The transient reflected-field response of an arbitrarily incident plane wave from planarly-layered, dispersive materials is investigated. The reflection coefficient for the layered media is first determined in the frequency domain as a ratio of functions and a series solution is derived. Each partial sum of this series represents the reflection coefficient for a layered material consisting of a subregion of the problem of interest. It is shown that the transient reflected field may be written as a sequence of events, each of which is the late-time response of a subregion. This result can be used in time-domain methods to determine the properties of layered materials.

Calculation of the Transient Plane-Wave Reflection From an $N$ -Layer Medium by the Method of Subregions

A theoretical study of the pulsed electromagnetic radiation from a vertical magnetic dipole placed on a plane-conducting earth is presented. The application of a Laplace transformation in time and a Fourier transformation in the two orthogonal, horizontal, spatial components leads, under consideration of initial, boundary, and transition conditions, to an integral representation of the solution of the wave equation in frequency space. A modified Cagniard method is then used to derive closed-form expressions for the magnetic Hertz vector anywhere above the conducting earth. The method is used to perform numeric calculations of the magnetic Hertz vector, for different source-receiver distances, as well as different values of the earth's conductivity and permittivity. PACS Nos.: 41.20Jb, 42.25Bs, 42.25Gy, 44.05+e

Response above a plane-conducting earth to a pulsed vertical magnetic dipole at the surface

Propagation of electromagnetic waves in a rectangular tunnel

The problem of communication in the sea has been considered as propagation of radio waves in a three-layered medium (air, sea, and ground). With the aid of the perturbation calculus, this paper analyzes the influence exerted onto the electromagnetic field of arrangements radiating a pure transverse electric field in the sea. The sea height varies continuously with the distance from the transmitting end due to sea waves. Knowledge of the solution for the case of uniform sea height is presumed. The problem of the transition conditions at the upper boundary of the sea is solved in the imaging space of a Hankel transformation. Its reversal produces an integral presentation of the interfering field, which was previously quite difficult to evaluate. In this study, closed-form expressions for the far-field of a vertical magnetic dipole embedded below the sea surface are obtained by using a new technique to evaluate this integral with the aid of the complex image theory. The results obtained are compared with those mentioned elsewhere

Far-field radiated from a vertical magnetic dipole in the sea with a rough upper surface

Research related to the radiation and propagation of the electromagnetic fields in half space or stratified media is of interest and is considered by many authors. In this paper, a theoretical study is discussed about the propagation of radio waves in the sea (three-layered media). The variations which occur in the shape of the sea surface and sea bottom are considered. The effects of the roughness exercised onto the electromagnetic field of arrangements radiating a pure transverse electric field in the sea are studied by using the perturbation method. Closed-form expression for the far field generated by a vertical magnetic dipole embedded below the sea surface is calculated by using a simple technique to evaluate Sommerfeld integrals with the aid of the complex image theory, which was quite difficult to evaluate previously. The results obtained are compared with those mentioned elsewhere.

Electromagnetic Radiation Fields in Three-Layered Media With Rough Interfaces

The transient field-frequency domain of magnetic dipole in a two-layered conducting Earth has been studied. It is obtained as a summation of waveguide modes plus contributions from branch cuts in the complex-plane of the longitudinal wave number. Results can be used to evaluate numerical solutions of more complicated modeling algorithms.

Transient electromagnetic field of a vertical magnetic dipole on a two-layer conducting Earth

The time-domain fields originating from a vertical magnetic dipole placed on the surface of two-layered ground have been derived in an analytical form. The displacement currents in both the two ground layers have been taken into consideration. A previously obtained approximate solution [8] thus represents the late time part of the present solution. It is noteworthy to mention that the term “late time” used in the present work is not considered independently. It depends on both the separation and depth parameters X and D. The condition defining the late time term in [eq.(44), 8] thus seems to be overrestrictive in the case of the layered ground.

Time-Domain Study of Transient Fields For a Thin Circular Loop Antenna

In this paper, the field scattered in the upper medium (air) by a system composed of three homogeneous media (air–sea–ground) that are separated by two rough interfaces is derived from a perturbation technique. The source is located in the inner medium (seawater), which is a vertical magnetic dipole. Then, by applying the boundary conditions at each interface, the scattered field in each medium is derived analytically and expressed using the Hankel transformation (integral over the radial distance r). This research assumes that the modulus of the sea permittivity ( ) is much larger than that of the air and that the parameter (far field assumption), closed-form expressions of the involved integrals are found for the scattered field in the air by using an approximate method. No pole is considered and therefore the formulation is consistent with previous published results. Numerical results are given and represented graphically. In addition, this research presents a comparison of the results obtained here wi...

Samira T. Bishay

Papers

Transient electromagnetic field of a vertical magnetic dipole on a two-layer conducting Earth

Response above a plane-conducting earth to a pulsed vertical magnetic dipole at the surface

Electromagnetic Radiation Fields in Three-Layered Media With Rough Interfaces

Time-Domain Study of Transient Fields For a Thin Circular Loop Antenna

Wave propagation in air from a vertical magnetic dipole located in three rough-layered structures