Approximate boundary conditions are a means for simulating material and surface effects in scattering and propagation. A number of conditions are discussed, and criteria are given for their validity.

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Approximate boundary conditions

Perfect electric conductor (PEC) and perfect magnetic conductor (PMC) can be generalized to perfect electromagnetic conductor (PEMC), a medium where certain linear combinations of electromagnetic fields are required to vanish. In differential-form representation, the corresponding medium is characterized as the simplest possible medium. It is defined through a scalar admittance parameter, whose zero and infinite limits yield the PMC and PEC media, respectively. In this paper a duality transformation is found that has the property of transforming PEMC to PEC and an isotropic medium to itself. Thus, problems involving PEMC objects in air can be transformed to problems with PEC objects in air which can be solved through traditional techniques and then transformed back. Several simple examples are treated to demonstrate the principle. PEMC has the potential of having similar applications as PMC in antenna engineering and finding structures for its realization is a challenge.

Transformation method for problems involving perfect electromagnetic conductor (PEMC) structures

A general formulation for the characterization of corrugated waveguides is presented. The formulation is based on modal expansion in the different smooth-walled waveguides which constitute the corrugated structure and on the use of mode matching at discontinuities. The use of an admittance matrix formulation and a suitable root-finding algorithm leads to a rigorous and efficient technique. Dispersion curves are presented for corrugated waveguides of circular and rectangular cross-sections. Complex modes are obtained for deep corrugations. The effect of the finite thickness and width of teeth and slots on the dispersion behavior is shown. >

Characterization of corrugated waveguides by modal analysis

The asymptotic properties of the fundamental mode HE /sub 11/ inside a large waveguide of finite surface impedances are discussed. The analysis applies to corrugated waveguides, certain optical fibers and wave-guides with metal walls coated by a dielectric layer. It is shown that for k-->/spl infin/ the HE /sub 11/ mode has the following two properties: it is polarized in one direction and the field vanishes at the boundary. Because of these properties, it is useful in the design of microwave feeds, since it minimizes cross-polarization and edge illumination at the aperture. It is also useful for long distance communication because of its low attenuation constant. Both the far field of a feed and the attenuation constant are discussed. It is shown that rectangular apertures have negligible cross-polarization over wider bandwidth than circular apertures. Furthermore, if the medium inside a waveguide is Iossless, so that power is lost only at the boundary, then the attenuation constant is very small, it is asymptotic to (ka)/sup -2/ for large ka, where k= 2 pi/lambda and a is a characteristic dimension of the waveguide. A rectangular waveguide consisting of four metal plates coated with thin dielectric layers is shown to be attractive for long distance communication, because of its simplicity of fabrication and its low attenuation.

Attenuation and Radiation Characteristics of the HE /Sub 11/ - Mode

The nonstandard (general) eigenvalue problem is defined in operator form by L (Lambda) f = 0 and B (Lambda) f = 0, where L and B are linear operators, and for a standard problem L is a linear function of the parameter Lambda and B does not depend on Lambda. It is shown by examples, that nonstandard problems arise in electromagnetic problems, and a unified variational principle is formulated from which stationary functional for the nonstandard eigenvalues can be constructed. The examples include cutoff problem of a waveguide with surface reactance, propagation problem of an azimuthally magnetized ferrite-filled waveguide, the cutoff problem of a corrugated waveguide and the problem of a material insert in a resonator. It is demonstrated with these simple but nontrivial examples that the present method leads to a good engineering accuracy with very elementary test functions.

Variational Methods for Nonstandard Eigenvalue Problems in Waveguide and Resonator Analysis

The propagation of guided waves in a rectangular geometry having impedance boundary conditions is investigated. An impedance compatibility relation is derived that must be satisfied in order that a separable modal solution exists for a given impedance configuration. Several new rectangular waveguides are developed; among them are 1) a tall rectangular waveguide operating in a dominant H/sub 10/ mode with no H/sub 0N/ modes; 2) a rectangular waveguide with two parallel anisotropic impedance surfaces; 3) a rectangular waveguide with two parallel walls having isotropic impedance surfaces, the other two walls being anisotropic; 4) a rectangular waveguide supporting only E modes; and 5) rectangular coaxial systems containing impedance surfaces. The modal structure of rectangular waveguides with impedance boundary conditions offers advantages over the conventional waveguide. The potential of oversizing for low-loss and high-power applications is enhanced because of the additional modal control provided by the impedance surfaces. Other applications are suggested.

W.H. Peake

Papers

Rectangular Waveguides with Impedance Walls