the numerical examples. Excellent agreements between theoretical and experimental results are obtained in all the numerical examples     

Scattering from a Layered Medium Connected with Rough Interfaces: Matrx Doubling Method

A theoretical scattering model is developed that computes the scattered and transmitted intensities from an inhomogeneous layered medium above the half-space. A matrix doubling method technique is extended to handle multilayer scattering problems of which each scattering layer of spherical particles has rough boundary interfaces. Incoherent scattering is assumed in the formulation so that the Stokes vector representations are used to calculate the polarimetric multiple scattering effects. The scattering coefficients are computed for a two-layered Rayleigh scattering medium with a rough boundary. The developed scattering model of a radiative transfer approach is useful for scattering computations dealing with a random medium often encountered in active and passive microwave remote-sensing problems.     

用于计算任意截面二维电磁散射的多心柱谐函数展开法

本文提出了一种计算任意截面二维电磁散射的方法多心柱谐函数展开法。它用多点的柱谐波函数展开散射场,代替柱谐函数展开中一点展开,并用最小均方边界误差准则处理边界条件。多极子法和柱谐函数展开法是该方法的两个特例。     

Scattering of electromagnetic waves by a layer of air plasma surrounding a conducting cylinder

In this paper, the total scattering and back-scattering cross-sections (respectively represented by σ and σ_b) of an air plasma layer surrounding a conducting cylinder are studied. The plasma layer can be turned ON and OFF to allow for a comparison between the scattering cross-section of the bare cylinder and the plasma covered cylinder. The plasma layer is generated at atmospheric pressure, which results in a very highly collisional case. The scattered fields are calculated using a cylindrical expansion, with coefficients satisfying the appropriate boundary conditions, and which are a function of the refractive index of the air plasma. The results of our study are presented as plots of the total scattering cross-section, σ, and back-scattering cross-section, σ_b, versus frequency. The scattering cross-section gives an average characteristic of the scattering process from obstacles. Once the scattering cross-section is known, the actual scattered energy per unit length per second can be calculated by multiplying σ by the incident energy per unit area per second.     

Application of the unimoment method to electromagnetic scattering of dielectric cylinders

The unimoment method is applied to calculate the scattered fields of dielectric cylinders of arbitrary cross section or of inhomogeneous material. The basic technique of the method is the use of the finite element methods inside a mathematical circle, which encloses the inhomogeneous body. The fields outside are expanded in the usual cylindrical harmonics. The interior and exterior problems are then coupled at the circle. The versatility is increased greatly by introducing the method of "inhomogeneous element." The advantage of the proposed method is the simplicity and efficiency in programming. The validity of the computer program has been verified by comparing results with calculations from other methods for i) an off-centered circular cylinder, ii) two circular cylinders, and iii) a circular cylindrical shell.     

A new numerical approach to the calculation of electromagnetic scattering properties of two-dimensional bodies of arbitrary cross section

A new method is introduced for formulating the scattering problem in which the scattered fields (and the interior fields in the case of a dielectric scatterer) are represented in an expansion in terms of free-space modal wave functions in cylindrical coordinates, the coefficients of which are the unknowns. The boundary conditions are satisfied using either an analytic continuation procedure, in which the far-field pattern (in Fourier series form) is continued into the near field and the boundary conditions are applied at the surface of the scatterer; or the completeness of the modal wave functions, to approximately represent the fields in the interior and exterior regions of the scatterer directly. The methods were applied to the scattering of two-dimensional cylindrical scatterers of arbitrary cross section and only the TM polarization of the excitation is considered. The solution for the coefficients of the modal wave functions are obtained by inversion of a matrix which depends only on the shape and material of the scatterer. The methods are illustrated using perfectly conducting square and elliptic cylinders and elliptic dielectric cylinders. A solution to the problem of multiple scattering by two conducting scatterers is also obtained using only the matrices characterizing each of the single scatterers. As an example, the method is illustrated by application to a two-body configuration.     

The Solution of Waveguide Scattering Problems by Application of an Extended Huygens Formulation

The implementation of a recent new hybrid integral-equation/vector finite-element method formulation applicable to inhomogeneous obstacle scattering in hollow waveguide, requiring discretization just of the obstacle, is presented. The integral equation links the given incident modes with the discontinuity-surface electric and magnetic fields. The finite-element equation is expressed in terms of the entire magnetic and surface electric field of the obstacle. Compatible vector finite-element basis function expansions are inserted, resulting in a pair of matrix equations soluble for the unknown electric and magnetic basis coefficients. Corresponding two-port scattering parameters are further derived. Test cases of posts in the$ TE_10$waveguide, with details of the matrix constructions, are described. Numerical results verified against an established commercial code are given. The ability to model inhomogeneous, lossy, and multiple scatterers is demonstrated.     

导行波在非均匀双各向异性平板波导中的传播特性

本文应用模式本征展开和模匹配方法，首先给出了非均匀双各向异性平板波导中混合模的场分布和相应的奇偶模分量色散方程．借助数值分析技术，揭示了低阶模的反射和透射系数随双各向异性介质的几何和本构参数变化规律     

Rigorous modal analysis of structures containing inhomogeneous dielectric cylinders

The orthogonal expansion method and modified iterative scattering procedure is proposed to analyze structures containing asymmetrically located, partial-height, or multilayered inhomogeneous dielectric posts. The analysis is based on a novel concept called the hybrid impedance matrix (HIM), which describes the relation between the total scattered electric and magnetic fields obtained from all posts. As a result, the HIM can be easily applied to match it with other known incident fields and finds applications in closed (waveguide junctions, resonators) and open structures (posts in free space for plane-wave excitation). Additionally, a procedure for constructing eigenmode functions describing field components in the inhomogeneous dielectric cylinders is presented. The proposed method has been extensively verified for a rectangular waveguide junction by a finite-difference time-domain software package, as well as our own measurements and, in both cases, very good agreement can be observed.