Theory of characteristic modes for conducting bodies

A theory of characteristic modes for conducting bodies is developed starting from the operator formulation for the current. The mode currents form a weighted orthogonal set over the conductor surface, and the mode fields form an orthogonal set over the sphere at infinity. It is shown that the modes are the same ones introduced by Garbacz to diagonalize the scattering matrix of the body. Formulas for the use of these modes in antenna and scatterer problems are given. For electrically small and intermediate size bodies, only a few modes are needed to characterize the electromagnetic behavior of the body.     

Computation of characteristic modes for conducting bodies

A procedure for computing the characteristic modes for conducting bodies of arbitrary shape is developed. The method is applied to conducting bodies of revolution and to wire objects, and general computer programs are discussed. Illustrative examples of the computation of characteristic currents and characteristic fields are given for a cone-sphere, a disk, and a wire arrow. Modal solutions using these modes are computed for representative antenna and scattering problems to illustrate convergence of the solution as the number of modes is increased.     

Creeping wave modes for a dielectric coated cylinder

A new system of poles for the Green's function for a dielectric-coated cylinder has been found. In general, these poles correspond to creeping waves, which are strongly attenuated except for very thick coatings. For radii below a critical value, one of the new poles replaces one of those previously described in the literature and gives rise to a creeping wave of Elliott type with low attenuation     

Electromagnetic scattering from dielectric bodies

Far-field results obtained by two different methods are compared for the problem of electromagnetic scattering from dielectric objects. The two methods are the surface integral formulation, utilizing equivalent electric and magnetic surface currents, and the volume formulation, utilizing the equivalent electric polarization current. Triangular patches are used in the surface formulation and cubical cells are used in the volume formulation. The far-scattered fields obtained by the two methods are in good agreement, thereby validating both the approaches for the analysis of scattering problems. Numerical problems associated with the fields in the source region are also addressed     

Attenuation of cutoff modes and leaky modes of dielectric slab structures

A simple formula is developed for the attenuation constant of higher order cutoff modes of a dielectric slab guide and of the modes of leaky guides. The formula is based on a perturbation analysis that reduces the problem to that of the transmission characteristic of a Fabry-Perot resonator. Under certain approximations, the formula for leaky guides reduces to that of Hall and Yeh, but the formula has a wider range of applicability.     

Green's function for arbitrarily shaped dielectric bodies of revolution

In this paper, a solution is developed to calculate the electric field at one point in space due to an electric dipole exciting an arbitrarily shaped dielectric body of revolution (BOR). Specifically, the electric field is determined from the solution of coupled surface integral equations (SIE) for the induced surface electric and magnetic currents on the dielectric body excited by an elementary electric current dipole source. Both the interior and exterior fields to the dielectric BOR may be accurately evaluated via this approach. For a highly lossy dielectric body, the numerical Green's function is also obtainable from an approximate integral equation (AIE) based on a surface boundary condition. If this equation is solved by the method of moments, significant numerical efficiency over SIE is realized. Numerical results obtained by both SIE and AIE approaches agree with the exact solution for the special case of a dielectric sphere. With this numerical Green's function, the complicated radiation and scattering problems in the presence of an arbitrarily shaped dielectric BOR are readily solvable by the method of moments.     

A surface formulation for characteristic modes of material bodies

A theory of characteristic modes for material bodies is developed using equivalent surface currents. This is in contrast to the alternative approach using induced volume currents. The mode currents form a weighted orthogonal set over the material body surface, and the mode fields form an orthogonal set over the sphere at infinity. The characteristic modes of material bodies have most of the properties of those for perfectly conducting bodies. Formulas for the use of these modes in electromagnetic scattering problems are given. A procedure for computing the characteristic modes is developed, and applied to two-dimensional bodies. Illustrative examples of file computation of characteristic currents and scattering cross sections are given for cylinders of different material constants.     

Group velocity of dielectric waveguide modes

The group velocity and dispersion of surface-wave modes propagating along a circular dielectric rod are computed and presented graphically in normalised form. The group velocity as each mode approaches the cutoff frequency is calculated approximately.     

Hybrid modes on anisotropic dielectric rods

The boundary value problem for wave propagation on a cylindrical anisotropic rod has been solved for hybrid modes, i.e., those having angular dependence. Solutions for the rod radius, normalized by the free space wavelength, as a function of the phase velocity, are presented for various values of the transverse and longitudinal dielectric constants. When the rod is terminated by conducting end plates, a highQmicrowave resonator results. The electric and magnetic energies stored in the rod have been calculated, as has the cavityQ. Experimental resonant frequencies for various modes in anX-band cavity using a ruby laser rod are compared with theory.     

