Field Representation In Terms Research Articles

On the evaluation of Sommerfeld integrals

Some of the basic recent developments in the evaluation of Sommerfeld integrals are reviewed. The image approximation of the integrals is extended to include both the earth permeability and the effect of the displacement currents. The non-uniqueness of the field representation in terms of Hertz vectors is stressed and a proper representation for horizontal dipoles is used. The semi-analytical evaluation of the integrals using the fast fourier transform (FFT) is extended via proper decomposition of the integrand. The analysis increases the range of applicability of these techniques.

Coupled mode analysis for a nonuniform tropospheric wave guide

We employ a two‐dimensional cylindrical model to analyze the normal modes in a laterally nonuniform tropospheric duct. The utilization of the impedance boundary condition at the earth's surface permits us to use a complete field representation in terms of discrete modes only. These modes are chosen to be locally orthogonal so that a tapered‐type nonuniformity can be handled with a systematic accounting of the mode conversion. Explicit formulas are given for the coupling coefficients. It is shown that the general coupled mode analysis reduces to the appropriate form when dealing with an abrupt but small lateral change of the refractive index structure. This step model had been treated previously using a nonrigorous mode matching procedure that neglected reflected waves at the outset.

High‐frequency surface fields excited by a point source on a concave perfectly conducting cylindrical boundary

A previous analysis of the surface currents excited by a line source located on a perfectly conducting concave cylindrical boundary is here extended to point‐source excitation. Alternative field representations in terms of geometric optical contributions, whispering gallery modes, and canonical integrals are explored, and their utility is assessed by extensive numerical computations. As for the two‐dimensional case, it is found that a combination of rays and whispering gallery modes provides an efficient and physically appealing method for calculating the field. The results are applicable to all observation points lying outside a narrow angular region surrounding the axial direction as seen from the source point.

Electromagnetic field representation in inhomogeneous anisotropic media

Some of the basic developments in the theory of electromagnetic field representation in terms of Hertz vectors are reviewed. A solution for the field in an inhomogeneous anisotropic medium is given in terms of the two Hertz vectors. Conditions for presentation of the field in terms of uncoupled transverse electric and transverse magnetic modes, in a general orthogonal coordinate system, are derived when the permeability and permittivity tensors have only diagonal components. These conditions are compared with some known special cases.