George W. Hanson

On the Applicability of the Surface Impedance Integral Equation for Optical and Near Infrared Copper Dipole Antennas

The applicability of the surface impedance integral equation (SI-IE) method for the analysis of optical and near-infrared copper dipole antennas is assessed, and some issues relative to resonant half-wavelength optical dipoles are highlighted. Since at these frequencies the conductivity of copper (and of all metals) is relatively small, the appropriateness of using the standard integral equation method for imperfectly conducting wires, based on a surface impedance boundary condition, needs to be examined. Here it is found that the SI-IE method yields accurate results in the near-infrared regime, and for suitably small wire radius values at low optical frequencies. For the middle and upper optical frequencies the approximate SI-IE is not generally valid. Some results are presented for a half-wave dipole resonant in the upper near-infrared/low optical range, and a discussion of the trade-off between maintaining good polarization selectivity and radiation efficiency is provided

A numerical formulation of dyadic Green's functions for planar bianisotropic media with application to printed transmission lines

An integral equation (IE) method with numerical solution is presented to determine the complete Greens dyadic for planar bianisotropic media. This method follows directly from the linearity of Maxwells equations upon applying the volume equivalence principle for general linear media. The Greens function components are determined by the solution of two coupled one-dimensional IEs, with the regular part determined numerically and the depolarizing dyad contribution determined analytically. This method is appropriate for generating Greens functions for the computation of guided-wave propagation characteristics of conducting transmission lines and dielectric waveguides. The formulation is relatively simple, with the kernels of the IEs to be solved involving only linear combinations of Greens functions for an isotropic half-space. This method is verified by examining various results for microstrip transmission lines with electrically and magnetically anisotropic substrates, nonreciprocal ferrite superstrates, and chiral substrates. New results are presented for microstrip embedded in chiroferrite media.

An improved de-embedding technique for the measurement of the complex constitutive parameters of materials using a stripline field applicator

A method for measuring the electromagnetic constitutive parameters of materials using a strip-transmission-line field applicator is presented. A technique is developed to measure the scattering parameters of the imperfect transition regions between the applicator coaxial terminal ports and the front and back terminal planes of the material sample in stripline, S-parameters of the sample region are subsequently deembedded from the coaxial-terminal model. The complex permittivity and permeability of the sample are easily related to the samples S-parameters through well-known analytic relations. Measured constitutive parameters are presented for several representative materials. >

Integral equation formulation for inhomogeneous anisotropic media Green's dyad with application to microstrip transmission line propagation and leakage

A straightforward numerical technique based on the equivalence principle is presented to determine the complete spectral Greens dyad for inhomogeneous anisotropic media. This method is relevant to guided-wave problems where propagation characteristics are desired in the axial transform domain. Spectral Greens components are determined from a one-dimensional polarization-type integral equation. This method is very simple and versatile, and can be used to model continuously varying or stratified dielectric media with permittivity dyads of the most general form. As an application, a microstrip transmission line residing on a generally orientated uniaxial and biaxial substrate is considered, and new results for higher-order mode leakage are presented. >

Complex media microstrip ridge structures: formulation and basic characteristics of ferrite structures

Microstrip transmission lines residing on bianisotropic material ridges embedded in a multilayered environment are studied using a coupled set of integral equations (IEs). The full-wave IE formulation accounts for general linear media in the ridge region using equivalent polarization currents residing in a multilayered bianisotropic background. Numerical results showing basic propagation characteristics are presented for a variety of single and coupled ferrite ridge structures. It is shown that the use of finite width ferrite ridges as either substrates or superstrates can produce nonreciprocity while confining the ferrite material to a small area in the vicinity of the transmission line.