Radiation modes and step discontinuities in dielectric ribwaveguide

The continuous spectrum of the rib waveguide is derived by a method that ensures orthonormality and completeness of the spectrum. A relatively simple approximation of this continuum for most cases of common interest is obtained. The theory is applied to the abrupt step discontinuity in the E-plane of the rib guide under LSE polarization and to the abrupt termination problem, including radiative effects never before investigated     

An integral equation for electromagnetic scattering from homogeneous dielectric bodies

A single surface integral equation for problems involving electromagnetic scattering from homogeneous dielectric bodies illuminated by time-harmonic sources is developed via the equivalence principle. The equation is formulated in terms of an equivalent electric current defined at the body surface. When allowed to radiate in a homogeneous medium having the material parameters of the exterior medium of the original problem, the electric current solution to the integral equation produces the correct scattered electric and magnetic fields external to the body.     

A stable integral equation for electromagnetic scattering fromhomogeneous dielectric bodies

It is shown that a previously derived integral equation for electromagnetic scattering from a homogeneous dielectric body (see ibid., vol.AP-32, p.166-172, Feb. 1984) does not have a unique solution at resonant frequencies of the cavity formed by making the surface S of the body perfectly conducting and filling the region internal to S with the external medium. This integral equation was formulated so that an equivalent electric current radiates in the presence of the homogeneous external medium to produce the scattered field external to the body. A combination of equivalent electric and magnetic currents is used to formulate an integral equation whose solution is always unique     

A modified geometrical optics method for scattering by dielectric bodies

A method based on ray optics is developed for calculating the scattering from dielectric bodies. The fields of geometrical optics are used except for two types of rays where the fields must be corrected from physical optics solutions. The customary advantages of ray techniques are realized, namely, a simplicity in the resulting formulas, a ready interpretation of the scattering mechanism and the possibility of extension to a wider class of problems through the inclusion of additional rays. The method has been applied to several lossless dielectric shapes: the circular cylinder, the sphere, the prolate spheroid and to a lossy dielectric shell. The relative dielectric constants considered range from 0.25 to 1.80, except in the case of the shell. The calculated results are compared with those obtained from boundary value solutions, with the exception of the spheroid where measured values are used. Good results are obtained for all sizes considered except those which are very small and behave as Rayleigh scatterers. The failure in the region of Rayleigh scattering is to be expected. Thus, for the class of dielectric scatterers treated here there is no region of scattering resonance corresponding to that of similar metallic shapes where the geometrical optics solution is no longer valid.     

Resonant modes in shielded uniaxial-anisotropic dielectric rodresonators

Rigorous field analysis by the mode-matching method is presented for dielectric rod resonators, including such uniaxial dielectrics as sapphire, which are placed between two parallel conducting plates or in a conducting cavity. The wave equations for E_Z and H_Z in a uniaxial anisotropic dielectric medium are derived in a cylindrical coordinate system. Based on these wave equations, the characteristic equations for the two resonator structures are derived and can be used to calculate the resonant frequencies of any resonant mode. Cutoff conditions of the resonant modes are discussed for parallel-plate-type resonators. Resonant frequencies of some lower order modes are calculated for both types of resonator. Mode charts useful for designing the resonators are presented. It is verified that the mode-matching method used commonly for the analysis of isotropic-dielectric resonators can be applied successfully to uniaxial-dielectric resonators     

TM modes guided by nonlinear dielectric slabs

Propagation of a TM₀ mode in a Kerr-type nonlinear dielectric slab is investigated. The exact analytical expression of E ²(x), E²=E_x²+E_Z ², the decoupled linear differential equation and its equivalent Volterra integral equation of E_x, and the eigenvalue equation of propagation constant β are presented. Finally, an example of approximate analytical solutions obtained by the method of successive approximation is given     

Scattering from multiple conducting and dielectric bodies ofarbitrary shape

A simple moment-method solution is presented for the problem of electromagnetic scattering from structures consisting of multiple perfectly conducting and dielectric bodies of arbitrary shape. The system is excited by a plane wave. The surface equivalence principle is used to replace the bodies by equivalent electric and magnetic surface currents, radiating into an unbounded medium. A set of coupled integral equations, involving the surface currents, is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the bodies are approximated by planar triangular patches, and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the scattering cross sections are presented. The computed results are in very good agreement with the exact solutions and with published data     

A NEW METHOD FOR SOLVING THE SCATTERING PROBLEM OF DIELECTRIC BODIES

A new approach to the EM scattering problem of an inhomogeneous lossy dielectric body is pro-posed.It is shown that the entire interior electric field distribution can be obtained from the measured exteri-or field distribution by simple recurrence relations.Detailed derivations of these recurrence relations for thefield distribution inside the scattering body are presented,and the results obtained by computer simulationsare given.     

Unrelated illumination method for electromagnetic inversescattering of inhomogeneous lossy dielectric bodies

A method aimed at reconstructing the complex permittivities of inhomogeneous lossy dielectric bodies is proposed. The method is based on the principle that sufficient information about a dielectric body can be obtained from the scattered field when the body is illuminated by an incident field composed of unrelated components. The derivations of the formulas are presented, and some numerical examples are given. The accuracy of the results show that the method has great potential in electromagnetic inverse scattering and microwave imaging