The RCS of a microstrip dipole deduced from an expansion of pole singularities

The singularity expansion method (SEM) is applied to the steady-state analysis of plane wave scattering from microstrip dipoles. The current induced on the antenna is expanded in a series of natural modes, where the amplitude of each term in the expansion is expressed as a coupling coefficient weighted by a simple frequency pole. Natural modes occur at pole singularities of the antenna current in the complex frequency plane, and are found by a numerical root search of a homogeneous matrix equation. This formulation results in an accurate and efficient calculation of the radar cross section (RCS) of microstrip dipoles which exhibit some appreciable resonant characteristics, where it is found that the current resonance dominates the response of the antenna. The SEM applied yields good physical insight into the scattering behavior of such antennas. Results obtained with the SEM analysis are compared with a full-wave method-of-moments solution. >

Full-wave perturbation theory for the analysis of coupled microstrip resonant structures

A full-wave perturbation theory for the system of coupled microstrip disk structures is presented. The theory is based on the electric field integral equation description of the circuit, which includes all of the wave phenomena associated with the conductors and the surrounding media. This method is suitable for quantification of nearly degenerate coupling between open microstrip disks, yielding the complex system eigenmodes. For the case of two coupled disks, the perturbation theory analytically separates, though simultaneously solves for, the symmetric and antisymmetric system eigenmodes. The development of the perturbation theory leads to good physical insight for this mode-splitting phenomena. Numerical results obtained with the perturbation theory agree well with those obtained by a more accurate method of moments solution to the coupled set of electric field integral equations, as well as with experimental data. >

Leaky wave excitation on three-dimensional printed interconnects

Leaky wave excitation on three-dimensional single and coupled microstrip interconnects is studied. Closed-form asymptotic expressions for the fields associated with the interconnect are derived, and are applicable in both the travelling/standing wave and leaky wave regimes, both of which lead to radiation. The leaky-wave beam angle is found to correspond to the usual two-dimensional ray-optics leakage angle for long interconnects, as expected, and depends on interconnect length and spacing for shorter interconnects. Comparisons with fullwave results are shown for the case of coupled interconnects.

Asymptotic analysis of the natural system modes of coupled bodies in the large-separation low-frequency regime

We examine the natural system modes (characteristic frequencies and currents) of two coupled bodies in the limit of large separation. It is known that when objects are oriented such that they may interact electromagnetically, natural modes of the coupled system occur. These modes differ from, but may be related to, the natural modes of the isolated bodies. For example, the first antisymmetric and symmetric system frequencies of two identical bodies separated by some intermediate distance spiral around the dominant natural frequency of the isolated body as separation is varied. As separation further increases, these system resonances tend toward the origin in the complex frequency plane, rather than approaching the isolated body-dominant natural frequency. Here we treat an N-body scattering problem in the limit of large separation by replacing the bodies with equivalent dipole moments. The natural frequencies are obtained as singular points in the scattering solution. For the special case of two coupled objects, a simple equation for the natural system frequencies is obtained that shows that the real radian-system frequency approaches the origin as 1/r, independent of the relative orientation and type of the two bodies. The damping coefficient approaches the origin approximately logarithmically as a function of the body orientation and type. Using this formulation, the natural system modes of two coupled wires are investigated for large separation between the wires and compared to an integral equation solution.

Propagation characteristics of microstrip transmission line on an anisotropic material ridge

A microstrip transmission line residing on an electrically anisotropic material ridge embedded in a multilayered environment is studied using a coupled set of integral equations (IEs). The full-wave IE formulation easily accommodates arbitrary material anisotropy and inhomogeneity in the finite ridge region using equivalent polarization currents residing in a multilayered isotropic background. New results are presented for uniaxially anisotropic ridge structures which show that the transmission line propagation constant is sensitive to anisotropy for certain ridge structures and insensitive for others, compared to the conventional line on an infinite substrate. Results are also presented for a transmission line printed on a nonreciprocal solid-state magnetoplasma ridge. The current distribution associated with the dominant microstrip mode is investigated, where it is found that the transverse component of current is much larger for the ridge geometry than for the infinite substrate case, although the transverse component is still small compared to the longitudinal component. >